CubicHermiteSpline3d (Artisynth API documentation)

java.lang.Object
- maspack.interpolation.CubicHermiteSpline3d

All Implemented Interfaces:

java.lang.Iterable<CubicHermiteSpline3d.Knot>, Scannable
```
public class CubicHermiteSpline3d
extends java.lang.Object
implements Scannable, java.lang.Iterable<CubicHermiteSpline3d.Knot>
```
Implements a three dimensional cubic Hermite spline interpolated by an independent parameter s. The spline is defined by a sequence of knots delimiting the boundaries between cubic interpolation segements.

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class CubicHermiteSpline3d.Knot

Nested Classes
Modifier and Type	Class and Description
`static class`	`CubicHermiteSpline3d.Knot`

Constructor Summary

Constructors
Constructor and Description
`CubicHermiteSpline3d()` Creates a empty spline
`CubicHermiteSpline3d(java.util.ArrayList<? extends Vector3d> xVals, java.util.ArrayList<Vector3d> dxdsVals)` Creates a spline from data containing the values of x and dxds at each knot point, with the interval between each knot point assumed to have a length of 1.
`CubicHermiteSpline3d(CubicHermiteSpline3d spline)` Creates a spline from a copy of an existing one.
`CubicHermiteSpline3d(double[] sVals, java.util.ArrayList<? extends Vector3d> xVals, java.util.ArrayList<Vector3d> dxdsVals)` Creates a spline from data containing the values of s, x and dxds at each knot point.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`CubicHermiteSpline3d.Knot`	`addKnot(double s, Vector3d x, Vector3d dxds)` Adds another knot point to this cubic hermite spline, consisting of an s coordinate, along with x and dxds values.
`void`	`clearKnots()` Removes all knots from from this spline.
`CubicHermiteSpline3d`	`copy()` Creates a copy of this spline.
`boolean`	`epsilonEquals(CubicHermiteSpline3d spline, double tol)` Queries whether this spline is equal to another spline within a specified absolute tolerance.
`boolean`	`equals(CubicHermiteSpline3d spline)` Queries whether this spline is equal to another spline.
`Vector3d`	`eval(double s)` Evaluates the value of this spline for a specific parameter value.
`Vector3d`	`eval(double s, IntHolder lastIdx)` Evaluates the value of this spline for a specific parameter value.
`Vector3d`	`evalDx(double s)` Evaluates the derivative (with respect to the parameter) of this spline for a specific parameter value.
`Vector3d`	`evalDx(double s, IntHolder lastIdx)` Evaluates the derivative (with respect to the parameter) of this spline for a specific parameter value.
`Vector3d`	`evalDx2(double s)` Evaluates the second derivative (with respect to the parameter) of this spline for a specific parameter value.
`Vector3d`	`evalDx2(double s, IntHolder lastIdx)` Evaluates the second derivative (with respect to the parameter) of this spline for a specific parameter value.
`CubicHermiteSpline3d.Knot`	`getFirstKnot()` Returns the first knot in this spline, or `null` if there are no knots.
`CubicHermiteSpline3d.Knot`	`getKnot(int idx)` Returns the `idx`-th knot in this spline.
`CubicHermiteSpline3d.Knot`	`getLastKnot()` Returns the last knot in this spline, or `null` if there are no knots.
`CubicHermiteSpline3d.Knot`	`getNextKnot(double s)` Find the knot immediately following s.
`CubicHermiteSpline3d.Knot`	`getPreceedingKnot(double s)` Find the knot immediately preceeding s.
`CubicHermiteSpline3d.Knot`	`getPreceedingKnot(double s, IntHolder lastIdx)` Find the knot immediately preceeding s.
`double`	`getS0()` Returns the start value of the parameter controlling this spline.
`java.util.ArrayList<Vector3d>`	`getSampledValues(int numv)` Creates and returns a list of values sampled uniformly along this spline.
`double`	`getSLast()` Returns the last value of the parameter controlling this spline.
`double`	`getSLength()` Returns the length of the parameter interval controlling this spline.
`boolean`	`isWritable()` Returns `true` if this component should in fact be written to secondary storage.
`java.util.Iterator<CubicHermiteSpline3d.Knot>`	`iterator()` Returns an iterator for the knots in this spline.
`int`	`numKnots()` Returns the number of knots in this spline.
`boolean`	`removeKnot(CubicHermiteSpline3d.Knot knot)` Removes a knot from this spline.
`void`	`scan(ReaderTokenizer rtok, java.lang.Object ref)` Scans this spline from a ReaderTokenizer.
`void`	`set(CubicHermiteSpline3d spline)` Sets this spline to be a copy of another spline.
`void`	`set(double[] sVals, java.util.ArrayList<? extends Vector3d> xVals, java.util.ArrayList<Vector3d> dxdsVals)` Sets this spline from specified values of s, x and dxds at each knot point.
`void`	`setMultiSegment(java.util.ArrayList<? extends Vector3d> xVals, double[] svals)` Sets this spline to one consisting of n segments with n+1 knots, at s values given by `svals`, with the coeffcients computed to best fit a set of x values uniformly placed along the entire interval.
`void`	`setSingleSegment(java.util.ArrayList<? extends Vector3d> xVals, double s0, double s1)` Sets this spline to one consisting of a single segment with two knots, with the coeffcients computed to best fit a set of x values uniformly placed along the interval s in [s0, s1].
`void`	`write(java.io.PrintWriter pw, NumberFormat fmt, java.lang.Object ref)` Writes a text description of this spline to a PrintWriter.

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface java.lang.Iterable
forEach, spliterator

- Constructor Detail
  - CubicHermiteSpline3d
```
public CubicHermiteSpline3d()
```
    Creates a empty spline
  - CubicHermiteSpline3d
```
public CubicHermiteSpline3d(java.util.ArrayList<? extends Vector3d> xVals,
                            java.util.ArrayList<Vector3d> dxdsVals)
```
    Creates a spline from data containing the values of x and dxds at each knot point, with the interval between each knot point assumed to have a length of 1. Note that x and dxds correspond to the a0 and a1 coefficient values for the knot.
    
    Parameters:
    
    xVals - x values for each knot point
    
    dxdsVals - dxds values for each knot point
  - CubicHermiteSpline3d
```
public CubicHermiteSpline3d(double[] sVals,
                            java.util.ArrayList<? extends Vector3d> xVals,
                            java.util.ArrayList<Vector3d> dxdsVals)
```
    Creates a spline from data containing the values of s, x and dxds at each knot point. The values of s should be in strictly ascending order. Note that x and dxds correspond to the a0 and a1 coefficient values for the knot.
    
    Parameters:
    
    sVals - s values at each knot point
    
    xVals - x values for each knot point
    
    dxdsVals - dxds values for each knot point
  - CubicHermiteSpline3d
```
public CubicHermiteSpline3d(CubicHermiteSpline3d spline)
```
    Creates a spline from a copy of an existing one.
    
    Parameters:
    
    spline - spline to copy
- Method Detail
  - set
```
public void set(double[] sVals,
                java.util.ArrayList<? extends Vector3d> xVals,
                java.util.ArrayList<Vector3d> dxdsVals)
```
    Sets this spline from specified values of s, x and dxds at each knot point. The values of s should be in strictly ascending order.
    
    Parameters:
    
    sVals - s values at each knot point
    
    xVals - x values for each knot point
    
    dxdsVals - dxds values for each knot point
  - setSingleSegment
```
public void setSingleSegment(java.util.ArrayList<? extends Vector3d> xVals,
                             double s0,
                             double s1)
```
    Sets this spline to one consisting of a single segment with two knots, with the coeffcients computed to best fit a set of x values uniformly placed along the interval s in [s0, s1].
  - setMultiSegment
```
public void setMultiSegment(java.util.ArrayList<? extends Vector3d> xVals,
                            double[] svals)
```
    Sets this spline to one consisting of n segments with n+1 knots, at s values given by svals, with the coeffcients computed to best fit a set of x values uniformly placed along the entire interval. C(2) continuity is enforced between intervals, with the second derivatives at the end points equal to 0.
  - addKnot
```
public CubicHermiteSpline3d.Knot addKnot(double s,
                                         Vector3d x,
                                         Vector3d dxds)
```
    Adds another knot point to this cubic hermite spline, consisting of an s coordinate, along with x and dxds values.
    
    Parameters:
    
    s - parameter value at which the knot should be added
    
    x - value at the knot
    
    x - derivative value at the knot
  - removeKnot
```
public boolean removeKnot(CubicHermiteSpline3d.Knot knot)
```
    Removes a knot from this spline.
    
    Parameters:
    
    knot - knot to remove
  - clearKnots
```
public void clearKnots()
```
    Removes all knots from from this spline.
  - getPreceedingKnot
```
public CubicHermiteSpline3d.Knot getPreceedingKnot(double s)
```
    Find the knot immediately preceeding s. Specifically, find the nearest knot for which knot.getS0() <= s. If no such knot exists, null is returned.
    
    Parameters:
    
    s - value for which preceeding knot is sought
  - getPreceedingKnot
```
public CubicHermiteSpline3d.Knot getPreceedingKnot(double s,
                                                   IntHolder lastIdx)
```
    Find the knot immediately preceeding s. Specifically, find the nearest knot for which knot.x0 <= s. If no such knot exists, null is returned.
    The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of s.
    
    Parameters:
    
    s - value for which preceeding knot is sought
    
    lastIdx - if non-null, specifies a index value giving a hint on where to start the knot search. On output, this value is set to the index of the returned knot, or -1 if no knot is found.
  - getNextKnot
```
public CubicHermiteSpline3d.Knot getNextKnot(double s)
```
    Find the knot immediately following s. Specifically, find the nearest knot for which knot.x0 > s. If no such knot exists, null is returned.
    
    Parameters:
    
    s - value for which next knot is sought
  - eval
```
public Vector3d eval(double s)
```
    Evaluates the value of this spline for a specific parameter value. For parameter values outside the knot range, the value is lineraly extrapolated based on derivatives at the first or last knots. An empty spline evaluates to 0.
    
    Parameters:
    
    s - parameter for which the value should be computed
  - eval
```
public Vector3d eval(double s,
                     IntHolder lastIdx)
```
    Evaluates the value of this spline for a specific parameter value. For parameter values outside the knot range, the value is lineraly extrapolated based on derivatives at the first or last knots. An empty spline evaluates to 0.
    The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of s.
    
    Parameters:
    
    s - parameter for which the value should be computed
    
    lastIdx - if non-null, specifies a index value giving a hint on where to search for the knot preceeding s. On output, this value is set to the index of the preceeding knot, or -1 if no preceeding knot is found.
  - evalDx
```
public Vector3d evalDx(double s)
```
    Evaluates the derivative (with respect to the parameter) of this spline for a specific parameter value. For parameter values outside the knot range, the value is set to the derivative at either the first or last knot. An empty spline evaluates to 0.
    
    Parameters:
    
    s - parameter for which the derivative should be computed
  - evalDx
```
public Vector3d evalDx(double s,
                       IntHolder lastIdx)
```
    Evaluates the derivative (with respect to the parameter) of this spline for a specific parameter value. For parameter values outside the knot range, the value is set to the derivative at either the first or last knot. An empty spline evaluates to 0.
    The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of s.
    
    Parameters:
    
    s - parameter for which the derivative should be computed
    
    lastIdx - if non-null, specifies a index value giving a hint on where to search for the knot preceeding s. On output, this value is set to the index of the preceeding knot, or -1 if no preceeding knot is found.
  - evalDx2
```
public Vector3d evalDx2(double s)
```
    Evaluates the second derivative (with respect to the parameter) of this spline for a specific parameter value. For parameter values outside the knot range, the value is set to 0.
    
    Parameters:
    
    s - parameter for which the derivative should be computed
  - evalDx2
```
public Vector3d evalDx2(double s,
                        IntHolder lastIdx)
```
    Evaluates the second derivative (with respect to the parameter) of this spline for a specific parameter value. For parameter values outside the knot range, the value is set to 0.
    The optional parameter lastIdx, described below, can be used to significantly reduce the search speed when queries are made with increasing values of s.
    
    Parameters:
    
    s - parameter for which the derivative should be computed
    
    lastIdx - if non-null, specifies a index value giving a hint on where to search for the knot preceeding s. On output, this value is set to the index of the preceeding knot, or -1 if no preceeding knot is found.
  - scan
```
public void scan(ReaderTokenizer rtok,
                 java.lang.Object ref)
          throws java.io.IOException
```
    Scans this spline from a ReaderTokenizer. The expected format consists of an opening square bracket, followed by 7 n numeric values giving the s, x and dxdx values for each of the n knots, and terminated with a closing square bracket. Whitespace characters are ignored. For example,
```
  [  0.0
     0.0 4.0 1.0
     2.0 5.0 -1.0
     1.0
     0.0 5.0 1.2
     -2.0 1.0 0.0
  ]
 
```
    describes a spline with two knots, with s, x and dxds equal to 0, (0, 4, 1) and (2, 5, -1) for the first knot and 1, (0, 5, 1.2) and (-2, 1, 0) for the second knot.
    Specified by:
    
    scan in interface Scannable
    
    Parameters:
    
    rtok - Tokenizer from which to scan the spline
    
    ref - optional reference object (not used)
    
    Throws:
    
    java.io.IOException - if an I/O or formatting error occured
  - write
```
public void write(java.io.PrintWriter pw,
                  NumberFormat fmt,
                  java.lang.Object ref)
           throws java.io.IOException
```
    Writes a text description of this spline to a PrintWriter. The format is the same as that described for scan.
    
    Specified by:
    
    write in interface Scannable
    
    Parameters:
    
    pw - writer to which the spline should be written
    
    fmt - describes how the numbers should be formatted
    
    ref - optional reference object (not used)
    
    Throws:
    
    java.io.IOException - if an I/O error occured
  - isWritable
```
public boolean isWritable()
```
    Returns true if this component should in fact be written to secondary storage. This gives subclasses control over whether or not they are actually written out.
    
    Specified by:
    
    isWritable in interface Scannable
    
    Returns:
    
    true if this component should be written to secondary storage.
  - numKnots
```
public int numKnots()
```
    Returns the number of knots in this spline.
    
    Returns:
    
    number of knots
  - getKnot
```
public CubicHermiteSpline3d.Knot getKnot(int idx)
```
    Returns the idx-th knot in this spline.
    
    Parameters:
    
    idx - index of the requested knot
    
    Returns:
    
    idx-th knot
  - getFirstKnot
```
public CubicHermiteSpline3d.Knot getFirstKnot()
```
    Returns the first knot in this spline, or null if there are no knots.
    
    Returns:
    
    first knot
  - getLastKnot
```
public CubicHermiteSpline3d.Knot getLastKnot()
```
    Returns the last knot in this spline, or null if there are no knots.
    
    Returns:
    
    last knot
  - getS0
```
public double getS0()
```
    Returns the start value of the parameter controlling this spline.
    
    Returns:
    
    starting parameter value
  - getSLast
```
public double getSLast()
```
    Returns the last value of the parameter controlling this spline.
    
    Returns:
    
    last parameter value
  - getSLength
```
public double getSLength()
```
    Returns the length of the parameter interval controlling this spline.
    
    Returns:
    
    parameter interval length
  - iterator
```
public java.util.Iterator<CubicHermiteSpline3d.Knot> iterator()
```
    Returns an iterator for the knots in this spline.
    
    Specified by:
    
    iterator in interface java.lang.Iterable<CubicHermiteSpline3d.Knot>
    
    Returns:
    
    spline knot iterator
  - set
```
public void set(CubicHermiteSpline3d spline)
```
    Sets this spline to be a copy of another spline.
    
    Parameters:
    
    spline - spline to copy
  - getSampledValues
```
public java.util.ArrayList<Vector3d> getSampledValues(int numv)
```
    Creates and returns a list of values sampled uniformly along this spline.
    
    Parameters:
    
    numv - number of values to sample
  - copy
```
public CubicHermiteSpline3d copy()
```
    Creates a copy of this spline.
  - equals
```
public boolean equals(CubicHermiteSpline3d spline)
```
    Queries whether this spline is equal to another spline.
    
    Parameters:
    
    spline - spline to compare to this one
    
    Returns:
    
    true if the splines are equal
  - epsilonEquals
```
public boolean epsilonEquals(CubicHermiteSpline3d spline,
                             double tol)
```
    Queries whether this spline is equal to another spline within a specified absolute tolerance. Only the s0, a0 and a1 values of each knot are compared, since other values are derived from these.
    
    Parameters:
    
    spline - spline to compare to this one
    
    tol - absolute tolerance with which to compare the splines
    
    Returns:
    
    true if the splines are equal within tolerance

Class CubicHermiteSpline3d

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Methods inherited from interface java.lang.Iterable

Constructor Detail

CubicHermiteSpline3d

CubicHermiteSpline3d

CubicHermiteSpline3d

CubicHermiteSpline3d

Method Detail

set

setSingleSegment

setMultiSegment

addKnot

removeKnot

clearKnots

getPreceedingKnot

getPreceedingKnot

getNextKnot

eval

eval

evalDx

evalDx

evalDx2

evalDx2

scan

write

isWritable

numKnots

getKnot

getFirstKnot

getLastKnot

getS0

getSLast

getSLength

iterator

set

getSampledValues

copy

equals

epsilonEquals