maspack.geometry

Class LineSegment

java.lang.Object

maspack.geometry.Feature

maspack.geometry.LineSegment

All Implemented Interfaces:

Boundable

public class LineSegment
extends Feature
implements Boundable

Field Summary

Fields

Modifier and Type	Field and Description
Vertex3d	myVtx0
Vertex3d	myVtx1

Fields inherited from class maspack.geometry.Feature

CELL, EDGE, FACE, FACET, HALF_EDGE, LINE_SEGMENT, TYPE_MASK, UNKNOWN, VERTEX_3D, VISITED

Constructor Summary

Constructors

Constructor and Description
LineSegment(Vertex3d vtx0, Vertex3d vtx1)

Method Summary

Modifier and Type	Method and Description
void	computeCentroid(Vector3d centroid) Computed the centroid of this element.
double	computeCovariance(Matrix3d C) Computes covariance of this line segment and returns its length.
double	distance(Point3d pnt) Computes the distance of a point
static double	distance(Point3d p0, Point3d p1, Point3d px) Computes the distance of a point px to a line segment defined by points p0 and p1.
void	getDirection(Vector3d dir) Determine the line segment direction
double	getLength()
Point3d	getPoint(int idx) Returns the idx-th point associated with this element.
double	getProjectionParameter(Point3d pnt)
void	nearestPoint(Point3d nearest, Point3d pnt) Determine nearest point to this feature
static boolean	nearestPointParameters(double[] params, Point3d p0, Point3d p1, Point3d pa, Point3d pb) For two lines defined by the points p0, p1 and pa, pb, computes the parameters s and t such that
int	numPoints() Returns the number of points associated with this element, if any, or zero otherwise.
static double	projectionParameter(Point3d p0, Point3d p1, Point3d px) Computes the projection parameter of a point px with respect to a line defined by points p0 and p1.
void	updateBounds(Vector3d min, Vector3d max) Updates the axis-aligned bounds of this element.

Methods inherited from class maspack.geometry.Feature

checkFlag, clearFlag, clearVisited, getType, getTypeName, isVisited, setFlag, setVisited

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

myVtx0

public Vertex3d myVtx0

myVtx1

public Vertex3d myVtx1

Constructor Detail

LineSegment

public LineSegment(Vertex3d vtx0,
                   Vertex3d vtx1)

Method Detail

computeCentroid

public void computeCentroid(Vector3d centroid)

Description copied from interface: Boundable

Computed the centroid of this element.

Specified by:

computeCentroid in interface Boundable

Parameters:

centroid - returns the computed centroid value.

computeCovariance

public double computeCovariance(Matrix3d C)

Computes covariance of this line segment and returns its length.

The formula was determined by substituting the the parametric form for x

 x = (1-s) p0 + s p1
 

into the general formula for C

 C = \int_V \rho x x^T dV
 

and evaluating the integral over the s interval [0,1].

Specified by:

computeCovariance in interface Boundable

Parameters:

C - returns the covariance

Returns:

length of the line segment

getLength

public double getLength()

updateBounds

public void updateBounds(Vector3d min,
                         Vector3d max)

Description copied from interface: Boundable

Updates the axis-aligned bounds of this element. The value in min and max should be decreased or increased, respectively, so that all spatial points associated with this element lie within the axis-aligned box defined by min and max.

Specified by:

updateBounds in interface Boundable

Parameters:

min - minimum values to be updated

max - maximum values to be updated

numPoints

public int numPoints()

Description copied from interface: Boundable

Returns the number of points associated with this element, if any, or zero otherwise. If the element has points, then it's spatial extent is assumed to be enclosed within their convex hull. At present, elements that do not have points cannot be enclosed within oriented bounding box (OBB) trees.

Specified by:

numPoints in interface Boundable

Returns:

number of points associated with this element

getPoint

public Point3d getPoint(int idx)

Description copied from interface: Boundable

Returns the idx-th point associated with this element.

Specified by:

getPoint in interface Boundable

Parameters:

idx - index of the point (must be on the range 0 to Boundable.numPoints()).

Returns:

idx-th point associated with this element. Must not be modified.

getDirection

public void getDirection(Vector3d dir)

Determine the line segment direction

Parameters:

dir - direction vector to populate

projectionParameter

public static double projectionParameter(Point3d p0,
                                         Point3d p1,
                                         Point3d px)

Computes the projection parameter of a point px with respect to a line defined by points p0 and p1. This is the value s such that

 pp = (1-s) p0 + s p1
 

gives the projection of px-p0 onto the line. If p0 and p1 are identical, the method returns positive infinity.

Parameters:

p0 - first point defining the line

p1 - second point defining the libe

px - point for which the project parameter should be computed

Returns:

parameter s which projects px onto the line

nearestPointParameters

public static boolean nearestPointParameters(double[] params,
                                             Point3d p0,
                                             Point3d p1,
                                             Point3d pa,
                                             Point3d pb)

For two lines defined by the points p0, p1 and pa, pb, computes the parameters s and t such that

 ps = (1-s) p0 + s p1
 pt = (1-t) pa + t pb
 

are the points on the two lines which are nearest to each other. If the two lines are parallel, s and t are both set to 0 and the method returns false.

Parameters:

params - returns the values of s and t

p0 - first point defining the first line

p1 - second point defining the first line

pa - first point defining the second line

pb - second point defining the second line

Returns:

returns true if the lines are not parallel and false if they are

distance

public double distance(Point3d pnt)

Computes the distance of a point

Parameters:

pnt - point to compute nearest distance from

Returns:

nearest distance to point

distance

public static double distance(Point3d p0,
                              Point3d p1,
                              Point3d px)

Computes the distance of a point px to a line segment defined by points p0 and p1.

Parameters:

p0 - first point defining the segment

p1 - second point defining the segment

px - point to compute distance to

Returns:

distance of px from the segment

getProjectionParameter

public double getProjectionParameter(Point3d pnt)

nearestPoint

public void nearestPoint(Point3d nearest,
                         Point3d pnt)

Description copied from class: Feature

Determine nearest point to this feature

Specified by:

nearestPoint in class Feature

Parameters:

nearest - populated nearest point

pnt - point to check distance to