Maspack Reference Manual

John Lloyd

Last update: Aug 5, 2018



Maspack (modeling and simulation package) is a set of Java packages to support physical modeling and simulation. The purpose of this guide is to document some of these packages in detail, one package per chapter. At present, the guide is incomplete and documents only the property and rendering packages. More chapters will be added as resources permit.

Chapter 1 Properties

The maspack property package ( provides a uniform means by which classes can export specific attributes and information about them to application software. The main purpose of properties is to

  1. 1.

    Provide generic code for accessing and modifying attributes.

  2. 2.

    Remove the need for "boiler-plate" code to read or write attributes from persistent storage, or modify them by other means such as a GUI panel.

The property software uses Java reflection to obtain information about a property’s value and its associated class, in a manner similar to that used by the properties of Java Beans.

1.1 Accessing Properties

Any class can export properties by implementing the interface HasProperties:

interface HasProperties
   // get a handle for a specific named property
   Property getProperty (String name);
   // get a list of all properties associated with this class
   PropertyInfoList getAllPropertyInfo ();

Each property is associated with a name, which must be a valid Java identifier. The getProperty() method returns a Property handle to the named property, which can in turn be used to access that property’s values or obtain other information about it. getAllPropertyInfo() returns a PropertyInfoList providing information about all the properties associated with the class.

A Property handle supplies the following methods:

interface Property
   Object get();
   void set (Object value);
   Range getRange ();
   HasProperties getHost();
   PropertyInfo getInfo();

Returns the property’s value. As a rule, returned returned values should be treated as read-only.


Sets the property’s value (unless it is read-only, see Section 1.2).


Returns a Range object for a property (see Section 1.1.1), which is used to determine which values are admissible to set. If all values are admissible, getRange() can return null.


Returns the object to which this property handle belongs.


Returns static information about this property (see Section 1.2).

A simple example of property usage is given below. Assume that we have a class called DeformableModel which contains a property called stiffness, and we want to set the stiffness to 1000. This could be done as follows:

   DeformableModel defo = new DeformableModel();
   Property stiff = defo.getProperty("stiffness");
   stiff.set (1000.0); // (uses Java 1.5 autoboxing to turn
                       // 1000.0 into Double(1000.0)

Of course, DeformableModel will likely have a method called setStiffness that can be used to set the stiffness directly, without having to got through the Property interface. However, the purpose of properties is not to facilitate attribute access within specially constructed code; it is to facilitate attribute access within generic code that is hidden from the user. For instance, suppose I want to query a property value from a GUI. The GUI must obtain the name of the desired property from the user (e.g., through a menu or a text box), and then given only that name, it must go and obtain the necessary information from the object exporting that property. A Property allows this to be done in a manner independent of the nature of the property itself.

1.1.1 Why Property Handles?

In theory, one could embed the methods of Property directly within the HasProperties interface, using methods with signatures like

   Object getPropertyValue (String name);
   void setPropertyValue (String name, Object value);

The main reason for not doing this is performance: a property handle can access the attribute quickly, without having to resolve the property’s name each time.

Each property handle contains a back-pointer to the object containing, or hosting, the property, which can be obtained with the getHost() method.

1.2 Property Ranges

A Range object supplies information about what values a particular Property can be set to. It contains the following methods:

interface Range
   boolean isValid (Object obj, StringHolder errMsg);
   Object projectToRange (Object obj);
   void intersect (Range range);
   boolean isEmpty();

Returns true if obj is a valid argument to the property’s set method. The optional argument errMsg, if not null, is used to return an error message in case the object is not valid.


Trys to turn obj into a valid argument for set(). If obj is a valid argument, then it is returned directly. Otherwise, the method tries to return an object close to obj that is in the valid range. If this is not possible, the method returns Range.IllegalValue.


Intersects the current range with another range and placed the result in this range. The resulting range should admit values that were admissible by both previous ranges.


Returns true if this range has no admissible values. This is most likely to occur as the result of an intersection operation.

Possible usage of a range object is shown below:

   Property prop = hostHost.get ("radius");
   Range range = prop.getRange();
   StringHolder errMsg = new StringHolder();
   double r;
   if (!range.isValid (r, errMsg)) {
      System.err.println ("Radius r invalid, reason: " {\tt  errMsg.value);
   else {
      prop.set (r);

Two common examples of Range objects are DoubleInterval and IntegerInterval, which implement intervals of double and integer values, respectively. Ranges are also Clonable, which means that they can be duplicated by calling range.clone().

1.3 Obtaining Property Information

Additional information about a property is available through the PropertyInfo interface, which can be obtained using the getInfo() method of the property handle. Information supplied by PropertyInfo is static with respect to the exporting class and does not change (unlike the property values themselves, which do change). Such information includes the property’s name, whether or not it is read-only, and a comment describing what the property does.

Some of the PropertyInfo methods include:

interface PropertyInfo
   // gets the name of this property
   String getName();
   // returns true if this property cannot be set
   boolean isReadonly();
   // returns a string description of the property
   String getDescription();
   // returns an optional format string describing how the
   // propertys values should be formatted when printed.
   String getPrintFormat();
   // returns the class associated with this propertys value.
   Class getValueClass();
   // returns the class associated with this propertys host
   Class getHostClass();
   // returns true if the properties value should be written
   // by the PropertyList write method.
   boolean getAutoWrite();
   // returns the conditions under which this property
   // should be interactively edited.
   Edit getEditing();
   // Returns information about whether the propertys editing widget
   // should be able to expand or contract in order to save GUI space.
   ExpandState getWidgetExpandState();
   // Indicates if a slider is allowed in this propertys editing
   // widget
   boolean isSliderAllowed();
   // returns the default value for this property
   Object getDefaultValue();
   // returns a default numeric range for this property, if any
   public NumericInterval getDefaultNumericRange();
   // writes a value of this object out to a PrintStream
   void writeValue (
       Object value, PrintWriter pw, NumberFormat fmt);
   // scans a value of this object from a ReaderTokenizer
   Object scanValue (ReaderTokenizer rtok);
   // creates a Property for this property, attached
   // to the specified host object
   Property createHandle (HasProperties host);
   // returns true if a specified value equals this
   // propertys default value
   boolean valueEqualsDefault();
   // returns true if the property is inheritable
   boolean isInheritable();
   // returns the propertys numeric dimension, or -1 if it
   // is not numeric or does not have a fixed dimension
   int getDimension();
   // indicates that the property value can be shared among
   // several hosts.
   boolean isSharable();

Property information can also be obtained directly from the exporting class, using getAllPropertyInfo(), which returns information for all the properties exported by that class. This information is contained within a PropertyInfoList:

interface PropertyInfoList
   // number of properties in this list
   int size();
   // returns an iterator over all the property infos
   Iterator<PropertyInfo> iterator();
   // returns info for a specific named property
   PropertyInfo get (String name);
   // returns true if this list has no inheritable properties
   boolean hasNoInheritableProperties();

For example, suppose we want to print the names of all the properties associated with a given class. This could be done as follows:

   HasProperties exportingObject;
   PropertyInfoList infoList =
   for (PropertyInfo info : infoList) {
      System.out.println (info.getName());

1.4 Exporting Properties from a Class

As indicated above, a class can export properties by implementing the interface HasProperties, along with the supporting interfaces Property, PropertyInfo, and PropertyInfoList. The class developer can do this in any way desired, but support is provided to make this fairly easy.

The standard approach is to create a static instance of PropertyList for the exporting class, and then populate it with PropertyInfo structures for the various exported properties. This PropertyList (which implements PropertyInfoList) can then be used to implement the getProperty() and getAllPropertyInfo() methods required by HasProperties:

   protected static PropertyList myProps;
   ... initialize myProps in a static code block ...
   // returns an information list for all properties
   public PropertyInfoList getAllPropertyInfo () {
      return myProps;
   // returns a handle for a specific property
   public Property getProperty (String name) {
      getAllPropertyInfo().getProperty (name, this);

Information about specific properties should be added to PropertyList within a static code block (second line in the above fragment). This can be done directly using the method

   void add (PropertyInfo info)

but this requires creating and initializing a PropertyInfo object. An easier way is to use a different version of the add method, which creates the required PropertyInfo structure based on information supplied through its arguments. In the example below, we have a class called ThisHost which exports three properties called visible, lineWidth, and color:

   // default values for the properties
   protected static int defaultLineWidth = 1;
   protected static boolean defaultVisibleP = true;
   protected static Color defaultColor =
      new Color (0.5f, 0.5f, 0.5f);
   // fields containing the property values
   protected int myLineWidth = defaultLineWidth;
   protected boolean myVisibleP = defaultVisibleP;
   protected Color myColor = defaultColor;
   // create a PropertyList ...
   protected static PropertyList myProps =
      new PropertyList(ThisHost.class);
   // ... and add information for each property:
   static {
      myProps.add (
         "visible isVisible *", "object is visible",
      myProps.add (
         "lineWidth", "line width (pixels)",
      myProps.add (
         "color", "color ", defaultColor);
   public PropertyInfoList getAllPropertyInfo () {
      return myProps;
   public Property getProperty (String name) {
      getAllPropertyInfo().get (name, this);

The values for the three properties are stored in the fields myLineWidth, myVisibleP, and myColor. Default values for these are defined by static fields.

A static instance of a PropertyList is created, using a constructor which takes the exporting class as an argument (in Java 1.5, the class object for a class can be referenced as ClassName.class). Information for each property is then added within a static block, using the convenience method

   void add (String nameAndMethods, String description,
             Object defaultValue)

The first argument, nameAndMethods, is a string which gives the name of the property, optionally followed by whitespace-separated names of the accessor methods for the property’s value:

   "<propertyName> [<getMethodName>] [<setMethodName>] [<getRangeMethodName>]"

These accessor methods should have the signatures

   Object getMethod();
   void setMethod (Object value);
   Range getRangeMethod ();

If any of the methods are not specified, or are specified by a ’*’ character, then the system with look for accessor methods with the names getXxx, setXxx, and getXxxRange, where xxx is the name of the property. If no getRangeMethod is defined (and no numeric range is specfied in the options argument string, as described below), then the property will be assumed to have no range limitations and its getRange() method will return null.

The second argument, description, gives a textual description of the property, and is used for generating help messages or tool-tip text.

The third argument, defaultValue, is a default property value, which is used for automatic initialization and for deciding whether the property’s value needs to be written explicitly to persistent storage.

An extended version of the add method takes an additional argument options:

   void add (String nameAndMethods, String description,
             Object defaultValue, String options)

The options argument is a sequence of option tokens specifing various property attributes, each of which can be queried using an associated PropertyInfo method. Token are separated by white space and may appear in any order. Some have have both long and abbreviated forms. They include:

NW, NoAutoWrite

Disables this property from being automatically written using the PropertyList methods write and writeNonDefaults (Section 1.5). Causes the PropertyInfo method getAutoWrite() to return false.

AW, AutoWrite (Default setting)

Enables this property to be automatically written using the PropertyList methods write and writeNonDefaults (Section 1.5). Causes the PropertyInfo method getAutoWrite() to return true.

NE, NeverEdit

Disables this property from being interactively edited. Causes the PropertyInfo method getEditing() to return Edit.Never.

AE, AlwaysEdit (Default setting)

Enables this property to be interactively edited. Causes the PropertyInfo method getEditing() to return Edit.Always.

1E, SingleEdit

Enables this property to be interactively edited for one property host at a time. Causes the PropertyInfo method getEditing() to return Edit.Single.

XE, ExpandedEdit

Indicates, where appropriate, that the widget for editing this property can be expanded or contracted to conserve GUI space, and that it is initially expanded. Causes the PropertyInfo method getWidgetExpandState() to return ExpandState.Expanded. This is generally relevant only for properties such as CompositeProperties (Section 1.4.2) whose editing widgets have several sub-widgets.

CE, ContractedEdit

Indicates, where appropriate, that the widget for editing this property can be expanded or contracted to conserve GUI space, and that it is initially contracted. Causes the PropertyInfo method getWidgetExpandState() to return ExpandState.Contracted. This is generally relevant only for properties such as CompositeProperties (Section 1.4.2) whose editing widgets have several sub-widgets.

NS, NoSlider

Indicates that a slider should not be allowed in the widget for editing this property. Causes the PropertyInfo method isSliderAllowed() to return false. In order for the editing widget to contain a slider, the property must also have both a numeric value and a defined range.

DX, DimensionX

Sets the numeric dimension of this property to X. The dimension can be queried using the PropertyInfo method getDimension(). For properties which are non-numeric or do not have a fixed dimension, the dimension will be returned as -1. Note the for some numeric properties, the dimension can be determined automatically and there is no need to explicitly specify this attribute.

SH, Sharable

Indicates that the property value is not copied internally by the host and can therefore be shared among several hosts. This may improve memory efficiency but means that changes to the value itself may be reflected among several hosts. This attribute can be queried by the PropertyInfo method isSharable().

NV, NullOK

Indicates that the property value may be null. By default, this is false, unless the default value has been specified as null. Whether or not a property may be set to null is particularly relevant in the case of CompositeProperties (Section 1.4.2), where one may choose between setting individual sub-properties or setting the entrie structure to null altogether.


A printf-style format string, beginning with %, used to format numeric information for this property’s value, either in a GUI or when writing to persistent storage. A good general purpose format string to use is often "%.6g", which specifies a free format with six significant characters.


A numeric range interval with a lower bound of l and an upper bound of u. If specified, this defines the value returned by PropertyInfo.getDefaultNumericRange(); otherwise, that method returns null. If a getRangeMethod is not defined for the property, and the property has a numeric type, then the default numeric range is returned by the property’s Property.getRange() method. The default numeric range is also used to determine bounds on slider widgets for manipulating the property’s value, in case the upper or lower limits returned by the Property.getRange() method are unbounded. The symbol inf can be used in an interval range, so that [0,inf] represents the set of non-negative numbers.

The following code fragment shows an example of using the option argument:

   myProps.add (
      "radius", "radius of the sphere (mm)", defaultRadius,
      "%8.3f [0,100] NE");

The property named radius is given a numeric format string of "%8.3f", a numeric range in the interval [0,100], and set so that it will not be displayed in an automatically created GUI panel.

1.4.1 Read-only properties

A property can be read-only, which means that it can be read but not set. In particular, the set() for a read-only Property handle is inoperative.

Read-only properties can be specified using the following PropertyList methods:

   void addReadOnly (String nameAndMethod, String description);
   void addReadOnly (String nameAndMethod, String description,
       String options);

These are identical to the add methods described above, except that the nameAndMethod argument includes at most a get accessor, and there is no argument for specifying a default value.

The method getAutoWrite() also returns false for read-only properties (since it does not make sense to store them in persistent storage).

1.4.2 Inheriting Properties from a superclass

By default, a subclass of a HasProperties class inherits all the properties exported by the class exports all the properties exported by it’s immediate superclass.

Alternatively, a subclass can create its own properties by creating it’s own PropertyList, as in the code example of Section 1.3:

   // create a PropertyList ...
   protected static PropertyList myProps =
      new PropertyList(ThisHost.class);
   public PropertyInfoList getAllPropertyInfo () {
      return myProps;

and none of the properties from the superclass will be exported. Note that it is necessary to redefine getAllPropertyInfo() so that the instance of myProps specific to ThisHost will be returned.

If one wishes to also export properties from the superclass (or some other ancestor class), then a PropertyList can be created which also contains property information from the desired ancestor class. This involves using a different constructor, which takes a second argument specifying the ancestor class from which to copy properties:

   protected static PropertyList myProps =
      new PropertyList(ThisHost.class, Ancestor.class);
   public PropertyInfoList getAllPropertyInfo () {
      return myProps;

All properties exported by Ancestor will now also be exported by ThisHost.

What if we want only some properties from an ancestor class? In that case, we can edit the PropertyList to remove properties we don’t want. We can also replace properties with new ones with the same name but possibly different attributes. The latter may be necessary if the class type of a property’s value changes in the sub-class:

       // remove the property "color"
       myProps.remove ("color");
       // replace the property called "mesh" with one which
       // uses a different kind of mesh object:
       myProps.remove ("mesh");
       myProps.add ("mesh", "quad mesh", null);

1.5 Composite Properties

A property’s value may itself be an object which exports properties; such an object is known as a composite property, and its properties are called sub-properties.

Property handles for sub-properties may be obtained from the top-level exporting class using getProperty(), with successive sub-property names delimited by a ’.’ character. For example, if a class exports a property textureProps, whose value is a composite property exporting a sub-property called mode, then a handle to the mode property can be obtained from the top-level class using

   Property mode = getProperty ("textureProps.mode");

which has the same effect as

   Property texture = getProperty ("textureProps");
   Property mode =
       ((HasProperties)texture).getProperty ("mode");

Composite properties should adhere to a couple of rules. First, they should be returned by reference; i.e., the hosting class should return a pointer to the original property, rather than a copy. Secondly, they should implement the CompositeProperty interface. This is an extension of HasProperties with the following methods:

interface CompositeProperty extends HasProperties
   // returns the host class exporting this property
   HasProperties getPropertyHost();
   // returns information about this property
   PropertyInfo getPropertyInfo();
   // sets the host class exporting this property
   void setPropertyHost (HasProperties host);
   // sets information for this property
   void setPropertyInfo (PropertyInfo info);

These methods can be easily implemented using local variables to store the relevant information, as in

   HasProperties myHost;
   HasProperties getPropertyHost() {
      return myHost;
   void setPropertyHost (HasProperties host) {
      myHost = host;

and similarly for the property information.

The purpose of the CompositeProperty interface is to allow traversal of the composite property tree by the property support code.

The accessor method that sets a composite property within a host should set it’s host and property information. This can be done using using the setPropertyHost and setPropertyInfo methods, as in the following example for a compound property of type TextureProps:

   setRenderProps (RenderProps props) {
      if (props != myProps) {
         if (props != null) {
         if (myProps != null) {
            props.setPropertyHost (null);
         myProps = props;

Alternatively, the same thing can be done using the static convenience method PropertyUtils.updateCompositeProperty:

   setRenderProps (RenderProps props) {
      if (props != myProps) {
         PropertyUtils.updateCompositeProperty (
            this, "textureProps", myProps, props);
         myProps = props;

1.6 Reading and Writing to Persistent Storage

Properties contain built-in support that make it easy to write and read their values to and from persistent storage.

First, PropertyInfo contains the methods

   void writeValue (Object value, PrintWriter pw,
                    NumberFormat fmt);
   Object scanValue (ReaderTokenizer rtok);

which allow an individual object value to written to a PrintStream or scanned from a ReaderTokenizer.

Second, if the host object maintains a PropertyList, it can use the convenience method

   void write (
       HasProperties host, PrintWriter pw, NumberFormat fmt);

to write out values for all properties for which getAutoWrite() returns true. Properties will be written in the form

   propertyName = value

where value is the output from the writeValue method of the PropertyInfo structure.

To economize on file space, there is another method which only writes out property values when those values differ from the property’s default value:

   boolean writeNonDefaults (
       HasProperties host, PrintWriter pw, NumberFormat fmt)

Again, values are written only for the properties for which getAutoWrite() returns true. The method returns false if not property values are written.

To read in property values, their are the methods

   boolean scanProperty (
       HasProperties host, ReaderTokenizer rtok);
   boolean scanSpecificProperty (
       HasProperties host, ReaderTokenizer rtok, String name);

where the former will inspect the input stream and scan in any recognized property of the form propertyName = value (returning true if such a property was found), while the latter will check the input for a property with a specific name (and return true if the specified property was found).

1.7 Inheritable Properties

Suppose we have a hierarchical arrangement of property-exporting objects, each exporting an identical property called stiffness whose value is a double (properties are considered identical if they have the same name and the same value type). It might then be desirable to have stiffness values propagate down to lower nodes in the hierarchy. For example, a higher level node might be a finite element model, with lower nodes corresponding to individual elements, and when we set stiffness in the model node, we would like it to propagate to all element nodes for which stiffness is not explicitly set. To implement this, each instance of stiffness is associated with a mode, which may be either explicit or inherited. When the mode is inherited, stiffness obtains its value from the first ancestor object with a stiffness property whose mode is explicit.

This is an example of property inheritance, as illustrated by Figure 1.1. Stiffness is explicitly set in the top node (A), and its value of 1 propagates down to nodes B and D whose stiffness mode is inherited. For node C, stiffness is also explicitly set, and its value of 4 propagate down to node F.

Figure 1.1: Inheritance of a property named “stiffness” within a hierarchy of property-exporting objects. Explicitly set instances of the property are surrounded by square boxes.

Another common use of property inheritance is in setting render properties: we might like some properties, such as color, to propagate down to descendant nodes for which a color has not been explicitly set.

To state things more generally: any property which can be inherited is called an inheritable property, and is associated with a mode whose value is either explicit or inherited. The basic operating principle of property inheritance is this:

An inherited property’s value should equal that of the nearest matching ancestor property which is explicitly set.

Other behaviors include:

  • Setting a property’s value (using either the set accessor in the host or the set method of the Property handle) will cause its mode to be set to explicit.

  • A property’s mode can be set directly. When set to explicit, all descendant nodes in the hierarchy are updated with the property’s value. When set to inherited, the property’s value is reset from the first explicit value in the ancestry, and then propagated to the descendants.

  • When a new node is added to the hierarchy, all inherited properties within the node are updated from the ancestry, and then propagated to the descendants.

If a property is inheritable, then the isInherited() method in its PropertyInfo structure will return true, and it’s property handle will be an instance of InheritableProperty:

interface InheritableProperty extends Property
   // sets the propertys mode
   public void setMode (PropertyMode mode);
   // returns the propertys mode
   public PropertyMode getMode();

Valid modes are PropertyMode.Explicit, PropertyMode.Inherited, and PropertyMode.Inactive. The latter is similar to Inherited, except that setting an Inactive property’s value will not cause its mode to be set to Explicit and its new value will not be propagated to hierarchy descendants.

The hierarchy structure which we have been describing is implemented by having host classes which correspond to hierarchy nodes implement the HierarchyNode interface.

interface HierarchyNode
   // returns an iterator over this nodes children
   Iterable<? extends HierarchyNode> getChildren();
   // returns true if this node has children
   boolean hasChildren();
   // returns the parent of this node, if any
   HierarchyNode getParent();

These methods should be implemented as wrappers to the underlying hierarchy implementation.

1.8 Exporting Inheritable Properties

The property package provides most of the code required to make inheritance work, and so all that is required to implement an inheritable property is to provide some simple template code within its exporting class. We will illustrate this with an example.

Suppose we have a property called “width” that is to be made inheritable. Then addition to it’s value variable and set/get accessors, the host class should provide a PropertyMode variable along with set/get accessors:

   int myWidth;
   PropertyMode myWidthMode = PropertyMode.Inherited;
   public PropertyMode getWidthMode() {
      return myWidthMode;
   public void setWidthMode (PropertyMode mode) {
      myWidthMode = PropertyUtils.setModeAndUpdate (
         this, "width", myWidthMode, mode);

The call to PropertyUtils.setModeAndUpdate() inside the set method ensures that inherited values within the hierarchy are properly whenever the mode is changed. If the mode is set to PropertyMode.Explicit, then the property’s value needs to be propagated to any descendent nodes for which it is inherited. If the mode is set to PropertyMode.Inherited, then the property’s value needs to be obtained from the ancestor nodes, and then also propagated to any descendent nodes for which it is inherited.

As mentioned in the previous section, explicitly setting a property’s value using the set accessor should cause it’s property mode to be set to Explicit and the new value to be propagated to hierarchy descendents. This can be accomplished by using PropertyUtils.propagateValue within the set accessor:

   public void setWidth (int w) {
      myWidth = w;
      myWidthMode = PropertyUtils.propagateValue (
         this, "width", myWidth, myWidthMode);

The actual creation of an inherited property can be done using the PropertyList methods

   void addInheritable (
      String nameAndMethods, String description,
      Object defaultValue)
   void addInheritable (
      String nameAndMethods, String description,
      Object defaultValue, String options)

instead of the add or addReadOnly methods. The nameAndMethods argument may now specify up to five method names, corresponding, in order, to the get/set accessors for the property value, the getRange accessor, and the get/set accessors for the property’s mode. If any of these are omitted or specified as ’*’, then the system searches for names of the form getXxx, setXxx, getXxxRange, getXxxNode, and setXxxMode, where xxx is the property name.

Finally, the host objects which actually correspond to hierarchy nodes must implement the HierarchyNode interface as described in the previous section, and any routine which adds a node to the hierarchy must also implement the following code fragment:

   public void addChild (HierarchyNode node) {
      ... add node to the hierarchy ...
      PropertyUtils.updateInheritedProperties (node);

This ensures that when a node is added, all property values within and beneath it are made consistent with the inheritance hierarchy.

1.9 Inheritable and Composite Properties

Property inheritance is not currently implemented for CompositeProperty objects, in order to avoid confusion of the inheritance rules. Suppose a class exports a composite property A, which in turn exports an inheritable property B. Now suppose that A is an inheritable property with its mode is set to Inherited. Then the entire structure of A, including the value of B and its mode, is inherited, and it is no longer possible to independently set the value of B, even if its mode is Explicit.

However, the leaf nodes of a composite property tree certainly can be inherited. Suppose a class ThisHost exports properties width, order, and renderProps, and that the latter is a composite property exporting width, color, and size. The leafs nodes of the composite property tree exported by ThisHost are the properties


Each of these may be inheritable, although renderProps may not be.

It should be noted that all the leaves in a composite property tree are considered to be unique properties and do not affect each other with respect to inheritance, even if some of the sub-component names are the same. For instance, in the above example, the properties width and renderProps.width are different; each may inherit, respectively, from occurrences of width and renderProps.width contained in ancestor nodes, but they do not affect each other. This is illustrated by Figure 1.2.

Figure 1.2: Inheritance of the properties width and renderProps.width within a hierarchy

Also, if a CompositeProperty is set to null within a particular node, then the inheritance of its sub-properties passes straight through that node as though the property was not defined there at all. For example, in Figure 1.2, renderProps is set to null in node C, and so renderProps.width in node F inherits its value directly from node A.

Composite property inheritance is fully supported if an inheritable property’s set accessor invokes PropertyUtils.updateCompositeProperty as shown in the code example at the end of Section 1.4.2.

Chapter 2 Rendering

2.1 Overview

This chapter describes the maspack rendering package (maspack.render), which provides a general interface for the graphical rendering of objects and allows them to implement their own rendering methods. An object makes itself renderable by implementing the IsRenderable interface, and renderable objects can then be displayed by a Viewer, which typically provides features such as viewpoint control, lighting arrangements, fixtures such as coordinate axes, grids and clipping planes, and component selection. The viewer also implements a Renderer interface which provides the actual graphics functionality which renderable objects use to draw themselves.

2.1.1 Renderables and Viewers

Any object to be rendered should implement the IsRenderable interface, which defines the following four methods,

   void prerender (RenderList list);
   void render (Renderer renderer, int flags);
   void updateBounds (Vector3d pmin, Vector3d pmax);
   int getRenderHints();

prerender() is called prior to rendering and allows the object to update internal rendering information and possibly give the viewer additional objects to render by placing them on the RenderList (Section 2.2.2). render() is the main method by which an object renders itself, using the functionality provided by the supplied Renderer. updateBounds() provides bounds information for the renderable’s spatial extent (which the viewer can use to auto-size the rendering volume); Vector3d describes a 3-vector and is defined in the package maspack.matrix. getRenderHints() returns flags giving additional information about rendering requirements, including whether the renderable is transparent (IsRenderable.TRANSPARENT) or two dimensional (IsRenderable.TWO_DIMENSIONAL).

Figure 2.1: General relationship between viewers, renderers, and renderables. A viewer is associated with a number of renderables, and provides the renderer interface with which renderables use to draw themselves via their render() methods.

A Viewer provides the machinery needed to display renderable objects, and implements the Renderer interface (Section 2.3) with which renderables draw themselves within their render() methods. Renderer includes methods for maintaining graphics state, drawing primitives such as points, lines, and triangles, and drawing simple solid shapes. The general relationship between viewers, renderables, and renderers is shown in Figure 2.1. Rendering is triggered within a viewer by calling its rerender() method, which causes the prerender() and render() methods to be called for every renderable, as discussed in detail in Section 2.2.

Figure 2.2: Viewer display of the example of Listing 1.

2.1.2 A Complete Example

Listing 1 shows a complete example of a renderable object being declared and displayed in a viewer.

Listing 1: Declaration and display of a renderable object.
package maspack.render;
import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.matrix.AxisAlignedRotation;
import maspack.render.GL.GLViewerFrame;
public class RenderableExample implements IsRenderable {
   public void prerender (RenderList list) {
      // can be used to cache rendering data or add extra renderables;
      // not used in this example
   public void render (Renderer renderer, int flags) {
      // draw two spheres and a connecting cylinder
      Vector3d pnt0 = new Vector3d (-1, 0, 0);
      Vector3d pnt1 = new Vector3d ( 1, 0.5, 0);
      renderer.setColor (Color.GRAY);
      renderer.drawSphere (pnt0, 0.5);
      renderer.drawSphere (pnt1, 0.5);
      renderer.setColor (Color.BLUE);
      renderer.drawCylinder (pnt0, pnt1, 0.1, /*capped=*/false);
   public void updateBounds (Vector3d pmin, Vector3d pmax) {
      // extend pmin and pmax to accommodate bounds of (-1, -1, 0) and (1, 1, 0)
      (new Vector3d (-1, -1, 0)).updateBoundsz (pmin, pmax);
      (new Vector3d ( 1,  1, 0)).updateBounds (pmin, pmax);
   public int getRenderHints() {
      // no specific hints
      return 0;
   public static void main (String[] args) {
      IsRenderable renderable = new RenderableExample();
      // create a glviewer in a 640 x 480 frame
      GLViewerFrame frame = new GLViewerFrame (
         "rendererExample", 640, 480);
      Viewer viewer = frame.getViewer();
      viewer.addRenderable (renderable);
      viewer.setAxialView (AxisAlignedRotation.X_Y); // set view transform
      frame.setVisible (true);

The example creates a class called RenderableExample which implements isRenderable and the associated methods: prerender(), which does nothing; render(), which draws two gray spheres connected by a blue cylinder; updateBounds(), which sets the maximum and minimum bounds to be the points (-1,-1,0) and (1,1,0), and getRenderHints() which returns no flags. The example then defines a main() method which creates an instance of RenderableExample, along with a GLViewerFrame which contains a viewer with which to display it. The renderable is added to the viewer, the viewpoint is set so that the x and y axes of the viewing plane are aligned with the world x and y axes, and the frame is set to be visible, with the result shown in Figure 2.2.

2.2 Viewers

This section summarizes viewer functionality as defined by the Viewer interface. Note that specific viewer implementations may provide significant additional functionality, such as interactive view control, keyboard and mouse event handling, or graphical fixtures such as coordinate axes, grids or transformers. The description of these extra features is beyond the scope of this document.

Rendering is triggered within a viewer by calling its rerender() method, which then initiates two rendering steps:

  1. 1.

    prerendering: The viewer calls the prerender() method for all its renderables, and adds those which are visible into a render list;

  2. 2.

    repainting: All components in the render list are redrawn using their render() method;

Another viewer method, repaint(), can subsequently be called to initiate repainting without invoking prerendering.

In general, rerender() should be called whenever there is a change in the graphical state of the renderables. This includes changes in geometry, color, or visibility. In the context of simulation, rerender() should be called after every simulation step.

Otherwise, repaint() should be called when the graphical state of the scene has not changed but the final screen display has, such as when the viewpoint is changed, or the display window is unhidden or resized. This is more efficient than calling rerender() because it avoids the overhead of the prerendering step.

The prerendering step is invoked directly within the rerender() method, whereas the repainting step is called in whatever thread implements the graphical display. Since, as described below, one of the functions of the prerendering step is to cache rendering information, rerender() should be called in synchronization with both the graphical display thread and whatever thread(s) (such as a simulation thread) might be altering the state of the renderables.

2.2.1 Render lists

A render list is implemented by the class RenderList and sorts renderable components into separate sublists depending on whether they are primarily opaque, transparent, 2d opaque, and 2d transparent. These designations are determined by examining the flags returned by the renderable’s getRenderHints() method, with TWO_DIMENSIONAL indicating a two dimensional component and TRANSPARENT indicating a transparent one. These sublists assist the viewer in rendering a scene more realistically. For example, in OpenGL, better results are obtained if opaque objects are drawn before transparent ones, and two dimensional objects are drawn after three dimensional ones, with the depth buffer disabled.

A viewer maintains its own internal render list, and rebuilds it once during every prerendering step, using the following algorithm:

RenderList list;
for (each renderable component r) {
   list.addIfVisible (r);

The list’s addIfVisible() method calls the component’s prerender() method, and then adds it to the appropriate sublist if it is visible:

addIfVisible (IsRenderable r) {
   if (r is visible) {
      add r to appropriate sublist;

A renderable’s visibility is determined as follows:

As discussed in Section 2.2.3, a viewer can also be provided with an external render list, which is maintained by the application. It is the responsbility of the application, and not the viewer, to rebuild the external render list during the prerendering step. However, in the repainting step, the viewer will handle the redrawing of all the components in both its internal and external render lists.

2.2.2 Prerendering and Rendering

Prerendering allows renderables to

  1. 1.

    update data structures anc cached data needed for rendering

  2. 2.

    add additional renderables to the render list.

The caching of graphical state is typically necessary when rendering is performed in a thread separate from the main application, which can otherwise cause synchronization and consistency problems for renderables which are changing dynamically. For example, suppose we are simulating the motion of two objects, A and B, and we wish to render their positions at a particular time t. If the render thread is allowed to run in parallel with the thread computing the simulation, then A and B might be drawn with positions corresponding to different times (or worse, positions which are indeterminate!).

Synchronizing the rendering and simulation threads will aleviate this problem, but that means foregoing the speed improvement of allowing the rendering to run in parallel. Instead, renderables can use the prerender() method to cache their current state for later use in the render() method, in a manner analagous to double buffering. For example, suppose a renderable describes the position of a point in space, inside a member variable called myPos. Then its prerender() method can be constructed to save this into another another member variable myRenderPos for later use in render():

import maspack.geometry.Vector3d;
import maspack.render.*;
   Vector3d myPos;         // point position
   float[] myRenderPos;   // cached value for rendering
   void prerender (RenderList list) {
      myPos.get (myRenderPos); // save cached value

In the example above, the cached value is stored using floating point values, since this saves space and usually provides sufficient precision for rendering purposes.

As described in Section 2.4, objects can sometimes make use of render objects when rendering themselves. These can result in improved graphical efficieny, and also provide an alternate means for caching graphical information. If render objects are being used, it is recommmended that they be created or updated within prerender().

The prerender() method can also be used to add additional renderables to the render list. This is done by recursively calling the list’s addIfVisible() method. For example, if a renderable has two subcomponents, A and B, which also need to be rendered, then it can add them to the render list as follows:

void prerender (RenderList list) {
   IsRenderable A, B;
   // add both A and B to the render list
   list.addIfVisible (A);
   list.addIfVisible (B);

In addition to adding A and B to the render list if they are visible, addIfVisible() will also call their prerender() methods, which will in turn give them the opportunity to add their own sub components to the render list. Note that prerender() is always called for the specified renderable, whether it is visible (and added to the list) or not (since even if a renderable is not visible, it might have subcomponents which are). This allows an entire hierarchy of renderables to be rendered by simply adding the root renderable to the viewer.

Note that any renderables added to the render list within prerender() are not added to the primary list of renderables maintained by the viewer.

Because of the functionality outlined above, calls to prerender() methods, and the viewer rerender() method that invokes them, should be synchronized with both the graphical display thread and whatever thread(s) might be altering the state of the renderables.

As indicated above, actual object rendering is done within its render() method, which is called during the repaint step, within whatever thread is responsible for graphical display. The render() method signature,

void render (Renderer renderer, int flags)

provides a Renderer interface (Section 2.3) which the object uses to draws itself, along with a flags argument that specifies additional rendering conditions. Currently only one flag is formally supported, Renderer.HIGHLIGHT, which requests that the object be rendered using highlighting (see Section

2.2.3 Viewer renderables and external render lists

Renderables can be added or removed from a viewer using the methods

   void addRenderable (IsRenderable r);
   void removeRenderale (IsRenderable r);
   void clearRenderables();

If renderables are arranged in a hierarchy, and add their own subcomponents to the render list during prerender(), as described in Section 2.2.2, then it may only be necessary to add top level renderable components to the viewer.

It is also possible to assign a viewer an external render list, for which the prerendering step is maintained by the application. This is useful in situations where multiple viewers are being used to simultaneously render a common set of renderables. In such cases, it would be wasteful for each viewer to repeatedly execute the prerender phase on the same renderable set. It may also lead to inconsistent results, if the state of renderables changes between different viewers’ invocation of the prerender phase.

To avoid this problem, an application may create its own render list and then give it to multiple viewers using setExternalRenderList(). A code sample for this is as follows:

import maspack.render.*;
   Viewer viewer1;
   Viewer viewer2;
   List<IsRenderable> renderables;
   RenderList extlist = new RenderList();
   // assign external list to the viewers
   viewer1.setExternalRenderList (extlist);
   viewer2.setExternalRenderList (extlist);
   for (each simulation step) {
      // execute the pre-render phase
      syncrhonized (extlist) {
         for (IsRenderable r : renderables) {
            extlist.addIfVisibleAll (r);

The statement synchronize(extlist) ensures that calls to extlist.addIfVisible(r) (and the subsequent internal calls to prerender()) are synchronized with render() method calls made by the viewer. This works because the viewer also wraps its usage of extlist inside synchronize(extlist) statements.

Once the viewers have been assigned an external render list, they will handle the repainting step for its renderables, along with their own internal renderables, every time repainting is invoked through a call to either rerender() (as in the above example) or repaint().

2.2.4 Coordinate frames and view point control

A viewer maintains three primary coordinate frames for describing the relative locations and orientations of scene objects and the observing “eye” (or camera). These are the eye, model, and world frames.

The eye frame (sometimes also known as the camera frame) is a right-handed frame located at the eye (or camera) focal point, with the z axis pointing toward the observer. The viewing frustum is located in the half space associated with the negative z axis of the eye frame (and usually centered on said axis), with the near and far clipping planes designated as the view plane and far plane, respectively. The viewer also maintains a viewing center, typically located along the negative z axis, and which defines the point about which the camera pivots in response to interactive view rotation.

The viewing frustum is defined by the view and far planes, in combination with a projection matrix that transforms eye coordinates into clip coordinates. Most commonly, the projection matrix is set up for perspective viewing (Figure 2.3), but orthographic viewing (Figure 2.4) is sometimes used as well.

Figure 2.3: Primary coordinate frames associated with the renderer, along with the viewing frustum and center point.
Figure 2.4: Primary coordinate frames with the projection matrix set up for orthographic viewing.

The model frame is the coordinate frame in which geometric information for rendered objects is specified, and the world frame is the base with respect to which the model and eye frames are defined. The model matrix is the 4\times 4 homogeneous affine transform {\bf X}_{MW} from model to world coordinates, while the view matrix is a 4\times 4 homogeneous rigid transform {\bf T}_{WE} from world to eye coordinates. The composition of {\bf T}_{WE} and {\bf X}_{MW} transforms a point from model coordinates {}^{M}{\bf p} into eye coordinates {}^{E}{\bf p}, according to:

\left(\begin{matrix}{}^{E}{\bf p}\\
1\end{matrix}\right)\;=\;{\bf T}_{WE}\,{\bf X}_{MW}\left(\begin{matrix}{}^{M}{%
\bf p}\\

Note: the renderer assumes that points and vectors are column-based and the coordinate transforms work by pre-multiplying these column vectors. This is in constrast to some computer graphics conventions in which vectors are row based. Our transformation matrices are therefore the transpose of those defined with respect to a row-based convention.

Initially the world and model frames are coincident, so that {\bf X}_{MW}={\bf I}. Rendering methods often redefine the model matrix, allowing existing object geometry or built-in drawing methods to be used at different scales and poses throughout the scene. The methods available for querying and controlling the model matrix are described in Section 2.3.8.

Figure 2.5: Determining the pose of the eye frame from the eye and center points, and an up vector parallel to the frame’s y axis.

Meanwhile, changing the view matrix allows the scene to be observed from different view points. A viewer provides the following direct methods for setting and querying the view matrix:

void setViewMatrix (RigidTransform3d TWE);
RigidTransform3d getViewMatrix();
void getViewMatrix (RigidTransform3d TWE);

where RigidTransform3d is defined in maspack.matrix and represents a 4 homogenous rigid transformation. Instead of specifying the view matrix, it is sometimes more convenient to specify its inverse, the eye-to-world transform {\bf T}_{EW}. This can be done with

void setEyeToWorld (RigidTransform3d TEW);
void setEyeToWorld (Point3d eye, Point3d center, Vector3d up);
void getEyeToWorld (RigidTransform3d TEW);

where Point3d and Vector3d are also defined in maspack.matrix and represent 3 dimensional points and vectors. The method setEyeToWorld(eye,center,up) sets {\bf T}_{EW} according to legacy OpenGL conventions so that (with respect to world coordinates) the eye frame’s origin is defined by the point eye, while its orientation is defined such that the -z axis points from eye to center and the y axis is parallel to up (see Figure 2.5).

Point3d is a subclass of Vector3d used to describe points in space. The only difference between the two is that they transform differently in response to rigid transforms (described by RigidTransform3d) or affine transforms (described by AffineTransform3d): point transformations include the translational component, while vector transformations do not.

The viewer also maintains a center position and an up vector that are used to modify {\bf T}_{EW} in conjunction with the following:

void setEye (Point3d eye);
Point3d getEye();
void setCenter (Point3d center);
Point3d getCenter();
void setUpVector (Vector3d up);
Vector3d getUpVector();

Again with respect to world coordinates, setEye(eye) sets the origin of the eye frame while recomputing its orientation from the current values of center and up, while setCenter(center) and setUpVector(up) set center and up and recompute the eye frame’s orientation accordingly.

It is also possible to specify axis-aligned views, so that the axes of the eye frame are exactly aligned with the axes of the world frame. This can be done using

void setAxialView (AxisAlignedRotation REW);
AxisAlignedRotation getAxialView();

setAxialView() sets the rotational component of {\bf T}_{EW} to REW, and moves the eye position so that the viewer’s center lies along the new -z axis. It also sets the up vector to the y axis of REW, and stores REW as the viewer’s nominal axial view which can be used for determining default orientations for fixtures such as grids. AxisAlignedRotation defines 24 possible axis-aligned orientations, and so there are 24 possible axis-aligned views. Some of those commonly used in association with setAxialView() are:

X_Y eye frame and world frame have the same orientaion
X_Z eye frame x-y axes correspond to world frame x-z
Y_Z eye frame x-y axes correspond to world frame y-z

There are several methods available to reset the viewing frustum:

void setPerspective (
   double left, double right, double bottom, double top, double near, double far);
void setPerspective (
   double fieldOfView, double near, double far);
void setOrthogonal (
   double left, double right, double bottom, double top, double near, double far);
void setOrthogonal (
   double fieldHeight, double near, double far);

The setPerspective methods create a perspective-based frustum (Figure 2.3). The first methods explicitly sets the left, right, bottom and top edges of the view plane, along with the (positive) distances to the near (i.e., view) and far planes, while the second method creates a frustum centered on the -z axis, using a specified vertical field of view. The setOrthogonal methods create an orthographic frustum (Figure 2.4) in a similar manner.

Information about the current frustum can be queried using

double getViewPlaneWidth();
double getViewPlaneHeight();
double getViewPlaneDistance();
double getFarPlaneDistance();
Vector3d getEyeZDirection();
boolean isOrthogonal();

For convenience, the viewer can also automatically determine appropriate values for the center and eye positions, and then fit a suitable viewing frustum around the scene. This is done using the renderables’ updateBounds() method to estimate a scene center and radius, along with the current value of the up vector to orient the eye frame. The auto-fitting methods are:

void autoFitOrtho();        // fit orthographic frustum
void autoFitPerspective();  // fit perspective frustum
void autoFit();             // fit frustum of the current type

These auto-fit methods also make use of a default vertical field-of-view, which is initially 35 degrees and which can be controlled using

double getVerticalFieldOfView();
void setVerticalFieldOfView (double fov);

Finally, the viewer’s background color can be controlled using

void setBackgroundColor (float[] rgba)
void setBackgroundColor (Color color);
Color getBackgroundColor();
float[] getBackgroundColor(float[] rgba);

2.2.5 Lights

Viewers also maintain scene lighting. Typically, a viewer will be initialized to a default set of lights, which can then be adjusted by the application. The existing light set can be queried using the methods

   int numLights();                   // number of lights currently in use
   Light getLight (int idx);          // get information for the idx-th light
   int getIndexOfLight (Light light); // return index for light, or -1

where Light is a class containing parameters for the light. Lights are described using the same parameters as those of OpenGL, as described in Chapter 5 of the OpenGL Programming Guide (Red book). Each has a position {\bf p} and (unit) direction \bf d in space, a type, colors associated with ambient, specular and diffuse lighting, and coefficients for its attenuation formula. The attenuation formula is


where f is the light intensity, d is the distance between the light and the point being lit, and C, L, and D are the constant, linear and quadratic attentuation factors.

Spot lights have the same properties as other lights, in addition to also having a cutoff angle \theta and an exponent e. The cutoff angle is the angle between the direction of the light and the edge of its cone, while the exponent, whose default value is 0, is used to determine how focused the light is. If \bf{v} is the unit direction from the light to the point being lit, and if {\bf d}\cdot{\bf v}\geq\cos\theta, then the point being lit is within the light cone and the light intensity f in the above equation is multiplied by the spotlight effect, given by

({\bf d}\cdot{\bf v})^{e}

Since |{\bf d}\cdot{\bf v}|\leq 1, a value of e=0 gives the least light reductuon, while valuse of e>0 increase the intensity of the spot light towards its center.

Information for a specific light is provided by a Light object, which contains the following fields:


A boolean describing whether or not the light is enabled.


An instance of Light.LightType describing the type of the light. Current values are DIRECTIONAL, POINT, and SPOT.


A 3-vector giving the position of the light in world coordinates.


A 3-vector giving the direction of the light in world coordinates.


RGBA values for the ambient light color.


RGBA values for the diffuse light color.


RGBA values for the specular light color.


Constant term C in the attenuation formula


Linear term L in the attenuation formula


Quadratic term Q in the attenuation formula


For spotlights, the cosine of the cutoff angle \theta.


For spotlights, the exponent e.

Each of these fields is associated with accessor methods inside Light.

An application can also add or remove lights using

void addLight (Light light);
boolean removeLight (Light light)
boolean removeLight (int idx);

To create a new light, the application instantiates a Light object, sets the appropriate fields, and then calls addLight(). Lights can be removed either by reference to the light object or its index.

Lights are updated by the viewer at the beginning of each repaint step. That means that for lights already added to the viewer, any changes made to the fields of the associated Light object will take effect at the beginning of the next repaint step.

2.3 The Renderer Interface

This section describes the Renderer interface, which supplies the methods which objects can use to draw themselves. This includes methods for setting graphics state, and drawing point, line and triangle primitives as well as simple solid shapes.

2.3.1 Drawing single points and lines

The most basic Renderer methods provide for the drawing of single points, lines, and triangles. The following can be used to draw a pixel-based point at a specified location pnt, or a pixel-based line segment between two points pnt0 and pnt1:

void drawPoint (Vector3d pnt);
void drawPoint (double px, double py, double pz);
void drawPoint (float[] pnt);
void drawLine (Vector3d pnt0, Vector3d pnt1);
void drawLine (double px0, double py0, double pz0,
               double px1, double py1, double pz1);
void drawLine (float[] pnt0, float[] pnt1);

where, as mentioned earlier, Vector3d represents a 3-vector and is defined in maspack.matrix.

Note: while convenient for drawing small numbers of points and lines, the methods described in this section can be quite inefficient. For rendering larger numbers of primitives, one should use either the draw mode methods of Section 2.3.4, or the even more efficient render objects described in Section 2.4.

The size of the points or lines (in pixels) can be controlled via following methods:

float getPointSize();
void setPointSize(float size);
float getLineWidth();
void setLineWidth (float width);
Figure 2.6: Simple square drawn with the renderer.

The following example draws a square in the x-z plane, with blue edges and red corners:

import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.Shading;
   void render (Renderer renderer, int flags) {
      // the corners of the square
      Vector3d p0 = new Vector3d (0, 0, 0);
      Vector3d p1 = new Vector3d (1, 0, 0);
      Vector3d p2 = new Vector3d (1, 0, 1);
      Vector3d p3 = new Vector3d (0, 0, 1);
      renderer.setShading (Shading.NONE); // turn off lighting
      // draw corners
      renderer.setPointSize (4);
      renderer.setColor (Color.RED);
      renderer.drawPoint (p0);
      renderer.drawPoint (p1);
      renderer.drawPoint (p2);
      renderer.drawPoint (p3);
      // draw edges
      renderer.setLineWidth (2);
      renderer.setColor (Color.BLUE);
      renderer.drawLine (p0, p1);
      renderer.drawLine (p1, p2);
      renderer.drawLine (p2, p3);
      renderer.drawLine (p3, p0);
      renderer.setShading (Shading.FLAT); // restore default shading

In addition to the draw methods described above, we use setShading() to disable and restore lighting (Section 2.3.6), and setColor() to set the point and edge colors (Section 2.3.3). It is generally necessary to disable lighting when drawing pixel-based points and lines which do not (as in this example) contain normal information. The result is shown in Figure 2.6.

For visualization and selection purposes, it is also possible to draw points and lines as solid spheres and cylinders; see the description of this in Section 2.3.1.

2.3.2 Drawing single triangles

Figure 2.7: An open tetrahedron, with the viewer also displaying the world frame x-y-z axes (as red, green and blue lines) to help show its orientation.

Another pair of methods are available for drawing solid triangles:

void drawTriangle (Vector3d pnt0, Vector3d pnt1, Vector3d pnt2);
void drawTriangle (float[] pnt0, float[] pnt1, float[] pnt2);

Each of these draws a single triangle, with a normal computed automatically with respect to the counter-clockwise orientation of the vertices.

Note: as with drawing single points and lines, the single triangle methods are inefficient. For rendering large numbers of triangles, one should use either the draw mode methods of Section 2.3.4, or the render objects described in Section 2.4.

When drawing triangles, the renderer can be asked to draw the front face, back face, or both faces. The methods to control this are:

FaceStyle getFaceStyle ();
void setFaceStyle (FaceStyle mode);

where FaceStyle is an enumerated type of Renderer with the possible values:


Draw the front face


Draw the back face


Draw both faces


Draw neither face

The example below draws a simple open tetrahedron with one face missing:

import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.FaceStyle;
   public void render (Renderer renderer, int flags) {
      // the corners of the tetrahedron
      Vector3d p0 = new Vector3d (0, 0, 0);
      Vector3d p1 = new Vector3d (1, 0, 0);
      Vector3d p2 = new Vector3d (0, 1, 0);
      Vector3d p3 = new Vector3d (0, 0, 1);
      // render both sides of each triangle:
      renderer.setFaceStyle (FaceStyle.FRONT_AND_BACK);
      renderer.drawTriangle (p0, p2, p1);
      renderer.drawTriangle (p0, p3, p2);
      renderer.drawTriangle (p0, p1, p3);
      renderer.setFaceStyle (FaceStyle.FRONT); // restore default

The result is drawn using the renderer’s default gray color, as seen in Figure 2.7.

2.3.3 Colors and associated attributes

The renderer maintains a set of attributes for controlling the color, reflectance and emission characteristics of whatever primitives or shapes are currently being drawn. Color values are stored as RGBA (red, green, blue, alpha) or RGB (red, green, blue) values in the range [0,1]. The attributes closely follow the OpenGL model for lighting materials and include:

Front color:

Specifies the reflected RGBA values for diffuse and ambient lighting. The default value is opaque gray: (0.5,0.5,0.5,1.0).

Back color:

Optional attribute, which, if not null, specifies the reflected RGBA values for diffuse and ambient lighting for back faces only. Otherwise, the front color is used. The default value is null.


Specifies the reflected RGB values for specular lighting. The default value is (0.1,0.1,0.1).


Specifies the RGB values for emitted light. The default value is (0,0,0).


Specifies the specular exponent of the lighting equation, in the range [0,128]. The default value is 32.

The resulting appearance of subsequently rendered primitives or shapes depends on the values of these attributes along with the shading settings (Section 2.3.6). When lighting is disabled (by calling setShading(Shading.NONE)), then rendering is done in a uniform color using only the front color (diffuse/ambient) attribute.

The primary methods for setting the color attributes are:

void setFrontColor (float[] rgba);
void setBackColor (float[] rgba);
void setSpecular (float[] rgb);
void setEmission (float[] rgb);
void setShininess (float s);

where rgba and rgb are arrays of length 4 or 3 that provide the required RGBA or RGB values. The rgba arguments may also have a length of 3, in which case an alpha value of 1.0 is assumed. For setBackColor(), rgba may also be null, which will cause the back color to be cleared.

Most commonly, there is no difference between the desired front and back colors, in which case one can simply use the various setColor methods instead:

void setColor (Color color);
void setColor (float[] rgba);
void setColor (float r, float g, float b);
void setColor (float r, float g, float b, float a);
void setFrontAlpha (float a);

These take RGB or RGBA values and set the front color, while at the same time clearing the back color, so that the front color is automatically applied to back faces. The method setFrontAlpha() independently sets the alpha value for the front color.

To query the color attributes, one may use:

float[] getFrontColor (float[] rgba);
float[] getBackColor (float[] rgba);
float[] getSpecular (float[] rgb);
float[] getEmission (float[] rgb);
float getShininess ();

The first four of these return the relevant RGBA or RGB values as an array of floats. Applications may supply the float arrays using the arguments rgba or rgb; otherwise, if these arguments are null, the necessary float arrays will be allocated. If no back color is set, then getBackColor() will return null. Highlighting

The renderer supports the notion of highlighting, which allows the application to indicate to the renderer that subsequently rendered components should be drawn in a highlighted manner. This is typically used to show (visually) that they are selected in some way.

The highlighting style used by the renderer can be queried using the method

HighlightStyle getHighlightStyle();

At present, only two values of HighlightStyle are supported:


Highlighting is done by rendering with a distinct color.


Highlighting is disabled.

The color used for color-based highlighting can be queried using

void getHighlightColor (float[] rgb);

To enable or disable highlighting, the application can use the methods

void setHighlighting (boolean enable)
boolean getHighlighting ()
Figure 2.8: Simple square with two points and one edge highlighted.

As an illustration, we alter the square drawing example of Section 2.3.1 to highlight the corners corresponding to points p1 and p1, as well as the edge between p1 and p1:

import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.Shading;
   public void render (Renderer renderer, int flags) {
       // the corners of the square
      Vector3d p0 = new Vector3d (0, 0, 0);
      Vector3d p1 = new Vector3d (1, 0, 0);
      Vector3d p2 = new Vector3d (1, 0, 1);
      Vector3d p3 = new Vector3d (0, 0, 1);
      renderer.setShading (Shading.NONE); // turn off lighting
      renderer.setPointSize (6);
      renderer.setColor (Color.RED);
      renderer.drawPoint (p0);
      renderer.setHighlighting (true); // turn highlighting on
      renderer.drawPoint (p1);
      renderer.drawPoint (p2);
      renderer.setHighlighting (false); // turn highlighting off
      renderer.drawPoint (p3);
      renderer.setLineWidth (3);
      renderer.setColor (Color.BLUE);
      renderer.drawLine (p0, p1);
      renderer.setHighlighting (true); // turn highlighting on
      renderer.drawLine (p1, p2);
      renderer.setHighlighting (false); // turn highlighting off
      renderer.drawLine (p2, p3);
      renderer.drawLine (p3, p0);
      renderer.setShading (Shading.FLAT); // restore default shading

The result, assuming a highlight style of HighlightStyle.COLOR and a yellow highlight color, is shown in Figure 2.8.

2.3.4 Drawing using draw mode

For convenience, the renderer provides a draw mode in which primitive sets consisting of points, lines and triangles can be assembled by specifying a sequence of vertices and (if necessary) normals, colors, and/or texture coordinates between calls to beginDraw(mode) and endDraw(). Because draw mode allows vertex and normal information to be collected together and sent to the GPU all at one time (when endDraw() is called), it can be significantly more efficient than the single point, line and triangle methods described in the previous sections. (However, using render objects can be even more efficient, as described in Section 2.4.)

DrawMode Description Equivalent OpenGL Mode
POINTS A set of independent points GL_POINTS
LINES A set of line segments, with two vertices per segment GL_LINES
LINE_STRIP A line strip connecting the vertices in order GL_LINE_STRIP
LINE_LOOP A line loop connecting the vertices in order GL_LINE_LOOP
TRIANGLES A set of triangles, with three vertices per triangle GL_TRIANGLES
Table 2.1: Draw mode primitive types.

Draw mode is closely analgous to immediate mode in older OpenGL specifications. The types of primitive sets that may be formed from the vertices are defined by Renderer.DrawMode and summarized in Table 2.1. The primitive type is specified by the mode argument of the beginDraw(mode) call that initiates draw mode.

Between calls to beginDraw(mode) and endDraw(), vertices may be added using the methods

void addVertex (float px, float py, float pz);
void addVertex (double px, double py, double pz);
void addVertex (Vector3d pnt);

each of which creates and adds a single vertex for the specified point. Normals may be specified using

void setNormal (float nx, float ny, float nz);
void setNormal (double nx, double ny, double nz);
void setNormal (Vector3d nrm);

It is not necessary to specify a normal for each vertex. Instead, the first setNormal call will specify the normal for all vertices defined to that point, and all subsequent vertices until the next setNormal call. If no setNormal call is made while in draw mode, then the vertices will not be associated with any normals, which typically means that the primitives will be rendered as black unless lighting is disabled (Section 2.3.6).

It is also possible to specify per-vertex colors during draw mode. This can be done by calling any of the methods of Section 2.3.3 that cause the front color to be set. The indicated front color will then be assigned to vertices defined up to that point, and all subsequent vertices until the next call that sets the front color. The primitives will then be rendered using vertex coloring, in which the vertex color values are interpolated to determine the color at any given point in a primitive. This color overrides the current front (or back) color value (or mixes with it; see Section 2.3.7). If vertex colors are not specified, then the primitives will be rendered using the color attributes that were in effect when draw mode was first entered.

Finally, per-vertex texture coordinates can be specified within draw mode. The methods for doing this are analagous to those for setting normals,

void setTextureCoord (float tx, float ty);
void setTextureCoord (double tx, double ty);
void setTextureCoord (Vector2d tex);

where Vector2d is defined in maspack.matrix. Texture coordinates are required for any rendering that involves texture mapping, including color, normal or bump maps (Section 2.5).

When draw mode is exited by calling endDraw(), the specified vertices, along with any normal, color or texture information, is sent to the GPU and rendered as the specified primitive set, using the current settings for shading, point size, line width, etc.

As an example, the code below uses draw mode to implement the square drawing of Section 2.3.1 (which is shown in Figure 2.6):

import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.Shading;
import maspack.render.Renderer.DrawMode;
   public void renderDrawMode (Renderer renderer) {
      // the corners of the square
      Vector3d p0 = new Vector3d (0, 0, 0);
      Vector3d p1 = new Vector3d (1, 0, 0);
      Vector3d p2 = new Vector3d (1, 0, 1);
      Vector3d p3 = new Vector3d (0, 0, 1);
      renderer.setShading (Shading.NONE);  // turn off lighting
      renderer.setPointSize (6);
      renderer.beginDraw (DrawMode.POINTS);
      renderer.setColor (Color.RED);
      renderer.addVertex (p0);
      renderer.addVertex (p1);
      renderer.addVertex (p2);
      renderer.addVertex (p3);
      renderer.setLineWidth (3);
      renderer.setColor (Color.BLUE);
      renderer.beginDraw (DrawMode.LINE_LOOP);
      renderer.addVertex (p0);
      renderer.addVertex (p1);
      renderer.addVertex (p2);
      renderer.addVertex (p3);
      renderer.setShading (Shading.FLAT);  // restore lighting

Note that no normals need to be specified since both primitive sets are rendered with lighting disabled.

Another example uses draw mode to implement the partial tetrahedron example from Section 2.3.2 (which is shown in Figure 2.7):

import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.FaceStyle;
import maspack.render.Renderer.DrawMode;
   public void render (Renderer renderer, int flags) {
      // the corners of the tetrahedron
      Vector3d p0 = new Vector3d (0, 0, 0);
      Vector3d p1 = new Vector3d (1, 0, 0);
      Vector3d p2 = new Vector3d (0, 1, 0);
      Vector3d p3 = new Vector3d (0, 0, 1);
      // render both sides of each triangle:
      renderer.setFaceStyle (FaceStyle.FRONT_AND_BACK);
      renderer.beginDraw (DrawMode.TRIANGLES);
      // first triangle
      renderer.setNormal (0, 0, -1); // normal along -z
      renderer.addVertex (p0);
      renderer.addVertex (p2);
      renderer.addVertex (p1);
      // second triangle
      renderer.setNormal (-1, 0, 0); // normal along -x
      renderer.addVertex (p0);
      renderer.addVertex (p3);
      renderer.addVertex (p2);
      // third triangle
      renderer.setNormal (0, -1, 0); // normal along -y
      renderer.addVertex (p0);
      renderer.addVertex (p1);
      renderer.addVertex (p3);
      renderer.setFaceStyle (FaceStyle.FRONT); // restore default

Note that because for this example we are displaying shaded faces, it is necessary to specify a normal for each triangle.

Figure 2.9: An open tetrahedron, drawn with colors specified at each vertex, which causes the renderer to initiate vertex coloring and interpolate the vertex colors across each face.

As a final example, we show the tetrahedon example again, but this time with colors specified for each vertex, which initiates vertex coloring. Vertices p0, p1, p2, and p3 are associated with the colors RED, GREEN, BLUE, and CYAN, respectively. The corresponding code looks like this:

   renderer.beginDraw (DrawMode.TRIANGLES);
   // first triangle
   renderer.setNormal (0, 0, -1);
   renderer.setColor (Color.RED);
   renderer.addVertex (p0);
   renderer.setColor (Color.BLUE);
   renderer.addVertex (p2);
   renderer.setColor (Color.GREEN);
   renderer.addVertex (p1);
   // second triangle
   renderer.setNormal (-1, 0, 0);
   renderer.setColor (Color.RED);
   renderer.addVertex (p0);
   renderer.setColor (Color.CYAN);
   renderer.addVertex (p3);
   renderer.setColor (Color.BLUE);
   renderer.addVertex (p2);
   // third triangle
   renderer.setNormal (0, -1, 0);
   renderer.setColor (Color.RED);
   renderer.addVertex (p0);
   renderer.setColor (Color.GREEN);
   renderer.addVertex (p1);
   renderer.setColor (Color.CYAN);
   renderer.addVertex (p3);

and the rendered result is shown in Figure 2.9.

2.3.5 Drawing solid shapes

For convenience, the renderer provides a number of methods for drawing solid shapes. These include spheres, cylinders, cubes, boxes, arrows, spindles, cones, and coordinate axes.

Methods for drawing spheres include

void drawSphere (Vector3d pnt, double rad);
void drawSphere (float[] pnt, double rad);

both of which draw a sphere with radius rad centered at the point pnt, using the current color and shading settings. For drawing cylinders, arrows, or spindles, one can use

void drawCylinder (float[] pnt0, float[] pnt1, double rad, boolean capped);
void drawArrow (float[] pnt0, float[] pnt1, double rad, boolean capped);
void drawSpindle (float[] pnt0, float[] pnt1, double rad);

each of which draws the indicated shape between points pnt0 and pnt1 with a cylindrical radius of rad, again using the current color and shading. The argument capped for cylinders and arrows indicates whether or not a solid cap should be drawn over any otherwise open ends. For arrows, the arrow head size is based on the radius and line segment length.

A cone can be drawn similarly to a cylinder, using

void drawCone (float[] pnt0, float[] pnt1, rad0, rad1, capped);

with the only difference being that there are now two radii, rad0 and rad1, at each end.

Figure 2.10: Some of the solids that can be drawn by the renderer. From left to right: coordinate axes; spindle, arrow, and cylinder (capped); a cone.

To draw cubes and boxes, one may use

void drawCube (Vector3d pnt, double width);
void drawCube (float[] pnt, double width);
void drawBox (Vector3d pnt, Vector3d widths);
void drawBox (float[] pnt, double wx, double wy, double wz);
void drawBox (RigidTransform3d TBM, Vector3d widths);

The drawCube methods draw an axis-aligned cube with a specified width centered on the point pnt. Similarly, the first two drawBox methods draw an axis-aligned box with the indicated x, y, and z widths. Finally, the last drawBox method draws a box centered on, and aligned with, the coordinate frame defined (with respect to model coordinates) by the RigidTransform3d TBM.

When rendering the curved solids described above, the renderer must create surface meshes that approximate their shapes. The resolution used for doing this can be controlled using a parameter called the surface resolution. This is defined to be the number of line segments that would be used to approximate a circle, and this level of resolution is then employed to create the mesh. The renderer initializes this parameter to a reasonable default value, but applications can query or modify it as needed using the following methods:

int getSurfaceResolution();
void setSurfaceResolution (int nsegs);

Coordinate axes can be drawn to show the position and orientation of a spatial coordinate frame:

void drawAxes (RigidTransform3d T, double len, width, boolean highlight);
void drawAxes (RigidTransform3d T, double[] lens, width, boolean highlight);

For these, the coordinate frame is described (with respect to the current model coordinates) by a RigidTransform3d T. The first method draws the frame’s axes as lines with the specified length len and width. The second method allows different lengths (lens) to be specified for each axis. The axis lines are rendered using regular pixel-based lines with non-shaded colors, with the x, y, and z axes normally being colored red, green, and blue. However, if highlight is true and the highlight style is HighlightStyle.COLOR (Section, then all axes are drawn using the using the highlight color.

Some of the solids are illustrated in Figure 2.10.

2.3.6 Shading and color mixing

Shading determines the coloring of each rendering primitive (point, line or triangle), as seen from the eye, as a result of its color attributes, surface normals and the current lighting conditions. At any given point on a primitive, the rendered color is the coloring seen from the eye that results from the incident illumination, color attributes, and surface normal at that point. In general, the rendered color varies across the primitive. How this variation is handled depends on the shading, defined by Renderer.Shading:


The rendered color is determined at the first vertex and applied to the entire primitive. This makes it easy to see the individual primitives, which can be desirable under some circumstances. Only one normal needs to be specified per primitive.


Rendered colors are computed across the primitive, based on interpolated normal information, resulting in a smooth appearance. The interpolation technique depends on the renderer. OpenGL 2 implementations use Gouraud shading, while the OpenGL 3 renderer uses Phong shading.


Rendered colors are computed using a smooth shading technique that may be more appropriate to metalic objects. For some renderer implementations, there may be no difference between METAL and SMOOTH.


Lighting is disabled. The rendered color becomes the diffuse color, which is applied uniformly across the primitive. No normals need to be specified.

Figure 2.11: A polygonal sphere with shading set to FLAT (left), SMOOTH (middle), and NONE (right).

Figure 2.11 shows different shading methods applied to a sphere.

The shading can be controlled and queried using the following methods,

Shading getShading();
Shading setShading (Shading shading);

where setShading() returns the previous shading setting.

Lighting is often disabled, using Shading.NONE, when rendering pixel-based points and lines. That’s because normal information is not naturally defined for these primitives, and also because even if normal information were to be provided, shading could make them either invisible or hard to see from certain viewing angles.

2.3.7 Vertex coloring, and color mixing and interpolation

As mentioned in Section 2.3.4, it is possible to specify vertex coloring for a primtive, in which vertex color values are interpolated to determine the color at any given point in the primitive. Vertex colors can be specified by calling setColor primitives while in draw mode. They can also be specified as part of a RenderObject (Section 2.4).

When vertex coloring is used, the interpolated vertex colors either replace or are combined with the current front (or back) diffuse color at each point in the primitive. Other color attributes, such as emission and specular, are unchanged. If lighting is disabled, then the rendered color is simply set to the resulting vertex/diffuse color combination.

Whether the vertex color replaces or combines with the underlying diffuse color is controlled by the enumerated type Renderer.ColorMixing, which has four different values:

REPLACE replace the diffuse color (default behavior)
MODULATE multiplicatively combine with the diffuse color
DECAL combine with the diffuse color based on the latter’s alpha value
NONE diffuse color is unchanged (vertex colors are ignored)
Figure 2.12: Vertex coloring applied to the pale blue sphere of Figure 2.3.6. Left: shading=NONE, color mixing=REPLACE; Middle: shading=SMOOTH, color mixing=REPLACE; Right: shading=SMOOTH, color mixing=MODULATE. The right sphere is slightly darker because MODULATE causes the vertex coloring to be multiplied by the underlying blue color, reducing its intensity.

Color mixing can be controlled using these methods:

ColorMixing getVertexColorMixing();
void setVertexColorMixing (ColorMixing cmix);
boolean hasVertexColorMixing (ColorMixing cmix);

A given Renderer implementation may not support all color mixing modes, and so the hasVertexColorMixing() can be used to query if a given mixing mode is supported. The OpenGL 2 renderer implementation does not support MODULATE or DECAL. Some examples of vertex coloring with different shading and color mixing settings are shown in Figure 2.12.

The renderer’s default color mixing mode is MODULATE. This has the advantage of allowing rendered objects to still appear differently when highlighting is enabled and the highlight style is HighlightStyle.COLOR (Section, since the highlight color is combined with the vertex color rather than being replaced by it.

Figure 2.13: Vertex coloring applied to a sphere, only with the vertices for each face now being given the same colors so as to color each face uniformly. Left: shading=NONE, color mixing=REPLACE; Right: shading=SMOOTH, color mixing=REPLACE.

Vertex coloring can be used in different ways. Assigning different colors to the vertices of a primitive will result in a blending of those colors within the primitive (Figures 2.9 and 2.12). Assigning the same colors to the vertices of a primitive can be used to give each primitive a uniform color. Figure 2.13 shows vertex coloring applied to the same sphere as Figures 2.3.6 and 2.12, only with the vertices for each face being uniformly set to red, green or blue, resulting in uniformly colored faces.

Figure 2.14: RGB interpolation (left) and HSV interpolation (right), applied to a triangle with vertices colored red, green and blue.

When using vertex coloring, the interpolation of colors across the primitive can be done either in RBG or HSV space. HSV stands for hue, saturation, and value (or brightness), and it is often the best interpolation method to use when the vertex colors have a uniform brightness that the interpolation should preserve. This leads to a “rainbow” look that is common in situations like color-based stress plots. Figure 2.14 illustrates the difference between RGB and HSV interpolation.

Color interpolation is specified with the enumerated type Renderer.ColorInterpolation, which currently has the two values RGB and HSV. Within the renderer, it can be controlled using the methods

ColorInterpolation getColorInterpolation();
void setColorInterpolation (ColorInterpolation interp);

2.3.8 Changing the model matrix

When point positions are specified to the renderer, either as the arguments to various draw methods, or for specifying vertex locations in draw mode, the positions are assumed to be defined with respect to the current model coordinate frame. As described in Section 2.2.4, this is one of the three primary coordinate frames associated with the viewer, with the other two being the world and eye frames.

The relationship between model and world frames is controlled by the model matrix {\bf X}_{MW}, which is a 4\times 4 homogeneous affine transform that transforms points in model coordinates (denoted by {}^{M}{\bf p}) to world coordinates (denoted by {}^{W}{\bf p}), according to

\left(\begin{matrix}{}^{W}{\bf p}\\
1\end{matrix}\right)\;=\;{\bf X}_{MW}\left(\begin{matrix}{}^{M}{\bf p}\\

Initially the world and model frames are coincident, so that {\bf X}_{MW}={\bf I}. Rendering methods often redefine the model matrix, allowing object geometry to be specified in a conveniently defined local coordinate frame, and, more critically, allowing the predefined geometry associated with existing rendering objects (Section 2.4) or built-in drawing methods to be used at different scales and poses throughout the scene. Methods for querying and controlling the model matrix include:

AffineTransform3dBase getModelMatrix();
void getModelMatrix (AffineTransform3d XMW);
void setModelMatrix (AffineTransform3dBase XMW);
void mulModelMatrix (AffineTransform3dBase X);
void translateModelMatrix (double tx, double ty, double tz);
void rotateModelMatrix (double zdeg, double ydeg, double xdeg);
void scaleModelMatrix (double s);
void pushModelMatrix();
boolean popModelMatrix();

Both getModelMatrix() and getModelMatrix(XMW) return the current model matrix value (where the value returned by the first method should not be modified). AffineTransform3dBase is a base class defined in maspack.matrix and represents a 4\times 4 homogeneous transform that is either a rigid transform (of type RigidTransform3d) or an affine transform (of type AffineTransform3d). setModelMatrix(XMW) explicitly sets the model matrix, while mulModelMatrix(X) post-multiplies the current matrix by another rigid or affine transform {\bf X}, which is equivalent to setting

{\bf X}_{MW}:={\bf X}_{MW}\,{\bf X}.

translateModelMatrix(tx,ty,tz) and rotateModelMatrix(zdeg,ydeg,xdeg) translate or rotate the model frame by post-multiplying the model matrix by a rigid transform describing either a translation (tx, ty, tz), or a rotation formed by three successive rotations: zdeg degrees about the z axis, ydeg degrees about the new y axis, and finally xdeg degrees about the new x axis. scaleModelMatrix(s) scales the current model frame by post multiplying the model matrix by a uniform scaling transform

{\bf X}\equiv\left(\begin{matrix}s&0&0&0\\

Finally, pushModelMatrix() and popModelMatrix() save and restore the model matrix from an internal stack. It is common to wrap changes to the model matrix inside calls to pushModelMatrix() and popModelMatrix() so that the model matrix is preserved unchanged for subsequent use elsewhere:

   ... specific rendering code ...

2.3.9 Render properties and RenderProps

The maspack.render package defines an object called RenderProps which encapsulates many of the properties that are needed to describe how an oject should be rendered. These properties control the color, size, and style of the three primary rendering primitives: faces, lines, and points, and all are exposed using the package, so that they can be easily set from a GUI or inherited from ancestor components.

A renderable object can maintain its own RenderProps object, and use the associated properties as it wishes to control rendering from within its render() method. Objects maintaining their own RenderProps can declare this by implementing the HasRenderProps interface, which declares the methods

  setRenderProps (RenderProps props); // set render properties
  RenderProps getRenderProps();       // get render properties (read-only)
  RenderProps createRenderProps();    // create render properties for this object

It is not intended for RenderProps to encapsulate all properties relevant to the rendering of objects, but only those which are commonly encountered. Any particular renderable may still need to define and maintain more specialized rendering properties.

Renderable objects that implement both HasRenderProps and IsSelectable (an extension of IsRenderable for selectable objects described in Section 2.7) are identified by the combined interface Renderable. Drawing points and lines as 3D solid objects

RenderProps contains two properties, pointStyle and lineStyle, that indicate whether points and lines should be drawn using standard pixel-based primitives or some type of solid 3D geometry. Often, the latter can be preferable for visualization and graphical selection. pointStyle and lineStyle are described by the enumerated types Renderer.PointStyle and Renderer.LineStyle, respectively, which contain the following entries:

POINT pixel-based point
SPHERE solid sphere
CUBE solid cube
LINE pixel-based line
CYLINDER solid cylinder
SOLID_ARROW solid arrow
SPINDLE spindle (an ellipsoid tapered at each end)

The size (in pixels) for pixel-based points is controlled by the property pointSize, whereas the radius for spherical points and half-width for cubic points is controlled by pointRadius. Likewise, the width (in pixels) for pixel-based lines is controlled by lineWidth, whereas the radii for lines rendered as cylinders, arrows or spindles is controlled by lineRadius. RenderProps taxonomy

All of the RenderProps properties are listed in table 2.2. Values for the shading, faceStyle, lineStyle and pointStyle properties are defined using the following enumerated types: Renderer.Shading, Renderer.FaceStyle, Renderer.PointStyle, and Renderer.LineStyle. Colors are specified using java.awt.Color.

property purpose default value
visible whether or not the component is visible true
alpha transparency for diffuse colors (range 0 to 1) 1 (opaque)
lighting lighting style: (FLAT, SMOOTH, METAL, NONE) FLAT
shininess shininess parameter (range 0 to 128) 32
specular specular color components null
faceStyle which polygonal faces are drawn (FRONT, BACK, FRONT_AND_BACK, NONE) FRONT
faceColor diffuse color for drawing faces GRAY
backColor diffuse color used for the backs of faces. If null, faceColor is used. null
drawEdges hint that polygon edges should be drawn explicitly false
colorMap color map properties (see Section 2.5) null
normalMap normal map properties (see Section 2.5) null
bumpMap bump map properties (see Section 2.5) null
edgeColor diffuse color for edges null
edgeWidth edge width in pixels 1
lineStyle: how lines are drawn (CYLINDER, LINE, or SPINDLE) LINE
lineColor diffuse color for lines GRAY
lineWidth width in pixels when LINE style is selected 1
lineRadius radius when CYLINDER or SPINDLE style is selected 1
pointStyle how points are drawn (SPHERE or POINT) POINT
pointColor diffuse color for points GRAY
pointSize point size in pixels when POINT style is selected 1
pointRadius sphere radius when SPHERE style is selected 1
Table 2.2: Render properties and their default values.

In addition to colors for points, lines, and faces, there are also optional colors for edges and back faces. Edge colors (and edge widths) are provided in case an object has both lines and faces, and may want to render the edges of the faces in a color separate from the line color, particularly if drawEdges is set to true. (PolygonalMeshRenderer, described in Section 2.6, responds to drawEdges by drawing the polygonal edges using edgeColor.) Back face colors are provided so that back faces can be rendered using a different color than the front face.

Exactly how a component interprets its render properties is up to the component (and more specifically, up to the render() method for that component). Not all render properties are relevant to all components, particularly if the rendering does not use all of the rendering primitives. For example, some components may use only the point primitives and others may use only the line primitives. For this reason, some components use subclasses of RenderProps, such as PointRenderProps and LineRenderProps, that expose only a subset of the available render properties. All renderable components provide the method createRenderProps() that will create and return a RenderProps object suitable for that component. Renderer methods that use RenderProps

Renderer provides a number of convenience methods for setting attributes and drawing primitives and shapes based on information supplied by RenderProps.

For drawing points and lines, there are

void drawPoint (RenderProps props, float[] pnt, boolean highlight);
void drawLine (
   RenderProps props, float[] pnt0, float[] pnt1, boolean highlight);
void drawLine (
   RenderProps props, float[] pnt0, float[] pnt1, float[] color,
   boolean capped, boolean highlight);

drawPoint() draws a point at location pnt using the pointStyle, pointColor, pointSize, pointRadius and shading properties of props, while the drawLine methods draw a line between pnt0 and pnt1 using the lineStyle, lineColor, lineSize, lineRadius and shading properties. The second drawLine method also allows an alternate color to be specified, as well as whether or not the line shape should be capped (if appropriate). Another method,

void drawArrow (
   RenderProps props, float[] pnt0, float[] pnt1, float[] color,
   boolean capped, boolean highlight);

is identical to the second drawLine method above except that the line style LineStyle.SOLID_ARROW is assumed. For all methods, the highlight argument can be used to request that the primitive or shape be drawn with highlighting enabled (Section

To draw a line strip, one can use

void drawLineStrip (
   RenderProps props, Iterable<float[]> pnts, LineStyle style, boolean highlight);

which draws a line strip with the specified pnts, using the indicated style along with the lineColor, lineSize, lineRadius and shading properties of props. The strip is rendered with highlighting if highlight is true.

There are also methods for setting the color attributes associated with pointColor, lineColor, edgeColor, or faceColor:

void setPointColoring (RenderProps props, boolean highlight);
void setLineColoring (RenderProps props, boolean highlight);
void setEdgeColoring (RenderProps props, boolean highlight);
void setFaceColoring (RenderProps props, boolean highlight);
void setFaceColoring (RenderProps props, float[] rgba, boolean highlight);

These set the renderer’s front color attribute to the value of the indicated color property, use props to also set the shininess and specular attributes, and restore emission to its default renderer value. The first three methods clear the back color attribute, while the setFace methods set it to the backColor value of props. setEdgeColoring() uses lineColor if edgeColor is null, and the second setFace method allows an alternate front color to be supplied as rgba. For all methods, highlighting is enabled or disabled based on the value of highlight. A related method is

void setPropsColoring (RenderProps props, float[] rgba, boolean highlight);

which behaves similarly except that the color is explicitly specified using rgba.

Lastly, there are methods to set the shading:

Shading setPropsShading (RenderProps props);
Shading setPointShading (RenderProps props);
Shading setLineShading (RenderProps props);

setPointShading() sets the shading to the shading property of props and returns the previous value. setPointShading() does the same, unless pointStyle is PointStyle.POINT, in which case lighting is turned off by setting the shading to Shading.NONE. Similarly, setLineShading() turns off the lighting if lineStyle is LineStyle.LINE.

2.3.10 Screen information and 2D rendering

The screen refers to the 2 dimensional pixelized display on which the viewer ultimately renders the scene. There is a direct linear mapping between the view plane (Figure 2.2.4) and the screen.

While the renderer does not give the application control over the screen dimensions, it does allow them to be queried using

int getScreenHeight();
int getScreenWidth();

It also allows distances in pixel space to be converted to distances in world space via

double distancePerPixel (Vector3d p);
double centerDistancePerPixel ();

distancePerPixel(p) computes the displacement distance of a point p, in a plane parallel to the view plane, that corresponds to a screen displacement of one pixel. centerDistancePerPixel() computes the same thing with p given by the center point (Section 2.2.4).

A renderer may also support 2D mode to facilitate the rendering of 2D objects directly in screen coordinates. 2D mode can be queried with the following methods:

boolean has2DRendering();            // true if renderer supports 2D mode
boolean is2DRendering();             // true if renderer is in 2D mode

In order for an object to be rendered in 2D, the renderable should return the flag IsRenderable.TWO_DIMENSIONAL from its getRenderHints() method. The viewer will then call the render() method in two dimensional mode, with the view matrix set to the identity, and the projection and model matrices set to provide an orthographic view (Figure 2.4) with the world frame located at the lower left screen corner, the x axis horizontal and pointing to the right, and the y axis vertical. The top right corner of the screen corresponds to the point (w,h), where w and h are the width and height of screen returned by getScreenWidth() and getScreenHeight(). Lighting is also disabled and the depth buffer is turned off, so that rendered objects will always be visible in the order they are drawn.

If a different scaling or origin for the x-y plane is desired, the application can call the renderer method

void setModelMatrix2d (double left, double right, double top, double bottom)

which will reset the model matrix so that the lower left and upper right of the screen correspond to the points (left, bottom) and (right, top), respectively.

Figure 2.15: Simple coordinate axes drawn using 2D mode.

The following example shows the code for a renderable that uses 2D rendering to draw a pair of coordinate axes in the lower left screen corner, with the result shown in Figure 2.15. Its getRenderHints() method returns the TWO_DIMENSIONAL flag to ensure that render() is called in 2D mode. The axis arrowheads are drawn using the method drawArrowHead, which draws an arrowhead in a fixed location and orientation, in combination with changes to the model matrix (Section 2.2.4) to adjust the base location and orientation as required.

import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.render.*;
import maspack.render.Renderer.DrawMode;
   // ensure that render() is called in 2d mode
   int getRenderHints() {
      return TWO_DIMENSIONAL;
   // draw a 2D arrowhead with a given size, centered on the origin
   private void drawArrowHead (Renderer renderer, int size) {
      Vector3d p0 = new Vector3d(size, 0, 0);
      Vector3d p1 = new Vector3d(-size, size/2, 0);
      Vector3d p2 = new Vector3d(-size, -size/2, 0);
      renderer.drawTriangle (p0, p1, p2);
   public void render (Renderer renderer, int flags) {
      // draw simple 2d coordinate frame axes in 2D mode
      int margin = 40;                   // distance from screen edge
      int arrowSize = 20;                // size of the axis arrows
      double length =
         0.6*renderer.getScreenHeight(); // axis length
      // po, px and py are the origin and the x and y axis end points
      Vector3d po = new Vector3d (margin, margin, 0);
      Vector3d px = new Vector3d (margin+length, margin, 0);
      Vector3d py = new Vector3d (margin, margin+length, 0);
      renderer.setColor (Color.RED);
      // draw the axis lines with a line strip
      renderer.setLineWidth (4);
      renderer.beginDraw (DrawMode.LINE_STRIP);
      renderer.addVertex (px);
      renderer.addVertex (po);
      renderer.addVertex (py);
      renderer.setLineWidth (1);
      // then draw an arrowhead at the tip of the x and y axes
      renderer.translateModelMatrix (px.x, px.y, 0);
      drawArrowHead (renderer, arrowSize);
      renderer.translateModelMatrix (py.x-px.x, py.y-px.y, 0);
      renderer.rotateModelMatrix (90, 0, 0);
      drawArrowHead (renderer, arrowSize);

2.3.11 Depth offsets

Sometimes, when drawing different primitives that lie on the same plane, the depth buffer cannot properly resolve which primitive should be visible. This artifact is known as “z fighting”. The renderer provides a means to address it via the method

void setDepthOffset (double zoffset)

This modifies the projection matrix to incorporate a small offset (in clip coordinates) along the eye frame’s z axis, so that subsequently rendered components are rendered slightly closer to (or farther from) the eye. Each unit of offset equals one unit of depth buffer precision. The depth offset can be queried using getDepthOffset(), and the default value is 0.

Figure 2.16: Triangles drawn on the surface of a cube. This nominally results in z fighting (left), which can be removed by setting a depth offset (right).

The listing below shows an example in which two colored triangles are drawn on faces of a cube. If no depth offset is set, the triangles compete for visibility with the underlying cube faces (Figure 2.16, left). To resolve this, the render() method sets a depth offset to move the triangles slighting closer to the eye.

import java.awt.Color;
import maspack.matrix.Vector3d;
import maspack.render.*;
   public void render (Renderer renderer, int flags) {
      // draw the cube
      renderer.setColor (Color.WHITE);
      renderer.drawCube (Vector3d.ZERO, 2.0);
      // points for the triangles on the cube faces
      Vector3d p0 = new Vector3d (   0, -1.0, -0.6);
      Vector3d p1 = new Vector3d ( 0.6, -1.0,  0.6);
      Vector3d p2 = new Vector3d (-0.6, -1.0,  0.6);
      Vector3d p3 = new Vector3d ( 1.0, -0.6, -0.6);
      Vector3d p4 = new Vector3d ( 1.0,  0.6, -0.6);
      Vector3d p5 = new Vector3d ( 1.0,    0,  0.6);
      // set a depth offset so the triangles will be visible ...
      renderer.setDepthOffset (1);
      // ... and draw the triangles
      renderer.setColor (Color.RED);
      renderer.drawTriangle (p0, p1, p2);
      renderer.setColor (Color.BLUE);
      renderer.drawTriangle (p3, p4, p5);

z-fighting may still occur if the plane in which the fighting occurs is tilted significantly with respect to the eye. In some situations it may be desirable to mitigate this with a larger offset value.

2.3.12 Maintaining the graphics state

Attribute Description Default value Restored
front color diffuse/ambient color (0.5, 0.5, 0.5, 1.0) no
back color optional color for back faces null yes
emission emission color (0, 0, 0) yes
specular specular color (0.1, 0.1, 0.1) yes
shininess specular color 32 yes
color interpolation interpolation method for vertex colors RGB yes
face style whether to draw front or back faces FRONT yes
line width width of pixel-based lines 1 yes
point size size of pixel-based points 1 yes
model matrix transform from model to world coordinates IDENTITY yes
highlighting highlight drawn primitives false yes
shading primitive shading based on normal information FLAT yes
surface resolution internal curved surface resolution 32 no
vertex color mixing how to combine underlying and vertex colors REPLACE yes
depth offset moves rendered objects slightly along the eye z axis 0 yes
color map color map properties (Section 2.5) null yes
normal map normal map properties (Section 2.5) null yes
bump map bump map properties (Section 2.5) null yes
Table 2.3: Attributes comprising the renderer graphics state, with their default values and whether or not they are restored by the renderer.

Attributes such as colors, face styles, line widths, matrix values, etc., constitute the graphics state associated with the renderer. Table 2.3 summarizes these attributes and their default values. The last column, Restored, indicates if the renderer will restore the attribute to its default value after calling each renderable’s render() method in the repaint step. All restored attributes can therefore be assumed to be set to their default value at the beginning of any render() method when that method is being called by the renderer.

Note that in some cases, a renderable’s render() method may not be called by the render. This will occur, for instance, when a renderable takes direct control of rendering its subcomponents, and calls their render() methods directly. In such cases, it will be up to either the subcomponents or the parent to maintain the graphics state as required. There are several ways to acccomplish this.

One way is to save and restore each attribute that is modified. To facilitate this, most attribute set methods return the attribute’s previous value. Save and restore can then be done using blocks of the form

   Shading savedShading = renderer.setShading (Shading.METAL);
   ... rendering operations ...
   renderer.setShading (savedShading);

As mentioned earlier, the model matrix can be saved and restored using the following:

   ... rendering operations ...

Alternatively, if it is sufficient to restore an attribute to its default value, one can do that directly:

   renderer.setShading (Shading.METAL);
   ... rendering operations ...
   renderer.setShading (Shading.FLAT);

Finally, the renderer method restoreDefaultState() can be used to restore that default state of all attributes except the front color:

   ... rendering operations ...
   renderer.restoreDefaultState (/*strictChecking=*/true);

If true, the strictChecking argument causes an exception to be thrown if the renderer is still in a draw mode block (Section 2.3.4) or the model matrix stack is not empty. restoreDefaultState() is used internally by the renderer to restore state.

2.3.13 Text rendering

Some renderer implementations provide the ability to render text objects, using fonts described by the Java class java.awt.Font. Support for text rendering can be querired using the method hasTextRendering(). The methods for drawing text include:

double drawText (String str, float[] pos, double emSize);
double drawText (Font font, String str, float[] pos, double emSize);
double drawText (String str, Vector3d pos, double emSize);
double drawText (Font font, String str, float[] pos, double emSize);

Each of these draws the string str in the x-y plane in model coordinates, using either a specified font or a default. The starting position of the lower left corner of the text box is given by pos, and emSize gives the size of an “em” unit. The methods return the horizontal advance distance of the draw operation.

Other supporting methods for text rendering include:

void setDefaultFont(Font font);
Font getDefaultFont();
Rectangle2D getTextBounds(Font font, String str, double emSize);

These set and query the default font, and return the bounds of a text box in a java.awt.geom.Rectangle2D.

Figure 2.17: Text rendering example.

Listing 2 below shows the code for the text rendering shown in Figure 2.17.

Listing 2: Using the renderer to draw text.
import java.awt.Font;
import java.awt.Font;
import java.awt.GraphicsEnvironment;
import java.awt.geom.Rectangle2D;
import maspack.matrix.*;
import maspack.render.*;
   Font myComic;
   Font mySerif;
   void setupFonts() {
      GraphicsEnvironment env =
      for (Font font : env.getAllFonts ()) {
         if (font.getName().equals ("Comic Sans MS")) {
            myComic = font;
      if (myComic == null) {
         myComic = new Font(Font.MONOSPACED, Font.BOLD, 32);
      else {
         myComic = myComic.deriveFont (Font.BOLD, 32);
      mySerif = new Font(Font.SERIF, Font.PLAIN, 64);
   public void render (Renderer renderer, int flags) {
      Vector3d pos = new Vector3d(-0.6, 0, 0);
      // draw text at (0,0)
      renderer.setColor (Color.WHITE);
      renderer.drawText ("Hello World!", pos, 0.2);
      // draw text rotated about the z axis
      renderer.setColor (Color.CYAN);
      String text = "Cowabunga";
      renderer.rotateModelMatrix (30, 0, 0);
      pos.set (-0.3, 0.6, 0);
      renderer.drawText (myComic, "Cowabunga", pos, 0.25);
      // draw several centered lines, in a plane rotated about the x axis
      renderer.setColor (Color.ORANGE);
      String[] textLines = new String[] {
         "Four score and", "seven years ago,",
         "in a galaxy", "far far", "away" };
      renderer.mulModelMatrix (
         new RigidTransform3d (0, -0.1, -1.0, 0, 0, -Math.toRadians(60)));
      pos.set (0, 0, 0);
      for (String line : textLines) {
         Rectangle2D rect = renderer.getTextBounds (mySerif, line, 0.25);
         pos.y -= rect.getHeight();
         pos.x = -rect.getWidth()/2;
         renderer.drawText (mySerif, line, pos, 0.25);

The method setupFonts() is called outside the render method to set up some fonts and store them in the member variables myComic and mySerif. Note that setting up fonts in general may be system specific. Three different blocks of text are then drawn within the render() method, with different colors, positions and orientations. The last block consists of multiple lines, with getTextBounds() used to obtain the text bounds necessary to center each line.

Note: Rendered text is shaded in the same way as other surfaces, so unless shading is set to Shading.NONE, light must be shining on it in order for it to be visible. If you want text to always render at full intensity, shading should be set to Shading.NONE.

2.4 Render Objects

In modern graphics interfaces, applications send geometric, color, and texture information to the GPU, which then applies the various computations associated with the graphics pipeline. Transferring this data to the GPU can be an expensive activity, and efficient applications try to minimize it. Modern OpenGL, in particular, requires applications to bundle the geometric, color, and texture information into buffer objects, which are transmitted to the GPU and then cached there. This generally increases efficiency because (a) large amounts of data can be transferred at once, and (b) the cached data can be reused in subsequent rendering operations.

For OpenGL renderer implementations, a buffer object must be created and transmitted to the GPU once for every invocation of a draw method or beginDraw()/endDraw() block. As a more efficient alternative, applications can create instances of render objects, which store geometric, color, and texture information and manage the transmission of this data to the GPU. Essentially, a render object provides a convenience wrapper for OpenGL-type buffer objects. However, the use of render objects is generic and not limited to OpenGL implementations of the renderer.

Render objects are implemented using the RenderObject class, which contains:

  • Attribute data, including positions, and (optionally) normals, colors, and texture coordinates.

  • vertex data, where each vertex points to a single position, as well as (optionally) a single normal, color, and texture attribute.

  • primitive data, consisting of zero or more “groups” of points, lines, and triangles.

Figure 2.18: Render object structure, showing the relationship between attributes, vertices, and primitives.

To summarize, primitives are made of vertices, which are in turn comprised of references to attributes (Figure 2.18).

Render objects can be created anywhere within the application program, although care must be taken to synchronize their modification with the render() methods. While an easy way to do this is to create them directly within the render method, care should then be taken to allow them to persist between render invocations, since each time a new object is created, all of its data must be transferred to the GPU. It is recommended to create render objects within prerender(), since this should automatically provide synchronization with both render() and any other thread this is modifying render data. A render object can itself be used to cache rendering data associated with a dynamically varying object, in which case creating (or updating) it from within the prerender method is even more appropriate.

2.4.1 Building a render object

Attributes can be added using a variety of RenderObject methods, including:

int addPosition (float px, float py, float pz);
int addPosition (Vector3d pos);
int addPosition (float[] pos);    // set by reference
int addNormal (float nx, float ny, float nz);
int addNormal (Vector3d nrm);
int addNormal (float[] nrm);      // set by reference
int addColor (float r, float g, float b, float a);
int addColor (Color color);
int addColor (byte[] rgba);       // set by reference
int addTextureCoord (float tx, float ty);
int addTextureCoord (Vector2d xy);
int addTextureCoord (float[] xy); // set by reference

Each of these creates an instance of the specified attribute, sets it to the indicated value, adds it to the render object, and assigns it a unique index, which is returned by the add method. The index can be referred to later when adding vertices, or when later changing the attribute’s value (Section 2.4.5). Indices are increased sequentially, starting from zero.

Methods above marked “set by reference” use the supplied array to directly store values within the attribute, so that subsequent changes to the array’s values will also cause the attribute’s values to change.

A vertex is defined by a 4-tuple of indices that can be used to refer to a previously defined instance of each of the four attributes: position, normal, color, and texture coordinate. A vertex does not need to reference all attributes, but it is required that all vertices have a consistent set of attributes (e.g. either all vertices have a normal reference, or none do). When adding a vertex, a negative index indicates that the attribute is not present. Since a vertex can refer to at most one of each attribute, this means that when building primitives, it may be necessary to define multiple vertices for the same position if different values are required for the other attributes (e.g., normals, colors, or texture coordinates). For example, for the corner of the cube at location (-1,-1,-1), there must be three vertices defined, one each with normals (-1,0,0), (0,-1,0), and (0,0,-1).

Referencing attributes by index allows for attributes to be reused, and also for the numbers of any given attribute to vary. For example, when rendering the faces of a solid cube, we typically need 24 vertices (4 for each of the 6 faces), but only 8 positions (one per corner) and 6 normals (one per face).

Vertices can be added using the RenderObject method

int addVertex (int pidx, int nidx, int cidx, int tidx);

where pidx, nidx, cidx, and tidx are the indices of the desired postion, normal, color and texture coordinate attributes (or -1 for attributes that are undefined). The method returns a unique index for the vertex, which can be referred to later when adding primitives. Indices are increased sequentially, starting from zero.

Once vertices are created, they can be used to define and add primitives. Three types of primitives are available: points (one vertex each), lines (two vertices each), and triangles (three vertices each). Methods for adding these include

addPoint (int v0idx);
addLine (int v0idx, int v1idx);
addTriangle (int v0idx, int v1idx, int v2idx);

Each of these takes a set of vertex indices, creates the corresponding primitive, and adds it to the current group for the that primitive (primitive groups are discussed in Section 2.4.7).

Once all the primitives have been added, the Renderer method draw(RenderObject) can then be used to draw all the primitives in the object using the current graphics state. A variety of other draw methods are available for drawing subsets of primitives; these are detailed in Section 2.4.6.

There are no methods to remove individual attributes, vertices, or primitives. However, as described in Section 2.4.5, it is possible to use clearAll() to clear the entire object, after which it may be rebuilt, or clearPrimitives() to clear just the primitive sets.

Listing 3 gives a complete example combining the above operations to create a render object that draws the open tetrahedron described in Section 2.3.2 and Figure 2.7. In this example, the object itself is created using the method createTetRenderObject(). This is in turn called once within prerender() to create the object and store it in the member field myRob, allowing it to then be used as needed within render(). As indicated above, it is generally recommended to create or update render objects within the prerender method, particularly if they need to be modfied to reflect dynamically changing geometry or colors.

Listing 3: Construction and use of a render object to draw a partial tetrahedron.
import maspack.render.*;
import maspack.render.Renderer.FaceStyle;
   RenderObject myRob;
   private RenderObject createTetRenderObject() {
      // the corners of the tetrahedron
      RenderObject robj = new RenderObject();
      // add positions and normals
      int pi0 = robj.addPosition (0, 0, 0);
      int pi1 = robj.addPosition (1, 0, 0);
      int pi2 = robj.addPosition (0, 1, 0);
      int pi3 = robj.addPosition (0, 0, 1);
      int ni0 = robj.addNormal (0, 0, -1);
      int ni1 = robj.addNormal (-1, 0, 0);
      int ni2 = robj.addNormal (0, -1, 0);
      // add three vertices per triangle, each with position and normal
      // information and color and texture coords undefined, and then
      // use these to define a triangle primitive
      int v0, v1, v2;
      // first triangle
      v0 = robj.addVertex (pi0, ni0, -1, -1);
      v1 = robj.addVertex (pi2, ni0, -1, -1);
      v2 = robj.addVertex (pi1, ni0, -1, -1);
      robj.addTriangle (v0, v1, v2);
      // second triangle
      v0 = robj.addVertex (pi0, ni1, -1, -1);
      v1 = robj.addVertex (pi3, ni1, -1, -1);
      v2 = robj.addVertex (pi2, ni1, -1, -1);
      robj.addTriangle (v0, v1, v2);
      // third triangle
      v0 = robj.addVertex (pi0, ni2, -1, -1);
      v1 = robj.addVertex (pi1, ni2, -1, -1);
      v2 = robj.addVertex (pi3, ni2, -1, -1);
      robj.addTriangle (v0, v1, v2);
      return robj;
   public void prerender (RenderList list) {
      if (myRob == null) {
         myRob = createTetRenderObject();
   public void render (Renderer renderer, int flags) {
      renderer.setFaceStyle (FaceStyle.FRONT_AND_BACK);
      renderer.draw (myRob);  // draw the render object
      renderer.setFaceStyle (FaceStyle.FRONT);

2.4.2 “Current” attributes

Keeping track of attribute indices as described in Section 2.4.1 can be tedious. Instead of doing this, one can use the fact that every attribute add method records the index of the added attribute, which then denotes the “current” value for that attribute. The following methods can then be used to add a vertex using various current attribute values:

// use current position, normal, color and texture coords:
int addVertex ();
// use position pidx with current normal, color and texture coords:
int addVertex (int pidx);
// use position pidx and normal nidx with current color and texture coords:
int addVertex (int pidx, int nidx);

If any of the attributes have no “current” value, then the corresponding index value is -1 and that attribute will be undefined for the vertex.

If desired, it is possible to set or query the current attribute index, using methods of the form

void setCurrent<Attribute>(int idx);
int getCurrent<Attribute>();

where <Attribute> is Position, Normal, Color, or TextureCoord and idx is the index of a currently added attribute. For convenience, another set of methods,

int vertex (float px, float py, float pz);
int vertex (Vector3d pos);

will create a new position at the specified location, and then also create a vertex using that position along with the current normal, color and texture coords.

We now give some examples. First, Listing 4 changes the tetrahedron code in Listing 3 to use a current normal in conjuction with vertex(px, py, pz).

Listing 4: Constructing a render object using current normals.
   // add three vertices per triangle, each with position and normal
   // information and color and texture coords undefined, and then
   // use these to define a triangle primitive
   int v0, v1, v2;
   // first triangle
   robj.addNormal (0, 0, -1);
   v0 = robj.vertex (0, 0, 0);
   v1 = robj.vertex (0, 1, 0);
   v2 = robj.vertex (1, 0, 0);
   robj.addTriangle (v0, v1, v2);
   // second triangle
   robj.addNormal (-1, 0, 0);
   v0 = robj.vertex (0, 0, 0);
   v1 = robj.vertex (0, 0, 1);
   v2 = robj.vertex (0, 1, 0);
   robj.addTriangle (v0, v1, v2);
   // third triangle
   robj.addNormal (0, -1, 0);
   v0 = robj.vertex (0, 0, 0);
   v1 = robj.vertex (1, 0, 0);
   v2 = robj.vertex (0, 0, 1);
   robj.addTriangle (v0, v1, v2);

One issue with using vertex(px, py, pz) is that it creates a new position for every vertex, even in situations where vertices can be shared. The example above (implicitly) creates 9 positions where only 4 would be sufficient. Instead, one can create the positions separately (as in Listing 3), and then use vertex(pidx) to add vertices created from predefined positions along with current attribute values. Listing 5 does this for the tetrahedron, while also using a current color to give each face it’s own color. The rendered results are shown in Figure 2.19.

Figure 2.19: An open tetrahedron drawn using a render object constructed using a different current color for each face.
Listing 5: Constructing a render object using current normals and colors.
   // add positions and normals
   int pi0 = robj.addPosition (0, 0, 0);
   int pi1 = robj.addPosition (1, 0, 0);
   int pi2 = robj.addPosition (0, 1, 0);
   int pi3 = robj.addPosition (0, 0, 1);
   // add three vertices per triangle, each with position and normal
   // information and color and texture coords undefined, and then
   // use these to define a triangle primitive
   int v0, v1, v2;
   // first triangle
   robj.addNormal (0, 0, -1);
   robj.addColor (Color.CYAN);
   v0 = robj.addVertex (pi0);
   v1 = robj.addVertex (pi2);
   v2 = robj.addVertex (pi1);
   robj.addTriangle (v0, v1, v2);
   // second triangle
   robj.addNormal (-1, 0, 0);
   robj.addColor (Color.WHITE);
   v0 = robj.addVertex (pi0);
   v1 = robj.addVertex (pi3);
   v2 = robj.addVertex (pi2);
   robj.addTriangle (v0, v1, v2);
   // third triangle
   robj.addNormal (0, -1, 0);
   robj.addColor (Color.MAGENTA);
   v0 = robj.addVertex (pi0);
   v1 = robj.addVertex (pi1);
   v2 = robj.addVertex (pi3);
   robj.addTriangle (v0, v1, v2);

2.4.3 Maintaining consistent attributes

As mentioned earlier, all vertices within a render object must have a consistent set of attributes. That means that if some vertices are defined with normals or colors, they all must be defined with normals or colors, even if it means giving some vertices “dummy” versions of these attributes for primitives that don’t need them.

Figure 2.20: A triangle with a separate red border.

For example, suppose we wish to create an oject that draws a triangular face surrounding by an outer border (Figure 2.20). One might write the following code to create and draw the render object:

import java.awt.Color;
import maspack.render.*;
import maspack.render.Renderer.Shading;
   RenderObject createRenderObj () {
      RenderObject robj = new RenderObject();
      // add vertices for outer border - created without a normal
      robj.vertex (-0.8f, -0.5f, 0);
      robj.vertex ( 0.8f, -0.5f, 0);
      robj.vertex ( 0.0f,  1.0f, 0);
      // add points for triangle - create with a normal
      robj.addNormal (0, 0, 1f);
      robj.vertex (-0.64f, -0.4f, 0);
      robj.vertex ( 0.64f, -0.4f, 0);
      robj.vertex ( 0.0f,   0.8f, 0);
      // add outer border using first three vertices
      robj.addLine (0, 1);
      robj.addLine (1, 2);
      robj.addLine (2, 0);
      // add triangle using next three vertices
      robj.addTriangle (3, 4, 5);
      return robj;
   RenderObject myRob;
   public void render (Renderer renderer, int flags) {
      if (myRob == null) {
         myRob = createRenderObj ();
      // draw border
      renderer.setShading (Shading.NONE); // turn off lighting
      renderer.setColor (Color.RED);
      renderer.setLineWidth (3);
      renderer.drawLines (myRob);
      // draw triangle
      renderer.setShading (Shading.FLAT); // reset shading
      renderer.setColor (Color.GRAY);
      renderer.drawTriangles (myRob);

This creates a render object containing vertices for the border and triangle, along with the line and triangle primitives. Then render() first draws the border and the triangle, using the renderer’s drawLines() and drawTriangles() methods (described in Section 2.4.6). Because the border is drawn with lighting disabled, no normal is required and so its vertices are created without one. However, as written, this example will crash, because the triangle vertices do contain a normal, and therefore the border vertices must as well. The example can be fixed by moving the addNormal() call in front of the creation of the first three vertices, which will then contain a normal even though it will remain unused.

2.4.4 Adding primitives in “build” mode

The RenderObject can also be systematically constructed using a “build mode”, similar to the draw mode described in Section 2.3.4. Build mode can be invoked for any of the primitive types defined by DrawMode (Table 2.1).

Primitive construction begins with beginBuild(DrawMode) and ends with endBuild(). While in build mode, the application adds vertices using any of the methods described in the previous sections. Then, when endBuild() is called, the render object uses those those vertices to create the primitives that were specified by the mode argument of beginBuild(mode).

Listing 6 shows a complete example where build mode is used to create a RenderObject for a cylinder. In this example, we first reserve memory for the required attributes, vertices and triangles. This is not a required step, but does help with internal storage. Then, we use a triangle strip to construct the rounded sides of the cylinder, and triangle fans to construct the caps. When constructing the sides, we use vertex(px,py,pz) to create positions and vertices at the same time. Then when constucting the caps, we use addVertex(pidx) to add vertices that reuse the positions created for the sides (knowing that the position indices start at 0). The final cylinder is shown using flat shading in Figure 2.21.

Figure 2.21: Render object cylinder created in Listing 6.
Listing 6: Building a cylinder.
RenderObject cylinder = new RenderObject();
int nSlices = 32;
float height = 2;
// reserve memory
cylinder.ensurePositionCapacity(2*nSlices);  // top and bottom ring
cylinder.ensureNormalCapacity(nSlices+2);    // sides and caps
cylinder.ensureVertexCapacity(4*nSlices);    // top/bottom sides, top/bottom caps
cylinder.ensureTriangleCapacity(2*nSlices+2*(nSlices-2));  // sides, caps
// create cylinder sides
for (int i=0; i<nSlices; i++) {
   double angle = 2*Math.PI/nSlices*i;
   float x = (float)Math.cos(angle);
   float y = (float)Math.sin(angle);
   cylinder.addNormal(x, y, 0);
   cylinder.vertex(x, y, height);  // top
   cylinder.vertex(x, y, 0);       // bottom
// connect ends around cylinder
cylinder.addTriangle(2*nSlices-2, 2*nSlices-1, 0);
cylinder.addTriangle(0, 2*nSlices-1, 1);
// create top cap, using addVertex(pidx) to reuse positions that
// were added when building the sides
for (int i=0; i<nSlices; i++) {
   cylinder.addVertex(2*i);    // even positions (top)
// create bottom cap
for (int i=1; i<nSlices; i++) {
   int j = nSlices-i;
   cylinder.addVertex(2*j+1);  // odd positions (bottom)

2.4.5 Modifying render objects

Sometimes, an application will build a render object once, and then never change any of its attributes, vertices, or primitives. Such objects are called static, and are the most efficient for rendering purposes since their data only needs to be transmitted to the GPU once. After the renderer first draws the object (using any of the draw methods described in Section 2.4.6), it can continue to draw a static object as many times as needed without having to send more information to the GPU. (Note however that such objects can still be repositioned within the scene by adjusting the model matrix as described in Section 2.2.4). Therefore, applications should attempt to use static render objects whenever possible.

However, often it is necessary to modify a render object. Such modifications may take three forms:

  • Vertex changes involving changes to the vertex structure;

  • Primitive changes involving changes to the primitive structure;

  • Attribute changes involving changes to the attribute structure or the modification of existing attribute values.

Vertex changes occur whenever new vertices are added (using any of the add methods described in the previous sections), or the entire object is cleared using clearAll(). These generally require retransmission of the vertex and attribute information to the GPU.

Primitive changes occur when new points, lines or triangles are added, when all the existing primitives are cleared using clearPrimitives(), or clearAll() is called. Primitive changes generally require retransmission of primitive index data to the GPU.

Attribute changes occur when new attributes are added, existing attribute data is modified, or clearAll() is called. These may require retransmission of the attribute and vertex data to the GPU.

The need to modify existing attribute data often arises when the render object represents some entity that is changing over time, perhaps as the result of a simulation. For instance, if the object represents a deformable surface, the positions and normals associated with that surface will typically be time varying. There are two main ways to modify attribute data. The first is to call one of the render object’s methods for directly setting the attribute’s value,

void setPosition (int idx, float px, float py, float pz);
void setPosition (int idx, Vector3d pos);
void setPosition (int idx, float[] pos);    // set by reference
void setNormal (int idx, float nx, float ny, float nz);
void setNormal (int idx, Vector3d nrm);
void setNormal (int idx, float[] nrm);      // set by reference
void setColor (int idx, float r, float g, float b, float a);
void setColor (int idx, Color color);
void setColor (int idx, byte[] rgba);       // set by reference
void setTextureCoord (int idx, float tx, float ty);
void setTextureCoord (int idx, Vector2d xy);
void setTextureCoord (int idx, float[] xy); // set by reference

where idx is the index of the attribute. This will set the attribute’s value within its current group. As with the add attribute methods, those methods marked “set by reference” use the specified array to directly store the values within the attribute, so that later changes to the array’s values will also cause the attribute values to change. (However, if a non-referencing set method is subsequently called, the attribute will allocate its own internal storage, and the reference will be lost.)

This indicates the second way in which attribute data may be modified: if the value was last set using a reference-based add or set method, the attribute can be changed by directly changing the values of that array. However, when this is done, the render object has no way to know that the corresponding attribute data was modfied, and so the application must notify the object directly, using one of the methods

void notifyPointsModified();
void notifyNormalsModified();
void notifyColorsModified();
void notifyTextureCoordsModified();

To facilitate the detection of changes, each RenderObject maintains a set of “version” numbers for its attributes, vertices, and primitives, which get incremented whenever changes are made to these quantities. While applications typically do not need to be concerned with this version information, it can be used by renderer implementations to determine what information needs to be retransmitted to the GPU and when. Version numbers can be queried using the following methods:

int getPositionsVersion();      // positions were added or modified
int getNormalsVersion();        // normals were added or modified
int getColorsVersion();         // colors were added or modified
int getTextureCoordsVersion();  // texture coordinates were added or modified
int getVerticesVersion();       // vertices were added
int getPointsVersion();         // points were added
int getLinesVersion();          // lines were added
int getTrianglesVersion();      // triangles were added
int getVerstion();              // one or more of the above changes occured

2.4.6 Drawing RenderObjects

In addition to draw(RenderObject), a variety of other Renderer methods allow the drawing of different subsets of a render objects’s primitives. These include:

// draw all primitives in the first group for each:
void draw(RenderObject robj);
// draw all points in the first point group:
void drawPoints(RenderObject robj);
void drawPoints(RenderObject robj, PointStyle style, float rad);
// draw all line in the first line group:
void drawLines(RenderObject robj);
void drawLines(RenderObject robj, LineStyle style, float rad);
// draw all triangles in the first triangle group:
void drawTriangles(RenderObject robj);
// draw all vertices, using them to create implicit primitives according
// to the indicated mode:
void drawVertices(RenderObject robj, DrawMode mode);

Point, line and triangle groups are presented in Section 2.4.7. The method drawPoints(robj,style,rad) draws the indicated points using the specified PointStyle, with rad being either the pixel size or radius, as appropriate. Likewise, drawLines(robj,style,rad) draws the indicated lines using the specified style, with rad being either the line width (in pixels) or the cylinder/spindle/arrow radius.

A common reason for drawing different graphics primitives separately is so that they can be drawn with different settings of the graphics state. For example, Listing 7 creates a render object for a simple grid in the x-y plane, and the render method draws the points and lines in different colors. One way to do this would be to assign the appropriate colors to the vertices of all the point and line primitives. Another way, as done in the example, is to simply draw the points and lines separately, with different color settings in the graphics state (this also allows different colors to be used in subsequent renders, without having to modify the graphics object). The result in shown in Figure 2.22.

Figure 2.22: Grid render object drawn with red points and green lines.
Listing 7: Building and drawing render object for a grid.
import java.awt.Color;
import maspack.render.*;
   // Creates the render object for a grid in the x-y plane, with width w,
   // height h, and nx and ny points in the x and y directions
   RenderObject createGridObj (double w, double h, int nx, int ny) {
      RenderObject robj = new RenderObject();
      // create vertices and points ...
      for (int j=0; j<ny; j++) {
         for (int i=0; i<nx; i++) {
            float x = (float)(-w/2+i*w/(nx-1));
            float y = (float)(-h/2+j*h/(ny-1));
            int vi = robj.vertex (x, y, 0);
            robj.addPoint (vi);
      // create horizontal lines ...
      for (int j=0; j<ny; j++) {
         for (int i=0; i<nx-1; i++) {
            int v0 = j*nx + i;
            robj.addLine (v0, v0+1);
      // create vertical lines ...
      for (int i=0; i<nx; i++) {
         for (int j=0; j<ny-1; j++) {
            int v0 = j*nx + i;
            robj.addLine (v0, v0+nx);
      return robj;
   RenderObject myRob; // store object between render calls
   public void render (Renderer renderer, int flags) {
      if (myRob == null) {
         myRob = createGridObj (2.0, 2.0, 5, 5);
      // draw the points and lines using separate colors
      renderer.setColor (Color.RED);
      renderer.setPointSize (6);
      renderer.drawPoints (myRob);
      renderer.setColor (0f, 0.5f, 0f); // dark green
      renderer.setLineWidth (3);
      renderer.drawLines (myRob);
Figure 2.23: Grid render object drawn with points as spheres and and lines as spindles.

The Renderer methods drawPoints(RenderObject,PointStyle,double) and drawLines(RenderObject,LineStyle,double), described above, can be particularly useful for drawing the points or lines of a render object using different styles. For example, the following code fragment draws the grid of Listing 7 with points drawn as spheres with radius 0.1 and lines drawn as spindles with radius 0.05, with the results shown in Figure 2.23.

   renderer.setColor (Color.RED);
   renderer.drawPoints (robj, PointStyle.SPHERE, 0.10);
   renderer.setColor (0f, 0.5f, 0f); // dark green
   renderer.drawLines (robj, LineStyle.SPINDLE, 0.05);

2.4.7 Multiple primitive groups

The RenderObject can have multiple groups of a particular primitive type. This is to allow for separate draw calls to render different parts of the object. For example, consider a triangular surface mesh consisting of a million faces that is to be drawn with the left half red, and the right half yellow. One way to accomplish this is to add a vertex color attribute to each vertex. This will end up being quite memory inefficient, since the renderer will need to duplicate the color for every vertex in the vertex buffer. The alternative is to create two distinct triangle groups and draw the mesh with two draw calls, changing the global color between them. New primitive groups can be created using the methods

int createPointGroup();
int createLineGroup();
int createTriangleGroup();

Each of these creates a new group for the associated primitive type, sets it to be the current group, and returns an index to it.

A group for a particular primitive type is created automatically, if necessary, the first time an instance of that primitive is added to a render object.

Once created, the following methods can be used to set and query the different primitive groups:

int numPointGroups();       // number of point groups
void pointGroup (gi);       // set current point group to gi
int getPointGroupIdx();     // get index of current point group
int numLineGroups();        // number of line groups
void lineGroup (gi);        // set current line group to gi
int getLineGroupIdx();      // get index of current line group
int numTriangleGroups();    // number of triangle groups
void triangleGroup (gi);    // set current triangle group to gi
int getTriangleGroupIdx();  // get index of current triangle group

Another set of methods can be used to query the primitives within a particular group:

int numPoints (gi);         // number of points in group gi
int[] getPoints (gi)        // get vertex indices for points in group gi
int numLines (gi);          // number of lines in group gi
int[] getLines (gi)         // get vertex indices for lines in group gi
int numTriangles (gi);      // number of triangles in group gi
int[] getTriangles (gi)     // get vertex indices for triangles in group gi

Finally, the draw primitives described in Section 2.4.6 all have companion methods that allow the primitive group to be specified:

// draw all points in point group gidx:
void drawPoints(RenderObject robj, int gidx);
void drawPoints(RenderObject robj, int gidx, PointStyle style, float r);
// draw all line in line group gidx:
void drawLines(RenderObject robj, int gidx);
void drawLines(RenderObject robj, int gidx, LineStyle style, float rad);
// draw all triangles in triangle group gidx:
void drawTriangles(RenderObject robj, int gidx);

To illustrate group usage, we modify the grid example of Listing 7 so that the vertical and horizontal lines are each placed into different line groups:

   // create horizontal lines inside first line group ...
   for (int j=0; j<ny; j++) {
      for (int i=0; i<nx-1; i++) {
         int v0 = j*nx + i;
         robj.addLine (v0, v0+1);
   // create vertical lines inside second line group ...
   for (int i=0; i<nx; i++) {
      for (int j=0; j<ny-1; j++) {
         int v0 = j*nx + i;
         robj.addLine (v0, v0+nx);

Once this is done, the horizontal and vertical lines can be drawn with different colors by drawing the different groups separately:

Figure 2.24: Grid render object created with two line groups, with one drawn in green and the other in yellow.
   renderer.setColor (Color.RED);
   renderer.drawPoints (grid, PointStyle.SPHERE, 0.10);
   renderer.setColor (0f, 0.5f, 0f); // dark green
   // draw lines in first line group
   renderer.drawLines (grid, 0, LineStyle.SPINDLE, 0.05);
   renderer.setColor (Color.YELLOW);
   // draw lines in second line group
   renderer.drawLines (grid, 1, LineStyle.SPINDLE, 0.05);

The results are show in Figure 2.24.

As noted in Section 2.4.5, it is possible to clear all primitives using clearPrimitives(). This will clear all primitives and their associated groups within the render object, while leaving vertices and attributes alone, allowing new primitives to then be constructed.

2.4.8 Drawing primitive subsets

In some circumstances, it may be useful to draw only a subset of the primitives in a render object, or to draw a subset of the vertices using a specified primitive type. There may be several reasons why this is necessary. The application may wish to draw different primitive subsets using different settings of the graphics context (such as different colors). Or, an application may use a single render object for drawing a collection of objects that are individually selectable. Then when rendering in selection mode (Section 2.7), it is it is necessary to render the objects separately so that the selection mechanism can distinquish them.

The two renderer methods for rendering primitive subsets are:

   void drawVertices (
      RenderObject robj, VertexIndexArray idxs, DrawMode mode);
   void drawVertices (
      RenderObject robj, VertexIndexArray idxs,
      int offset, int count, DrawMode mode);

Each of these draws primitive subsets for the render object robj, using the vertices specified by idxs and the primitive type specified by mode. VertexIndexArray is a dynamically-sized integer array specialized for vertices. The second method allows a subset of idxs to be specified by an offset and count, so that the same index array can be used to draw different features.

The following example creates a render object containing three squares, and then uses drawVertices() to render each square individually using a different color:

Listing 8: Example of rendering separate features from the same render object.
   RenderObject myRob;
   VertexIndexArray myIdxs;
   void addSquare (
      RenderObject robj, VertexIndexArray idxs,
      float x0, float y0, float x1, float y1,
      float x2, float y2, float x3, float y3) {
      // create the four vertices uses to define the square, based on
      // four points in the x-y plane
      int v0 = robj.vertex (x0, y0, 0);
      int v1 = robj.vertex (x1, y1, 0);
      int v2 = robj.vertex (x2, y2, 0);
      int v3 = robj.vertex (x3, y3, 0);
      // use these vertices to define the four line segments needed
      // to draw the square
      robj.addLine (v0, v1);
      robj.addLine (v1, v2);
      robj.addLine (v2, v3);
      robj.addLine (v3, v0);
      // and add the vertex indices for the line segments to the vertex
      // index array
      idxs.add (v0); idxs.add (v1);
      idxs.add (v1); idxs.add (v2);
      idxs.add (v2); idxs.add (v3);
      idxs.add (v3); idxs.add (v0);
   RenderObject createRenderObj (VertexIndexArray idxs) {
      // create a render object consisting of three squares, along with
      // an index array to keep track of all the vertices
      RenderObject robj = new RenderObject();
      addSquare (robj, idxs, -4f, -1f, -2f, -1f, -2f,  1f, -4f,  1f);
      addSquare (robj, idxs, -1f, -1f,  1f, -1f,  1f,  1f, -1f,  1f);
      addSquare (robj, idxs,  2f, -1f,  4f, -1f,  4f,  1f,  2f,  1f);
      return robj;
   public void render (Renderer renderer, int flags) {
      if (myRob == null) {
         // create render object and index array on demand
         myIdxs = new VertexIndexArray();
         myRob = createRenderObj (myIdxs);
      // render each square separately using a different color
      renderer.setLineWidth (4);
      renderer.setColor (Color.RED);
      renderer.drawVertices (myRob, myIdxs,  0, 8, DrawMode.LINES);
      renderer.setColor (Color.GREEN);
      renderer.drawVertices (myRob, myIdxs,  8, 8, DrawMode.LINES);
      renderer.setColor (Color.BLUE);
      renderer.drawVertices (myRob, myIdxs, 16, 8, DrawMode.LINES);

Each square is added to the render object using the method addSquare(), which creates and adds the necessary vertices and line segments, and also stores the line segment vertex indices in an index array. The render() method then uses subsets of this index array, specified by the offset/length pairs (0,8), (8,8), and (16,8), to render each square individually (using a different color) via a call to drawVertices(). The result is shown in Figure 2.25.

Figure 2.25: Three squares drawn individually from the same render object.

In the above example, each square uses the same number of vertices (8) to draw its line segments, making it easy to determine the offset/length pairs required for each square. However, in more general cases a render object may contain features with variable numbers of vertices, and so determining the offset/length pairs may be more difficult. In such cases the application may find it useful to instead collect the vertex indices inside a FeatureIndexArray, which allows them to be grouped on a per-feature basis, with each feature identified by a number. The usage model looks like this:

   FeatureIndexArray fidxs = new FeatureIndexArray();
   for (each feature fnum) {
      fidxs.beginFeature (fnum);
      for (each feature vertex vidx) {
         fidxs.add (vidx);

After the feature index array has been built, the vertex index buffer can be obtained using fidxs.getVertices(), and the feature number and offset/length pair for each feature can be recovered using

   int fnum = fidxs.getFeature (fidx);
   int offset = fidxs.getFeatureOffset (fidx);
   int length = fidxs.getFeatureLength (fidx);

where fidx is the index of the feature within the FeatureIndexArray. In some situations the feature number fnum and fidx may be the same, but in others they may be different. For example, each feature may be associated with an application component that has a unique number used for selection (Section 2.7), in which case the feature number can be set to the selection number.

The three squares example of Listing 8 can be reimplemented using FeatureIndexArray as follows:

Listing 9: Primitive subset rendering using a FeatureVertexArray.
   RenderObject myRob;
   FeatureIndexArray myFidxs;
   void addSquare (
      RenderObject robj, FeatureIndexArray fidxs, int fnum,
      float x0, float y0, float x1, float y1,
      float x2, float y2, float x3, float y3) {
      // create the four vertices uses to define the square, based on
      // four points in the x-y plane
      int v0 = robj.vertex (x0, y0, 0);
      int v1 = robj.vertex (x1, y1, 0);
      int v2 = robj.vertex (x2, y2, 0);
      int v3 = robj.vertex (x3, y3, 0);
      // use these vertices to define the four line segments needed
      // to draw the square
      robj.addLine (v0, v1);
      robj.addLine (v1, v2);
      robj.addLine (v2, v3);
      robj.addLine (v3, v0);
      // and add the vertex indices for the line segments to the feature
      // index array for the feature identified by fnum:
      fidxs.beginFeature (fnum);
      fidxs.addVertex (v0); fidxs.addVertex (v1);
      fidxs.addVertex (v1); fidxs.addVertex (v2);
      fidxs.addVertex (v2); fidxs.addVertex (v3);
      fidxs.addVertex (v3); fidxs.addVertex (v0);
   RenderObject createRenderObj (FeatureIndexArray idxs) {
      RenderObject robj = new RenderObject();
      addSquare (robj, idxs, 0, -4f, -1f, -2f, -1f, -2f,  1f, -4f,  1f);
      addSquare (robj, idxs, 1, -1f, -1f,  1f, -1f,  1f,  1f, -1f,  1f);
      addSquare (robj, idxs, 2,  2f, -1f,  4f, -1f,  4f,  1f,  2f,  1f);
      return robj;
   RenderObject myRob;
   FeatureIndexArray myFidxs;
   void drawSquare (
      Renderer renderer, RenderObject robj,
      FeatureIndexArray fidxs, int fidx) {
      // draw a single square using the vertex indices associated
      // with the feature fidx
      renderer.drawVertices (
         robj, fidxs.getVertices(),
         fidxs.getFeatureOffset(fnum), fidxs.getFeatureLength(fnum),
   public void render (Renderer renderer, int flags) {
      if (myRob == null) {
         // create render object and feature index array on demand
         myFidxs = new FeatureIndexArray();
         myRob = createRenderObj (myFidxs);
      // render each square separately using a different color
      renderer.setLineWidth (4);
      renderer.setColor (Color.RED);
      drawSquare (renderer, myRob, myFidxs, 0);
      renderer.setColor (Color.GREEN);
      drawSquare (renderer, myRob, myFidxs, 1);
      renderer.setColor (Color.BLUE);
      drawSquare (renderer, myRob, myFidxs, 2);

2.5 Texture mapping

Some renderers provide support for texture mapping, including color, normal, and bump maps; whether or not they do can be queried via the methods hasColorMapping(), hasNormalMapping(), and hasBumpMapping(). If supported, such mappings may be set up and queried using the methods

void setColorMap (ColorMapProps props);
ColorMapProps getColorMap();
void setNormalMap (NormalMapProps props);
NormalMapProps getNormalMap();
void setBumpMap (BumpMapProps props);
BumpMapProps getBumpMap();

The props argument to the set methods either contains the properties required to set up the mapping, or, if null, disables the mapping. When enabled, color, normal and bump maps will be applied to subsequent draw operations involving triangle primitives for which texture coordinates have been assigned to the vertices.

At present, texture coordinates can be defined for primitives using either draw mode (Section 2.3.4), or by creating a RenderObject (Sections 2.4 and 2.4.6). Texture coordinates are assigned using the OpenGL convention whereby (0,0) and (1,1) correspond to the lower left and upper right of the image, respectively.

Normal and bump mapping will not work if shading is set to Shading.NONE or Shading.FLAT. That’s because both of those shading modes restrict the use of normals when computing primitive lighting.

Renderers based on OpenGL 3 support color, normal and bump mapping. Those based on OpenGL 2 support only color mapping.

2.5.1 Texture mapping properties

The properties specified by ColorMapProps, NormalMapProps, or BumpMapProps contains the source data for the mapping along with information about how to map that data onto drawn primitives given their texture coordinates. These properties include:


A boolean specifying whether or not the mapping is enabled;


A string giving the name of the texture source file. This can be any image file in the format supported by the standrad package javax.imageio, which includes JPEG, PNG, BMP, and GIF;


An instance of TextureMapProps.TextureWrapping specifying the wrapping of the s texture coordinate;


An instance of TextureMapProps.TextureWrapping specifying the wrapping of the t texture coordinate;


An instance of TextureMapProps.TextureFilter specifing the minifying filter;


An instance of TextureMapProps.TextureFilter specifing the magnifying filter;


The color to be used when either sWrapping or tWrapping is set to TextureWrapping.CLAMP_TO_BORDER;


For ColorMapProps only, an instance of Renderer.ColorMixing that specifies how the color map is combined with the nominal coloring of the underlying primitive, which is in turn determined by the current diffuse/ambient color and any vertex coloring that may be present (Section 2.3.7). The default value for this is MODULATE, implying that the color map is modulated by the nominal coloring. Not all renderers support all mixing modes; whether or not a particular color mixing is supported can be queried using

   boolean hasColorMapMixing (ColorMixing cmix);

For ColorMapProps only, a boolean that specifies whether the color map should respond to diffuse/ambient lighting;


For ColorMapProps only, a boolean that specifies whether the color map should respond to specular lighting;


For NormalMapProps and BumpMapProps only, a float giving a scaling factor for either the x-y components of the normal map, or the depth of the bump map.

TextureMapProps.TextureWrapping is an enum that describes how texture coordinates outside the canonical range of [0,1] are handled. There are four available methods, which correspond to those available in OpenGL:

Method Description OpenGL equivalent
REPEAT pattern is repeated GL_REPEAT
MIRRORED_REPEAT pattern is repeated with mirroring GL_MIRRORED_REPEAT
CLAMP_TO_EDGE coordinates are clamped to [0,1] GL_CLAMP_TO_EDGE
CLAMP_TO_BORDER out of range coordinates are set to a border color GL_CLAMP_TO_BORDER

REPEAT is implemented by setting the integer part of the coordinate to 0. For MIRRORED_REPEAT, mirroring is applied when the integer part is odd. See Figure 2.26.

Figure 2.26: Wrapping applied to a texture coordinate s using REPEAT (top) and MIRRORED_REPEAT (bottom).

TextureMapProps.TextureFilter is an enum that describes the filtering that is applied when the source image needs to be either magnified or minified. Specifically, for a given pixel being textured, we use the filter to compute a texture value from the texels in the texture image. There are six filter types, corresponding to those available in OpenGL:

Method OpenGL equivalent

NEAREST uses the texel nearest to the pixel center, while