root/trunk/dep/include/g3dlite/G3D/CollisionDetection.h @ 2

/**
  @file CollisionDetection.h


  Moving collision detection for simple primitives.

  @author Morgan McGuire, matrix@graphics3d.com
  @cite Spherical collision based on Paul Nettle's
  ftp://ftp.3dmaileffects.com/pub/FluidStudios/CollisionDetection/Fluid_Studios_Generic_Collision_Detection_for_Games_Using_Ellipsoids.pdf
  and comments by Max McGuire.  Ray-sphere intersection by Eric Haines.
  Box-Box intersection written by Kevin Egan.
  Thanks to Max McGuire of Iron Lore for various bug fixes.

  @created 2001-11-19
  @edited  2006-01-10

  Copyright 2000-2006, Morgan McGuire.
  All rights reserved.
 */

#ifndef G3D_COLLISIONDETECTION_H
#define G3D_COLLISIONDETECTION_H

#include "G3D/platform.h"
#include "G3D/Vector3.h"
#include "G3D/Plane.h"
#include "G3D/Box.h"
#include "G3D/Triangle.h"
#include "G3D/Array.h"
#include "G3D/Ray.h"
#include "G3D/Line.h"

namespace G3D {


/**
  Collision detection primitives and tools for building
  higher order collision detection schemes.

  These routines provide <I>moving</I> and static collision detection.
  Moving collision detection allows the calculation of collisions that
  occur during a period of time -- as opposed to the intersection of 
  two static bodies.
  
  Moving collision detection routines detect collisions between
  <I>only</I> static primitives and moving spheres or points.  Since the 
  reference frame can be user defined, these functions can be used to
  detect the collision between two moving bodies by subtracting
  the velocity vector of one object from the velocity vector of the 
  sphere or point the detection is to occur with.  This unified 
  velocity vector will act as if both objects are moving simultaneously.

  Collisions are detected for single-sided objects only.  That is,
  no collision is detected when <I>leaving</I> a primitive or passing
  through a plane or triangle opposite the normal... except for the 
  point-sphere calculation or when otherwise noted.

  For a sphere, the collision location returned is the point in world
  space where the surface of the sphere and the fixed object meet.
  It is <B>not</B> the position of the center of the sphere at
  the time of the collision.

  The collision normal returned is the surface normal to the fixed
  object at the collision location.

  <p>
  <b>Static Collision Detection:</b> (Neither object is moving)

  <table>
  <tr><td></td><td><b>Vector3</b></td><td><b>LineSegment</b></td><td><b>Ray *</b></td><td><b>Line</b></td><td><b>Plane</b></td><td><b>Triangle</b></td><td><b>Sphere</b></td><td><b>Cylinder</b></td><td><b>Capsule</b></td><td><b>AABox</b></td><td><b>Box</b></td></tr>
  <tr><td><b>Vector3</b></td><td>Vector3::operator== Vector3::fuzzyEq G3D::distance</td><td bgcolor=#C0C0C0 colspan=10 ></td></tr>
  <tr><td><b>LineSegment</b></td><td>LineSegment::closestPoint LineSegment::distance CollisionDetection::closestPointOnLineSegment</td><td></td><td bgcolor=#C0C0C0 colspan=9 ></td></tr>
  <tr><td><b>Ray *</b></td><td>Ray::closestPoint Ray::distance</td><td></td><td></td><td bgcolor=#C0C0C0 colspan=8 ></td></tr>
  <tr><td><b>Line</b></td><td>Line::closestPoint Line::distance</td><td></td><td>CollisionDetection::closestPointsBetweenLineAndLine</td><td></td><td bgcolor=#C0C0C0 colspan=7 ></td></tr>
  <tr><td><b>Plane</b></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=6 ></td></tr>
  <tr><td><b>Triangle</b></td><td></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=5 ></td></tr>
  <tr><td><b>Sphere</b></td><td>Sphere::contains</td><td></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=4 ></td></tr>
  <tr><td><b>Cylinder</b></td><td>Cylinder::contains</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=3 ></td></tr>
  <tr><td><b>Capsule</b></td><td>Capsule::contains</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=2 ></td></tr>
  <tr><td><b>AABox</b></td><td>AABox::contains</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td bgcolor=#C0C0C0 colspan=1 ></td></tr>
  <tr><td><b>Box</b></td><td>Box::contains</td><td>(treat as Ray)</td><td>CollisionDetection::collisionTimeForMovingPointFixedBox</td><td>(treat as Ray)</td><td>CollisionDetection::penetrationDepthForFixedBoxFixedPlane</td><td>CollisionDetection::penetrationDepthForFixedBoxFixedPlane</td><td>CollisionDetection::penetrationDepthForFixedSphereFixedBox</td><td>None (use OPCODE)</td><td>CollisionDetection::movingSpherePassesThroughFixedBox</td><td>CollisionDetection::penetrationDepthForFixedBoxFixedBox</td><td>CollisionDetection::penetrationDepthForFixedBoxFixedBox</td></tr>
  </table>

  <p>
  <b>Moving Collision Detection:</b>

  <i>* Note: Moving collision detection against certain primitives is equivalent to static collision
   detection against a bigger primitive.  Ray, Line Segment == ``moving Point''; Capsule ==``moving Sphere''; Plane == ``moving Line''</i>
 */
class CollisionDetection {
private:

        /**
         Default parameter if value passed to a function as reference is
         not to be calculated.  Must be explicitly supported by function.
         */
        static Vector3 ignore;

        /**
         Default parameter if value passed to a function as reference is
         not to be calculated.  Must be explicitly supported by function.
         */
    static bool    ignoreBool;

        /**
         Default parameter if value passed to a function as reference is
         not to be calculated.  Must be explicitly supported by function.
         */
    static Array<Vector3> ignoreArray;


    // Static class!
    CollisionDetection() {}
    virtual ~CollisionDetection() {}

public:

    /**
      Converts an index [0, 15] to the corresponding separating axis.
      Does not return normalized vector in the edge-edge case
      (indices 6 through 15).

          @param separatingAxisIndex    Separating axis.
          @param box1                                   Box 1.
          @param box2                                   Box 2.

          @return Axis that separates the two boxes.
         */
    static Vector3 separatingAxisForSolidBoxSolidBox(
            const int       separatingAxisIndex,
            const Box &     box1,
            const Box &     box2);

    /**
          Tests whether two boxes have axes that are parallel to
          each other.  If they are, axis1 and axis2 are set to be
          the parallel axes for both box1 and box2 respectively.

          @param ca                     Dot products of each of the boxes axes
          @param epsilon        Fudge factor (small unit by which the dot
                                                products may vary and still be considered
                                                zero).
          @param axis1          Parallel Axis 1. [Post Condition]
          @param axis2          Parallel Axis 2. [Post Condition]

          @return true  - If boxes have a parallel axis
          @return false - otherwise.
         */
    static bool parallelAxisForSolidBoxSolidBox(
            const double*   ca,
            const double    epsilon,
            int &           axis1,
            int &           axis2);

    /**
      Calculates the projected distance between the two boxes along
      the specified separating axis, negative distances correspond
      to an overlap along that separating axis.  The distance is not
      divided by denominator dot(L, L), see
      penetrationDepthForFixedSphereFixedBox() for more details

      @param separatingAxisIndex
          @param a Box 1's bounding sphere vector
          @param b Box 2's bounding sphere vector
          @param D Vector between Box 1 and Box 2's center points
          @param c Pointer to array of dot products of the axes of Box 1
                   and Box 2.
          @param ca Pointer to array of unsigned dot products of the axes
                    of Box 1 and Box 2.
          @param ad Pointer to array of dot products of Box 1 axes and D.
          @param bd Pointer to array of dot products of Box 2 axes and D.

      @return Projected distance between the two boxes along the
      specified separating axis.
     */
    static float projectedDistanceForSolidBoxSolidBox(
            const int           separatingAxisIndex,
            const Vector3 &     a,
            const Vector3 &     b,
            const Vector3 &     D,
            const double*       c,
            const double*       ca,
            const double*       ad,
            const double*       bd);


        /**
          Creates a set of standard information about two boxes in order to
          solve for their collision.  This information includes a vector to
          the radius of the bounding sphere for each box, the vector between
          each boxes' center and a series of dot products between differing
          important vectors.  These dot products include those between the axes
          of both boxes (signed and unsigned values), and the dot products
          between all the axes of box1 and the boxes' center vector and box2
          and the boxes' center vector.

          @pre The following space requirements must be met:
                - c[]  9 elements
                - ca[] 9 elements
                - ad[] 3 elements
                - bd[] 3 elements

          @cite dobted from David Eberly's papers, variables used in this function
      correspond to variables used in pages 6 and 7 in the pdf
      http://www.magic-software.com/Intersection.html
      http://www.magic-software.com/Documentation/DynamicCollisionDetection.pdf

      @note Links are out-dated. (Kept to preserve origin and authorship)

          @param box1 Box 1
          @param box2 Box 2
          @param a Box 1's bounding sphere vector
          @param b Box 2's bounding sphere vector
          @param D Vector between Box 1 and Box 2's center points
          @param c Pointer to array of dot products of the axes of Box 1
                   and Box 2.
          @param ca Pointer to array of unsigned dot products of the axes
                    of Box 1 and Box 2.
          @param ad Pointer to array of dot products of Box 1 axes and D.
          @param bd Pointer to array of dot products of Box 2 axes and D.
         */
    static void fillSolidBoxSolidBoxInfo(
            const Box &     box1,
            const Box &     box2,
            Vector3 &       a,
            Vector3 &       b,
            Vector3 &       D,
            double*         c,
            double*         ca,
            double*         ad,
            double*         bd);

        /**
          Performs a simple bounding sphere check between two boxes to determine
          whether these boxes could <i>possibly</i> intersect.  This is a very
          cheap operation (three dot products, two sqrts and a few others).  If
          it returns true, an intersection is possible, but not necessarily
          guaranteed.

          @param a Vector from box A's center to an outer vertex
          @param b Vector from box B's center to an outer vertex
          @param D Distance between the centers of the two boxes

          @return true - if possible intersection
          @return false - otherwise (This does not guarantee an intersection)
         */
    static bool conservativeBoxBoxTest(
            const Vector3 &     a,
            const Vector3 &     b,
            const Vector3 &     D);

        /**
          Determines whether two fixed solid boxes intersect.

      @note To speed up collision detection, the lastSeparatingAxis from
      the previous time step can be passed in and that plane can be
      checked first.  If the separating axis was not saved, or if the
      two boxes intersected then lastSeparatingAxis should equal -1.

          @cite Adobted from David Eberly's papers, variables used in this function
      correspond to variables used in pages 6 and 7 in the pdf
      http://www.magic-software.com/Intersection.html
      http://www.magic-software.com/Documentation/DynamicCollisionDetection.pdf

          @param box1                           Box 1.
          @param box2                           Box 2.
          @param lastSeparatingAxis     Last separating axis.
                                                                (optimization - see note)

          @return true  - Intersection.
          @return false - otherwise.
         */
    static bool fixedSolidBoxIntersectsFixedSolidBox(
        const Box&      box1,
        const Box&      box2,
        const int       lastSeparatingAxis = -1);

    /**
          Calculates the closest points on two lines with each other.   If the
          lines are parallel then using the starting point, else calculate the
          closest point on each line to the other.

          @note This is very similiar to calculating the intersection of two lines.
          Logically then, the two points calculated would be identical if calculated
          with inifinite precision, but with the finite precision of floating point
          calculations, these values could (will) differ as the line slope approaches
          zero or inifinity.

          @cite variables and algorithm based on derivation at the following website:
            http://softsurfer.com/Archive/algorithm_0106/algorithm_0106.htm

          @param line1          Line 1.
          @param line2          Line 2.
          @param closest1       Closest point on line 1.
          @param closest2       Closest point on line 2.
        */
    static void closestPointsBetweenLineAndLine(
            const Line &    line1,
            const Line &    line2,
            Vector3 &       closest1,
            Vector3 &       closest2);

    /**
          Calculates the depth of penetration between two fixed boxes.
      Contact normal faces away from box1 and into box2.  If there is
      contact, only one contact point is returned.  The minimally
      violated separating plane is computed
         - if the separating axis corresponds to a face
              the contact point is half way between the deepest vertex
              and the face
         - if the separating axis corresponds to two edges
              the contact point is the midpoint of the smallest line
              segment between the two edge lines

          @note This is very similiar to calculating the intersection of two lines.
          Logically then, the two points calculated would be identical if calculated
          with inifinite precision, but with the finite precision of floating point
          calculations, these values could (will) differ as the line slope approaches
          zero or inifinity.

          @cite adobted from David Eberly's papers, variables used in this function
      correspond to variables used in pages 6 and 7 in the pdf
      http://www.magic-software.com/Intersection.html
      http://www.magic-software.com/Documentation/DynamicCollisionDetection.pdf

          @param box1                           Box 1
          @param box2                           Box 2
          @param contactPoints          Contact point between boxes. [Post Condition]
          @param contactNormals         Surface normal at contact point. [Post Condition]
          @param lastSeparatingAxis     Last separating axis. (Used for optimization)

          @return Depth of penetration between the two boxes.  If there is no
           intersection between the boxes, then a negative value is returned.
        */
    static float penetrationDepthForFixedBoxFixedBox(
        const Box&          box1,
        const Box&          box2,
        Array<Vector3>&     contactPoints,
        Array<Vector3>&     contactNormals,
        const int           lastSeparatingAxis = -1);

    /**
          Calculates the depth of penetration between two fixed spheres as well
          as the deepest point of Sphere A that penetrates Sphere B. The normal
      returned points <B>away</B> from the object A, although it may
      represent a perpendicular to either the faces of object B or object A
      depending on their relative orientations.

          @param sphereA                Fixed Sphere A.
          @param sphereB                Fixed Sphere B.
          @param contactPoints  Sphere A's deepest point that penetrates Sphere B.
                                                        [Post Condition]
          @param contactNormals Normal at penetration point. [Post Condition]

          @return Depth of penetration.  If there is no intersection between the
                         objects then the depth will be a negative value.
         */
    static float penetrationDepthForFixedSphereFixedSphere(
        const class Sphere& sphereA,
        const Sphere&       sphereB,
        Array<Vector3>&     contactPoints,
        Array<Vector3>&     contactNormals = ignoreArray);

    /**
          Calculates the depth of penetration between a fixed sphere and a fixed
          box as well as the deepest point of the sphere that penetrates the box
          and the normal at that intersection.

          @note There are three possible intersections between a sphere and box.
          - Sphere completely contained in the box
          - Sphere intersects one edge
          - Sphere intersects one vertex

          The contact point and contact normal vary for each of these situations.
          - Sphere contained in Box:
                - Normal is based on side of least penetration (as is the depth calculation).
                - Point is based on center of sphere
          - Sphere intersects one edge
                - Normal is based on vector from the box center to the point of depth.
                - Point is closest point to the sphere on the line
          - Sphere intersects one vertex
                - Normal is based on vector from the box center to the vertex of penetration.
                - Point is vertex of penetration.

      @cite Adapted from Jim Arvo's method in Graphics Gems
      See also http://www.win.tue.nl/~gino/solid/gdc2001depth.pdf

          @param sphere                 Fixed Sphere.
          @param box                    Fixed Box.
          @param contactPoints  Sphere point that penetrates the box. [Post Condition]
          @param contactNormals Normal at the penetration point. [Post Condition]

          @return Depth of penetration.  If there is no intersection between the
                          objects then the depth will be a negative value.
         */
    static float penetrationDepthForFixedSphereFixedBox(
        const Sphere&       sphere,
        const Box&          box,
        Array<Vector3>&     contactPoints,
        Array<Vector3>&     contactNormals = ignoreArray);

        /**
          Calculates the depth of penetration between a Fixed Sphere and a Fixed
          Plane as well as the deepest point of the sphere that penetrates the plane
          and the plane normal at that intersection.

          @param sphere                 Fixed Sphere.
          @param plane                  Fixed Plane.
          @param contactPoints  Sphere point that penetrates the plane.
                                                        [Post Condition]
          @param contactNormals Normal at penetration point. [Post Condition]

          @return Depth of penetration.  If there is no intersection between the
                         objects then the depth will be a negative value.
         */
    static float penetrationDepthForFixedSphereFixedPlane(
        const Sphere&       sphereA,
        const class Plane&  planeB,
        Array<Vector3>&     contactPoints,
        Array<Vector3>&     contactNormals = ignoreArray);

        /**
          Calculates the depth of penetration between a fixed box and a fixed
          plane as well as the vertexes of the box that penetrate the plane
          and the plane normals at those intersections.

          @param box                    Fixed Box.
          @param plane                  Fixed Plane.
          @param contactPoints  Box points that penetrate the plane.
                                                        [Post Condition]
          @param contactNormals Normals at penetration points [Post Condition]

          @return Depth of penetration.  If there is no intersection between the
                         objects then the depth will be a negative value.
        */
    static float penetrationDepthForFixedBoxFixedPlane(
        const Box&          box,
        const Plane&        plane,
        Array<Vector3>&     contactPoints,
        Array<Vector3>&     contactNormals = ignoreArray);

        /**
          Calculates time between the intersection of a moving point and a fixed
          plane.

          @note This is only a one sided collision test.   The side defined by
          the plane's surface normal is the only one tested.  For a two sided
          collision, call the function once for each side's surface normal.

          @param point          Moving point.
          @param velocity       Point's velocity.
          @param plane          Fixed plane.
          @param location       Location of collision. [Post Condition]
                                                (Infinite vector on no collision)
          @param outNormal      Plane's surface normal. [Post Condition]

          @return Time til collision.  If there is no collision then the return
                  value will be inf().
        */
    static float collisionTimeForMovingPointFixedPlane(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const class Plane&              plane,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
          Calculates time between the intersection of a moving point and a fixed
          triangle.

          @note This is only a one sided collision test.   The side defined by
          the triangle's surface normal is the only one tested.  For a two sided
          collision, call the function once for each side's surface normal.

          @param orig           Moving point.
          @param dir            Point's velocity.
          @param v0             Triangle vertex 1.
          @param v1             Triangle vertex 2.
          @param v2             Triangle vertex 3
          @param location       Location of collision. [Post Condition]
                                                (Infinite vector on no collision)

          @return Time til collision.  If there is no collision then the return
                  value will be inf().
        */
    inline static float collisionTimeForMovingPointFixedTriangle(
        const Vector3& orig,
        const Vector3& dir,
        const Vector3& v0,
        const Vector3& v1,
        const Vector3& v2) {
        return Ray::fromOriginAndDirection(orig, dir).intersectionTime(v0, v1, v2);
    }

        /**
          Calculates time between the intersection of a moving point and a fixed
          triangle.

          @note This is only a one sided collision test.   The side defined by
          the triangle's surface normal is the only one tested.  For a two sided
          collision, call the function once for each side's surface normal.

          @param orig           Moving point.
          @param dir            Point's velocity.
          @param v0             Triangle vertex 1.
          @param v1             Triangle vertex 2.
          @param v2             Triangle vertex 3
          @param location       Location of collision. [Post Condition]
                                                (Infinite vector on no collision)

          @return Time til collision.  If there is no collision then the return
                  value will be inf().
        */
    inline static float collisionTimeForMovingPointFixedTriangle(
        const Vector3& orig,
        const Vector3& dir,
        const Vector3& v0,
        const Vector3& v1,
        const Vector3& v2,
        Vector3&       location) {
        float t = collisionTimeForMovingPointFixedTriangle(orig, dir, v0, v1, v2);
        if (t < inf()) {
            location = orig + dir * t;
        }
        return t;
    }

        /**
          Calculates time between the intersection of a moving point and a fixed
          triangle.

          @note This is only a one sided collision test.   The side defined by
          the triangle's surface normal is the only one tested.  For a two sided
          collision, call the function once for each side's surface normal.

          @param orig           Moving point.
          @param dir            Point's velocity.
          @param tri            Fixed triangle.
          @param location       Location of collision. [Post Condition]
                                                (Infinite vector on no collision)
          @param normal         Triangle's surface normal. [Post Condition]

          @return Time til collision.  If there is no collision then the return
                  value will be inf().
        */
    inline static float collisionTimeForMovingPointFixedTriangle(
        const Vector3&  orig,
        const Vector3&  dir,
        const Triangle& tri,
        Vector3&        location = ignore,
        Vector3&        normal   = ignore) {

        float t = collisionTimeForMovingPointFixedTriangle(
            orig, dir, tri.vertex(0), tri.vertex(1), tri.vertex(2));
        
        if ((t < inf()) && (&location != &ignore)) {
            location = orig + dir * t;
            normal   = tri.normal();
        }
        return t;
    }

        /**
          Calculates time between the intersection of a moving point and a fixed
          triangle.

          @note This is only a one sided collision test.   The side defined by
          the triangle's surface normal is the only one tested.  For a two sided
          collision, call the function once for each side's surface normal.

          @param orig           Moving point.
          @param dir            Point's velocity.
          @param v0             Triangle vertex 1.
          @param v1             Triangle vertex 2.
          @param v2             Triangle vertex 3
          @param location       Location of collision. [Post Condition]
                                                (Infinite vector on no collision)
          @param normal         Triangle's surface normal. [Post Condition]

          @return Time til collision.  If there is no collision then the return
                  value will be inf().
        */
    inline static float collisionTimeForMovingPointFixedTriangle(
        const Vector3& orig,
        const Vector3& dir,
        const Vector3& v0,
        const Vector3& v1,
        const Vector3& v2,
        Vector3&       location,
        Vector3&       normal) {
        float t = collisionTimeForMovingPointFixedTriangle(orig, dir, v0, v1, v2);
        if (t < inf()) {
            location = orig + dir * t;
            normal   = (v2 - v0).cross(v1 - v0).direction();
        }
        return t;
    }

    /**
     Unlike other methods, does not support an output normal.
     If the ray origin is inside the box, returns inf() but inside
     is set to true.
     <B>Beta API</B>

     @cite Andrew Woo, from "Graphics Gems", Academic Press, 1990
         @cite Optimized code by Pierre Terdiman, 2000 (~20-30% faster on my Celeron 500)
     @cite Epsilon value added by Klaus Hartmann
     @cite http://www.codercorner.com/RayAABB.cpp
     */
    static float collisionTimeForMovingPointFixedAABox(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const class AABox&      box,
        Vector3&                                outLocation,
        bool&                   inside = ignoreBool,
        Vector3&                outNormal = ignore);

    /**
         Calculates time between the intersection of a moving point and a fixed
         Axis-Aligned Box (AABox).

         @note Avoids the sqrt from collisionTimeForMovingPointFixedAABox.

         @param point           Moving point.
         @param velocity        Sphere's velocity.
         @param box                     Fixed AAbox.
         @param location        Location of collision. [Post Condition]
         @param Inside          Does the ray originate inside the box? [Post Condition]
         @param normal          Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static bool collisionLocationForMovingPointFixedAABox(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const class AABox&      box,
        Vector3&                                outLocation,
        bool&                   inside = ignoreBool,
        Vector3&                normal = ignore);

    /**
         Calculates time between the intersection of a moving point and a fixed
         sphere.

         @note When ray is starts inside the rectangle, the exiting intersection
         is detected.

         @param point           Moving point.
         @param velocity        Point's velocity.
         @param Sphere          Fixed Sphere.
         @param location        Location of collision. [Post Condition]
         @param outNormal       Sphere's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingPointFixedSphere(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const class Sphere&             sphere,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

    /**
         Calculates time between the intersection of a moving point and a fixed
         box.

         @note If the point is already inside the box, no collision: inf is returned.

         @param point           Moving point.
         @param velocity        Sphere's velocity.
         @param box                     Fixed box.
         @param location        Position of collision. [Post Condition]
         @param outNormal       Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingPointFixedBox(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const class  Box&               box,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving point and a fixed
         rectangle defined by the points v0, v1, v2, & v3.

         @note This is only a one sided collision test.   The side defined by
         the rectangle's surface normal is the only one tested.  For a two sided
         collision, call the function once for each side's surface normal.

         @param point           Moving point.
         @param velocity        Sphere's velocity.
         @param v0                      Rectangle vertex 1.
         @param v1                      Rectangle vertex 2.
         @param v2                      Rectangle vertex 3
         @param v3                      Rectangle vertex 4.
         @param location        Location of collision [Post Condition]
         @param outNormal       Rectangle's surface normal. [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingPointFixedRectangle(
        const Vector3&                  point,
        const Vector3&                  velocity,
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  v3,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving point and a fixed
         capsule.

         @param point           Moving point.
         @param velocity        Point's velocity.
         @param capsule         Fixed capsule.
         @param location        Location of collision. [Post Condition]
         @param outNormal       Capsule's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
        static float collisionTimeForMovingPointFixedCapsule(
                const Vector3&              point,
                const Vector3&              velocity,
                const class Capsule&    capsule,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving sphere and a fixed
         triangle.

         @param sphere          Moving sphere.
         @param velocity        Sphere's velocity.
         @param plane           Fixed Plane.
         @param location        Location of collision -- not center position of sphere
                                                at the collision time. [Post Condition]
         @param outNormal       Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
         */
    static float collisionTimeForMovingSphereFixedPlane(
        const class Sphere&             sphere,
        const Vector3&          velocity,
        const class Plane&              plane,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving sphere and a fixed
         triangle.

         @param sphere          Moving sphere.
         @param velocity        Sphere's velocity.
         @param triangle        Fixed Triangle.
         @param location        Location of collision -- not center position of sphere
                                                at the collision time. [Post Condition]
         @param outNormal       Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingSphereFixedTriangle(
        const class Sphere&             sphere,
        const Vector3&              velocity,
        const Triangle&       triangle,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving sphere and a fixed
         rectangle defined by the points v0, v1, v2, & v3.

         @param sphere          Moving sphere.
         @param velocity        Sphere's velocity.
         @param v0                      Rectangle vertex 1.
         @param v1                      Rectangle vertex 2.
         @param v2                      Rectangle vertex 3
         @param v3                      Rectangle vertex 4.
         @param location        Location of collision -- not center position of sphere
                                                at the collision time. [Post Condition]
         @param outNormal       Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingSphereFixedRectangle(
        const class Sphere&             sphere,
        const Vector3&          velocity,
        const Vector3&          v0,
        const Vector3&          v1,
        const Vector3&          v2,
        const Vector3&          v3,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

        /**
         Calculates time between the intersection of a moving sphere and a fixed
         box.

         @note This function will not detect an intersection between a moving object
         that is already interpenetrating the fixed object.

         @param sphere          Moving sphere.
         @param velocity        Sphere's velocity.
         @param box                     Fixed box.
         @param location        Location of collision -- not center position of sphere
                                                at the collision time. [Post Condition]
         @param outNormal       Box's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
    static float collisionTimeForMovingSphereFixedBox(
        const class Sphere&             sphere,
        const Vector3&              velocity,
        const class Box&                box,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

    /**
         Calculates time between the intersection of a moving sphere and a fixed
         sphere.

         @note This won't detect a collision if the sphere is already interpenetrating
               the fixed sphere.

         @param movingSphere    Moving sphere.
         @param velocity                Sphere's velocity.
         @param fixedSphere             Fixed Sphere.
         @param location                Location of collision -- not center position of sphere
                                                        at the collision time. [Post Condition]
         @param outNormal               Sphere's surface normal to collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
        static float collisionTimeForMovingSphereFixedSphere(
                const class Sphere&             sphere,
                const Vector3&              velocity,
                const class Sphere&         fixedSphere,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

    /**
         Calculates time between the intersection of a moving sphere and a fixed
         capsule.

         @note This won't detect a collision if the sphere is already
               interpenetrating the capsule.

         @param sphere          Moving sphere.
         @param velocity        Sphere's velocity.
         @param capsule         Fixed capsule.
         @param location        Location of collision -- not center position of sphere
                                                at the collision time. [Post Condition]
         @param outNormal       Capsule's surface normal to the collision [Post Condition]

         @return Time til collision.  If there is no collision then the return
                 value will be inf().
        */
        static float collisionTimeForMovingSphereFixedCapsule(
                const class Sphere&             sphere,
                const Vector3&              velocity,
                const class Capsule&    capsule,
        Vector3&                                outLocation,
        Vector3&                outNormal = ignore);

    /**
         Finds the direction of bounce that a sphere would have when it 
         intersects an object with the  given time of collision, the 
         collision location and the collision normal.

         @note This function works like a pong style ball bounce.

         @param sphere                          Moving sphere.
         @param velocity                        Sphere's velocity.
         @param collisionTime           Time of collision.
         @param collisionLocation       Collision location.
         @param collisionNormal         Surface collision normal.

         @return Direction of bounce.
        */
    static Vector3 bounceDirection(
        const class Sphere&             sphere,
        const Vector3&                  velocity,
        const float                             collisionTime,
        const Vector3&                  collisionLocation,
        const Vector3&          collisionNormal);

    /**
         Finds the direction of slide given a moving sphere, its velocity, the
         time of collision and the collision location.  This function works as
         if the sphere intersects the surface and continues to hug it.

         @note The result will work well for calculating the movement of a player
         who collides with an object and continues moving along the object instead
         of just bouncing off it.

         @param sphere                          Moving sphere.
         @param velocity                        Sphere's velocity.
         @param collisionTime           Time of collision
         @param collisionLocation       Collision location.

         @return Direction of slide.
        */
    static Vector3 slideDirection(
        const class Sphere&             sphere,
        const Vector3&                  velocity,
        const float                             collisionTime,
        const Vector3&                  collisionLocation);

        /**
         Finds the closest point on a line segment to a given point.

         @param v0 line vertex 1.
         @param v1 line vertex 2.
         @param point External point.

         @return Closests point to <code>point</code> on the line segment.
        */
        static Vector3 closestPointOnLineSegment(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  point);

    /**
         Finds the closest point on a line segment to a given point.

         @note This is an optimization to closestPointOnLineSegment.  Edge length
         and direction can be used in this function if already pre-calculated.  This
         prevents doing the same work twice.

         @param v0 line vertex 1.
         @param v1 line vertex 2.
     @param edgeDirection The direction of the segment (unit length).
     @param edgeLength The length of the segment.
     @param point External point.

         @return Closests point to <code>point</code> on the line segment.
        */
    static Vector3 closestPointOnLineSegment(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&          edgeDirection,
        float                  edgeLength,
        const Vector3&                  point);

    /**
         Finds the closest point on the perimeter of the triangle to an external point;
         given a triangle defined by three points v0, v1, & v2, and the external point.

         @param v0 Triangle vertex 1.
         @param v1 Triangle vertex 2.
         @param v2 Triangle vertex 3.
         @param point External point.

         @return Closests point to <code>point</code> on the perimeter of the
         triangle.
        */
    static Vector3 closestPointToTrianglePerimeter(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  point);

        /**
         Finds the closest point on the perimeter of the triangle to an external point;
         given a triangle defined by the array of points v, its edge directions and
         their lengths, as well as the external point.

         @note This is an optimization to closestPointToTrianglePerimeter.  Edge length
         and direction can be used in this function if already pre-calculated.  This
         prevents doing the same work twice.

         @param v0 Triangle vertex 1.
         @param v1 Triangle vertex 2.
         @param v2 Triangle vertex 3.
         @param point External point.

         @return Closests point to <code>point</code> on the perimeter of the
         triangle.
        */
    static Vector3 closestPointToTrianglePerimeter(
        const Vector3           v[3],
        const Vector3           edgeDirection[3],
        const double            edgeLength[3],
        const Vector3&                  point);

    /**
         Tests whether a point is contained within the triangle defined by
         v0, v1, & v2 and its plane's normal.

         @param v0 Triangle vertex 1.
         @param v1 Triangle vertex 2.
         @param v2 Triangle vertex 3.
         @param normal Normal to triangle's plane.
         @param point The point in question.
         @param primaryAxis Primary axis of triangle.  This will be detected
                if not given. This parameter is provided as an optimization.

         @return true  - if point is inside the triangle.
         @return false - otherwise
        */
    static bool isPointInsideTriangle(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  normal,
        const Vector3&                  point,
        Vector3::Axis  primaryAxis = Vector3::DETECT_AXIS);

     /**
          Tests for the intersection of a moving sphere and a fixed box in a
          given time limit.

          @note Returns true if any part of the sphere is inside the box
                during the time period (inf means "ever").  Useful for
                    performing bounding-box collision detection.

          @param sphere                 Moving sphere.
          @param velocity       Velocity of moving sphere.
          @param box            Fixed box.
          @param timeLimit      Time limit for intersection test.

          @return true  -  if the two objects will touch.
          @return false - if there is no intersection.
        */
    static bool movingSpherePassesThroughFixedBox(
        const Sphere&           sphere,
        const Vector3&          velocity,
        const Box&              box,
        double                  timeLimit = inf());

        /**
         Tests for the intersection of a moving sphere and a fixed sphere in a
         given time limit.

         @note This function will not detect an intersection between a moving object
         that is already interpenetrating the fixed object.

         @param sphere          Moving sphere.
         @param velocity        Velocity of moving sphere.
         @param fixedSphere Fixed sphere.
         @param timeLimit       Time limit for intersection test.

         @return true  -  if the two spheres will touch.
         @return false - if there is no intersection.
        */
    static bool movingSpherePassesThroughFixedSphere(
        const Sphere&           sphere,
        const Vector3&          velocity,
        const Sphere&           fixedSphere,
        double                  timeLimit = inf());

        /**
         Tests for the intersection of two fixed spheres.

         @param sphere1 Fixed sphere 1.
         @param sphere2 Fixed sphere 2.

         @return true -  if the two spheres touch.
         @return false - if there is no intersection.
        */
    static bool fixedSolidSphereIntersectsFixedSolidSphere(
        const Sphere&           sphere1,
        const Sphere&           sphere2);

        /**
         Tests for the intersection of a fixed sphere and a fixed box.

         @param sphere Fixed sphere.
         @param box    Fixed box.

         @return true  -  if the two objects touch.
         @return false - if there is no intersection.
        */
    static bool fixedSolidSphereIntersectsFixedSolidBox(
        const Sphere&           sphere,
        const Box&              box);

    /**
         Tests whether a point is inside a rectangle defined by the vertexes
         v0, v1, v2, & v3, and the rectangle's plane normal.

         @param v0 Rectangle vertex 1.
         @param v1 Rectangle vertex 2.
         @param v2 Rectangle vertex 3.
         @param v3 Rectangle vertex 4.
         @param normal Normal to rectangle's plane.
         @param point The point in question.

         @return true  - if point is inside the rectangle.
         @return false - otherwise
        */
    static bool isPointInsideRectangle(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  v3,
        const Vector3&                  normal,
        const Vector3&                  point);

    /**
         Finds the closest point on the perimeter of the rectangle to an
         external point; given a rectangle defined by four points v0, v1,
         v2, & v3, and the external point.

         @param v0 Rectangle vertex 1.
         @param v1 Rectangle vertex 2.
         @param v2 Rectangle vertex 3.
         @param v3 Rectangle vertex 4.
         @param point External point.

         @return Closests point to <code>point</code> on the perimeter of the
         rectangle.
         */
    static Vector3 closestPointToRectanglePerimeter(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  v3,
        const Vector3&                  point);

     /**
          Finds the closest point in the rectangle to an external point; Given
          a rectangle defined by four points v0, v1, v2, & v3, and the external
          point.

          @param v0 Rectangle vertex 1.
          @param v1 Rectangle vertex 2.
          @param v2 Rectangle vertex 3
          @param v3 Rectangle vertex 4.
          @param point External point.

      @return Closet point in the rectangle to the external point.
          */
         static Vector3 closestPointToRectangle(
        const Vector3&                  v0,
        const Vector3&                  v1,
        const Vector3&                  v2,
        const Vector3&                  v3,
        const Vector3&                  point);
};

} // namespace

#endif // G3D_COLLISIONDETECTION_H