de.grogra.vecmath.geom
Class Sphere

java.lang.Object
  de.grogra.vecmath.geom.VolumeBase
      de.grogra.vecmath.geom.TransformableVolume
          de.grogra.vecmath.geom.Sphere

All Implemented Interfaces:

Volume

public class Sphere
extends TransformableVolume

This class represents the geometry of a sphere. In local object coordinates, its center is the origin, its radius is 1.

Author:

Ole Kniemeyer

Field Summary

Fields inherited from class de.grogra.vecmath.geom.TransformableVolume

m00, m01, m02, m10, m11, m12, m20, m21, m22, t0, t1, t2

Constructor Summary

Sphere()

Method Summary

boolean	boxContainsBoundary(BoundingBox box, Tuple3d center, double radius, Variables temp) Returns true if the specified box contains (part of) the boundary surface of this volume.
boolean	computeIntersections(Line line, int which, IntersectionList list, Intersection excludeStart, Intersection excludeEnd) Computes intersections between the boundary surface of this object and the specified line.
void	computeNormal(Intersection is, Vector3d normal) This method computes the unit normal vector of an intersection is which has been computed previously by the invocation of Volume.computeIntersections(de.grogra.vecmath.geom.Line, int, de.grogra.vecmath.geom.IntersectionList, de.grogra.vecmath.geom.Intersection, de.grogra.vecmath.geom.Intersection) on this volume.
void	computeTangents(Intersection is, Vector3d dpdu, Vector3d dpdv) This method computes the derivatives of the surface point (as function of the uv-coordinates, see Volume.computeUV(de.grogra.vecmath.geom.Intersection, javax.vecmath.Vector2d)) with respect to u and v at the intersection point.
void	computeUV(Intersection is, Vector2d uv) This method computes the uv-coordinates of an intersection point is which has been computed previously by the invocation of Volume.computeIntersections(de.grogra.vecmath.geom.Line, int, de.grogra.vecmath.geom.IntersectionList, de.grogra.vecmath.geom.Intersection, de.grogra.vecmath.geom.Intersection) on this volume.
boolean	contains(Tuple3d point, boolean open) Determines if the given point lies within this object.
void	getExtent(Tuple3d min, Tuple3d max, Variables temp) Computes the extent of this volume, i.e., an axis-aligned bounding box between min and max.

Methods inherited from class de.grogra.vecmath.geom.TransformableVolume

getDiscExtent, getDiscsExtent, getFrobeniusNorm, getObjectToWorldRotationScale, getTransformation, invalidate, invTransformPoint, scale, setTransformation, setTransformation, transformPoint, transformTranspose, transformVector, translate

Methods inherited from class de.grogra.vecmath.geom.VolumeBase

addConvexIntersections, getId, operator$and, operator$com, operator$or, operator$sub, setId

Methods inherited from class java.lang.Object

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

Constructor Detail

Sphere

public Sphere()

Method Detail

boxContainsBoundary

public boolean boxContainsBoundary(BoundingBox box,
                                   Tuple3d center,
                                   double radius,
                                   Variables temp)

Description copied from interface: Volume

Returns true if the specified box contains (part of) the boundary surface of this volume. Otherwise, if box and boundary do not overlap, this method should return false, but may also return true if an exact computation would be too expensive or complicated.

Note that a box contains the boundary of a closed set S iff both have a non-empty intersection and the box is not contained in the open set of S.

Parameters:

box - bounding box

center - center coordinates of box

radius - radius of enclosing sphere

temp - has to be provided by the invoker, may be used in implementations

Returns:

true if box contains (part of) the boundary of this volume

computeIntersections

public boolean computeIntersections(Line line,
                                    int which,
                                    IntersectionList list,
                                    Intersection excludeStart,
                                    Intersection excludeEnd)

Description copied from interface: Volume

Computes intersections between the boundary surface of this object and the specified line. The intersections are added to list in ascending order of distance (i.e., of Intersection.parameter), where the parameter has to lie between line.start and line.end. Implementations of this method must not clear or modify the existing intersections in list.

The parameter which has to be one of Intersection.ALL, Intersection.CLOSEST, Intersection.ANY. It determines if all intersections have to be added to the list, only the closest (minimal value of Intersection.parameter), or an arbitrary of the set of all intersections. Only in case of ALL, the return value of this method is precise.

If specific intersection points should be excluded from the list of computed intersections, they have to be specified in excludeStart and excludeEnd. The intersection point of excludeStart has to be the starting point of line, the intersection point of excludeEnd has to be the end point of line. The exclusion of intersections is a useful feature for ray-tracing, e.g., when a ray is re-emitted at an intersection point in another direction.

Parameters:

line - a line

which - one of Intersection.ALL, Intersection.CLOSEST, Intersection.ANY, this determines which intersections have to be added to list

list - the intersections are added to this list

excludeStart - intersection at start point which shall be excluded, or null

excludeEnd - intersection at end point which shall be excluded, or null

Returns:

true iff the beginning of the line lies within the volume (i.e., if the line starts within the volume or enters the volume at the starting point); however note that the returned value is valid only if which == Intersection.ALL

computeNormal

public void computeNormal(Intersection is,
                          Vector3d normal)

Description copied from interface: Volume

This method computes the unit normal vector of an intersection is which has been computed previously by the invocation of Volume.computeIntersections(de.grogra.vecmath.geom.Line, int, de.grogra.vecmath.geom.IntersectionList, de.grogra.vecmath.geom.Intersection, de.grogra.vecmath.geom.Intersection) on this volume.

Parameters:

is - a previously computed intersection

normal - resulting unit vector is placed in here

computeTangents

public void computeTangents(Intersection is,
                            Vector3d dpdu,
                            Vector3d dpdv)

Description copied from interface: Volume

This method computes the derivatives of the surface point (as function of the uv-coordinates, see Volume.computeUV(de.grogra.vecmath.geom.Intersection, javax.vecmath.Vector2d)) with respect to u and v at the intersection point.

Parameters:

is - a previously computed intersection

dpdu - resulting derivative with respect to u

dpdv - resulting derivative with respect to v

computeUV

public void computeUV(Intersection is,
                      Vector2d uv)

Description copied from interface: Volume

This method computes the uv-coordinates of an intersection point is which has been computed previously by the invocation of Volume.computeIntersections(de.grogra.vecmath.geom.Line, int, de.grogra.vecmath.geom.IntersectionList, de.grogra.vecmath.geom.Intersection, de.grogra.vecmath.geom.Intersection) on this volume.

Parameters:

is - a previously computed intersection

uv - resulting uv-coordinates are placed in here

contains

public boolean contains(Tuple3d point,
                        boolean open)

Description copied from interface: Volume

Determines if the given point lies within this object. If open is true, the interior of the volume is considered (the largest open set contained in the volume, i.e., excluding the boundary), otherwise the closure of the volume.

Parameters:

point - a point in global world coordinates

open - consider open or closed set

Returns:

true iff point is an element of the set

getExtent

public void getExtent(Tuple3d min,
                      Tuple3d max,
                      Variables temp)

Description copied from interface: Volume

Computes the extent of this volume, i.e., an axis-aligned bounding box between min and max.

Parameters:

min - minimum coordinates of bounding box are placed in here

max - maximum coordinates of bounding box are placed in here

temp - has to be provided by the invoker, may be used in implementations