raytrace.cpp

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#include "linden_common.h"

#include "math.h"
//#include "vmath.h"
#include "v3math.h"
#include "llquaternion.h"
#include "m3math.h"
#include "raytrace.h"


BOOL line_plane(const LLVector3 &line_point, const LLVector3 &line_direction,
                                const LLVector3 &plane_point, const LLVector3 plane_normal, 
                                LLVector3 &intersection)
{
        F32 N = line_direction * plane_normal;
        if (0.0f == N)
        {
                // line is perpendicular to plane normal
                // so it is either entirely on plane, or not on plane at all
                return FALSE;
        }
        // Ax + By, + Cz + D = 0
        // D = - (plane_point * plane_normal)
        // N = line_direction * plane_normal
        // intersection = line_point - ((D + plane_normal * line_point) / N) * line_direction
        intersection = line_point - ((plane_normal * line_point - plane_point * plane_normal) / N) * line_direction;
        return TRUE;
}


BOOL ray_plane(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                           const LLVector3 &plane_point, const LLVector3 plane_normal, 
                           LLVector3 &intersection)
{
        F32 N = ray_direction * plane_normal;
        if (0.0f == N)
        {
                // ray is perpendicular to plane normal
                // so it is either entirely on plane, or not on plane at all
                return FALSE;
        }
        // Ax + By, + Cz + D = 0
        // D = - (plane_point * plane_normal)
        // N = ray_direction * plane_normal
        // intersection = ray_point - ((D + plane_normal * ray_point) / N) * ray_direction
        F32 alpha = -(plane_normal * ray_point - plane_point * plane_normal) / N;
        if (alpha < 0.0f)
        {
                // ray points away from plane
                return FALSE;
        }
        intersection = ray_point + alpha * ray_direction;
        return TRUE;
}


BOOL ray_circle(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                const LLVector3 &circle_center, const LLVector3 plane_normal, F32 circle_radius,
                                LLVector3 &intersection)
{
        if (ray_plane(ray_point, ray_direction, circle_center, plane_normal, intersection))
        {
                if (circle_radius >= (intersection - circle_center).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL ray_triangle(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                  const LLVector3 &point_0, const LLVector3 &point_1, const LLVector3 &point_2, 
                                  LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 side_01 = point_1 - point_0;
        LLVector3 side_12 = point_2 - point_1;

        intersection_normal = side_01 % side_12;
        intersection_normal.normVec();

        if (ray_plane(ray_point, ray_direction, point_0, intersection_normal, intersection))
        {
                LLVector3 side_20 = point_0 - point_2;
                if (intersection_normal * (side_01 % (intersection - point_0)) >= 0.0f  &&
                        intersection_normal * (side_12 % (intersection - point_1)) >= 0.0f  &&
                        intersection_normal * (side_20 % (intersection - point_2)) >= 0.0f)
                {
                        return TRUE;
                }
        }
        return FALSE;
}


// assumes a parallelogram
BOOL ray_quadrangle(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                        const LLVector3 &point_0, const LLVector3 &point_1, const LLVector3 &point_2,
                                        LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 side_01 = point_1 - point_0;
        LLVector3 side_12 = point_2 - point_1;

        intersection_normal = side_01 % side_12;
        intersection_normal.normVec();

        if (ray_plane(ray_point, ray_direction, point_0, intersection_normal, intersection))
        {
                LLVector3 point_3 = point_0 + (side_12);
                LLVector3 side_23 = point_3 - point_2;
                LLVector3 side_30 = point_0 - point_3;
                if (intersection_normal * (side_01 % (intersection - point_0)) >= 0.0f  &&
                        intersection_normal * (side_12 % (intersection - point_1)) >= 0.0f  &&
                        intersection_normal * (side_23 % (intersection - point_2)) >= 0.0f  &&
                        intersection_normal * (side_30 % (intersection - point_3)) >= 0.0f)
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL ray_sphere(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                const LLVector3 &sphere_center, F32 sphere_radius,
                                LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_to_sphere = sphere_center - ray_point;
        F32 dot = ray_to_sphere * ray_direction;

        LLVector3 closest_approach = dot * ray_direction - ray_to_sphere;

        F32 shortest_distance = closest_approach.magVecSquared();
        F32 radius_squared = sphere_radius * sphere_radius;
        if (shortest_distance > radius_squared)
        {
                return FALSE;
        }

        F32 half_chord = (F32) sqrt(radius_squared - shortest_distance);
        closest_approach = sphere_center + closest_approach;                    // closest_approach now in absolute coordinates
        intersection = closest_approach + half_chord * ray_direction;
        dot = ray_direction * (intersection - ray_point);
        if (dot < 0.0f)
        {
                // ray shoots away from sphere and is not inside it
                return FALSE;
        }

        shortest_distance = ray_direction * ((closest_approach - half_chord * ray_direction) - ray_point);
        if (shortest_distance > 0.0f)
        {
                // ray enters sphere 
                intersection = intersection - (2.0f * half_chord) * ray_direction;
        }
        else
        {
                // do nothing
                // ray starts inside sphere and intersects as it leaves the sphere
        }

        intersection_normal = intersection - sphere_center;
        if (sphere_radius > 0.0f)
        {
                intersection_normal *= 1.0f / sphere_radius;
        }
        else
        {
                intersection_normal.setVec(0.0f, 0.0f, 0.0f);
        }
        
        return TRUE;
}


BOOL ray_cylinder(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                  const LLVector3 &cyl_center, const LLVector3 &cyl_scale, const LLQuaternion &cyl_rotation,
                                  LLVector3 &intersection, LLVector3 &intersection_normal)
{
        // calculate the centers of the cylinder caps in the absolute frame
        LLVector3 cyl_top(0.0f, 0.0f, 0.5f * cyl_scale.mV[VZ]);
        LLVector3 cyl_bottom(0.0f, 0.0f, -cyl_top.mV[VZ]);
        cyl_top = (cyl_top * cyl_rotation) + cyl_center;
        cyl_bottom = (cyl_bottom * cyl_rotation) + cyl_center;

        // we only handle cylinders with circular cross-sections at the moment
        F32 cyl_radius = 0.5f * llmax(cyl_scale.mV[VX], cyl_scale.mV[VY]);      // HACK until scaled cylinders are supported

        // This implementation is based on the intcyl() function from Graphics_Gems_IV, page 361
        LLVector3   cyl_axis;                                                           // axis direction (bottom toward top)
        LLVector3       ray_to_cyl;                                                             // ray_point to cyl_top
        F32             shortest_distance;                                              // shortest distance from ray to axis
        F32             cyl_length;
        LLVector3       shortest_direction;
        LLVector3       temp_vector;

        cyl_axis = cyl_bottom - cyl_top;
        cyl_length = cyl_axis.normVec();
        ray_to_cyl = ray_point - cyl_bottom;
        shortest_direction = ray_direction % cyl_axis;
        shortest_distance = shortest_direction.normVec();       // recycle shortest_distance

        // check for ray parallel to cylinder axis
        if (0.0f == shortest_distance)
        {
                // ray is parallel to cylinder axis
                temp_vector = ray_to_cyl - (ray_to_cyl * cyl_axis) * cyl_axis;
                shortest_distance = temp_vector.magVec();
                if (shortest_distance <= cyl_radius)
                {
                        shortest_distance = ray_to_cyl * cyl_axis;
                        F32 dot = ray_direction * cyl_axis;

                        if (shortest_distance > 0.0)
                        {
                                if (dot > 0.0f)
                                {
                                        // ray points away from cylinder bottom
                                        return FALSE;
                                }
                                // ray hit bottom of cylinder from outside 
                                intersection = ray_point - shortest_distance * cyl_axis;
                                intersection_normal = cyl_axis;

                        }
                        else if (shortest_distance > -cyl_length)
                        {
                                // ray starts inside cylinder
                                if (dot < 0.0f)
                                {
                                        // ray hit top from inside
                                        intersection = ray_point - (cyl_length + shortest_distance) * cyl_axis;
                                        intersection_normal = -cyl_axis;
                                }
                                else
                                {
                                        // ray hit bottom from inside
                                        intersection = ray_point - shortest_distance * cyl_axis;
                                        intersection_normal = cyl_axis;
                                }
                        }
                        else
                        {
                                if (dot < 0.0f)
                                {
                                        // ray points away from cylinder bottom
                                        return FALSE;
                                }
                                // ray hit top from outside
                                intersection = ray_point - (shortest_distance + cyl_length) * cyl_axis;
                                intersection_normal = -cyl_axis;
                        }
                        return TRUE;
                }
                return FALSE;
        }

        // check for intersection with infinite cylinder
        shortest_distance = (F32) fabs(ray_to_cyl * shortest_direction);
        if (shortest_distance <= cyl_radius)
        {
                F32             dist_to_closest_point;                          // dist from ray_point to closest_point
                F32             half_chord_length;                                      // half length of intersection chord
                F32             in, out;                                                        // distances to entering/exiting points
                temp_vector = ray_to_cyl % cyl_axis;
                dist_to_closest_point = - (temp_vector * shortest_direction);
                temp_vector = shortest_direction % cyl_axis;
                temp_vector.normVec();
                half_chord_length = (F32) fabs( sqrt(cyl_radius*cyl_radius - shortest_distance * shortest_distance) /
                                                        (ray_direction * temp_vector) );

                out = dist_to_closest_point + half_chord_length;        // dist to exiting point
                if (out < 0.0f)
                {
                        // cylinder is behind the ray, so we return FALSE
                        return FALSE;
                }

                in = dist_to_closest_point - half_chord_length;         // dist to entering point
                if (in < 0.0f)
                {
                        // ray_point is inside the cylinder
                        // so we store the exiting intersection
                        intersection = ray_point + out * ray_direction;
                        shortest_distance = out;
                }
                else
                {
                        // ray hit cylinder from outside
                        // so we store the entering intersection
                        intersection = ray_point + in * ray_direction;
                        shortest_distance = in;
                }

                // calculate the normal at intersection
                if (0.0f == cyl_radius)
                {
                        intersection_normal.setVec(0.0f, 0.0f, 0.0f);
                }
                else
                {
                        temp_vector = intersection - cyl_bottom;        
                        intersection_normal = temp_vector - (temp_vector * cyl_axis) * cyl_axis;
                        intersection_normal.normVec();
                }

                // check for intersection with end caps
                // calculate intersection of ray and top plane
                if (line_plane(ray_point, ray_direction, cyl_top, -cyl_axis, temp_vector))      // NOTE side-effect: changing temp_vector
                {
                        shortest_distance = (temp_vector - ray_point).magVec();
                        if ( (ray_direction * cyl_axis) > 0.0f)
                        {
                                // ray potentially enters the cylinder at top
                                if (shortest_distance > out)
                                {
                                        // ray missed the finite cylinder
                                        return FALSE;
                                }
                                if (shortest_distance > in)
                                {
                                        // ray intersects cylinder at top plane
                                        intersection = temp_vector;
                                        intersection_normal = -cyl_axis;
                                        return TRUE;
                                }
                        }
                        else
                        {
                                // ray potentially exits the cylinder at top
                                if (shortest_distance < in)
                                {
                                        // missed the finite cylinder
                                        return FALSE;
                                }
                        }

                        // calculate intersection of ray and bottom plane
                        line_plane(ray_point, ray_direction, cyl_bottom, cyl_axis, temp_vector); // NOTE side-effect: changing temp_vector
                        shortest_distance = (temp_vector - ray_point).magVec();
                        if ( (ray_direction * cyl_axis) < 0.0)
                        {
                                // ray potentially enters the cylinder at bottom
                                if (shortest_distance > out)
                                {
                                        // ray missed the finite cylinder
                                        return FALSE;
                                }
                                if (shortest_distance > in)
                                {
                                        // ray intersects cylinder at bottom plane
                                        intersection = temp_vector;
                                        intersection_normal = cyl_axis;
                                        return TRUE;
                                }
                        }
                        else
                        {
                                // ray potentially exits the cylinder at bottom
                                if (shortest_distance < in)
                                {
                                        // ray missed the finite cylinder
                                        return FALSE;
                                }
                        }

                }
                else
                {
                        // ray is parallel to end cap planes
                        temp_vector = cyl_bottom - ray_point;
                        shortest_distance = temp_vector * cyl_axis;
                        if (shortest_distance < 0.0f  ||  shortest_distance > cyl_length)
                        {
                                // ray missed finite cylinder
                                return FALSE;
                        }
                }

                return TRUE;
        }

        return FALSE;
}


U32 ray_box(const LLVector3 &ray_point, const LLVector3 &ray_direction, 
                        const LLVector3 &box_center, const LLVector3 &box_scale, const LLQuaternion &box_rotation,
                        LLVector3 &intersection, LLVector3 &intersection_normal)
{

        // Need to rotate into box frame
        LLQuaternion into_box_frame(box_rotation);              // rotates things from box frame to absolute
        into_box_frame.conjQuat();                                              // now rotates things into box frame
        LLVector3 line_point = (ray_point - box_center) * into_box_frame;
        LLVector3 line_direction = ray_direction * into_box_frame;

        // Suppose we have a plane:  Ax + By + Cz + D = 0
        // then, assuming [A, B, C] is a unit vector:
        //
        //    plane_normal = [A, B, C] 
        //    D = - (plane_normal * plane_point)
        // 
        // Suppose we have a line:  X = line_point + alpha * line_direction
        //
        // the intersection of the plane and line determines alpha
        //
        //    alpha = - (D + plane_normal * line_point) / (plane_normal * line_direction)

        LLVector3 line_plane_intersection;

        F32 pointX = line_point.mV[VX];
        F32 pointY = line_point.mV[VY];
        F32 pointZ = line_point.mV[VZ];

        F32 dirX = line_direction.mV[VX];
        F32 dirY = line_direction.mV[VY];
        F32 dirZ = line_direction.mV[VZ];

        // we'll be using the half-scales of the box
        F32 boxX = 0.5f * box_scale.mV[VX];
        F32 boxY = 0.5f * box_scale.mV[VY];
        F32 boxZ = 0.5f * box_scale.mV[VZ];

        // check to see if line_point is OUTSIDE the box
        if (pointX < -boxX ||
                pointX >  boxX ||
                pointY < -boxY ||
                pointY >  boxY ||
                pointZ < -boxZ ||
                pointZ >  boxZ) 
        {
                // -------------- point is OUTSIDE the box ----------------

                // front
                if (pointX > 0.0f  &&  dirX < 0.0f)
                {
                        // plane_normal                = [ 1, 0, 0]
                        // plane_normal*line_point     = pointX
                        // plane_normal*line_direction = dirX
                        // D                           = -boxX
                        // alpha                       = - (-boxX + pointX) / dirX
                        line_plane_intersection = line_point - ((pointX - boxX) / dirX) * line_direction;
                        if (line_plane_intersection.mV[VY] <  boxY &&
                                line_plane_intersection.mV[VY] > -boxY &&
                                line_plane_intersection.mV[VZ] <  boxZ &&
                                line_plane_intersection.mV[VZ] > -boxZ )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(1.0f, 0.0f, 0.0f) * box_rotation;
                                return FRONT_SIDE;
                        }
                }
        
                // back
                if (pointX < 0.0f  &&  dirX > 0.0f)
                {
                        // plane_normal                = [ -1, 0, 0]
                        // plane_normal*line_point     = -pX 
                        // plane_normal*line_direction = -direction.mV[VX]
                        // D                           = -bX
                        // alpha                       = - (-bX - pX) / (-dirX)
                        line_plane_intersection = line_point - ((boxX + pointX)/ dirX) * line_direction;
                        if (line_plane_intersection.mV[VY] <  boxY &&
                                line_plane_intersection.mV[VY] > -boxY &&
                                line_plane_intersection.mV[VZ] <  boxZ &&
                                line_plane_intersection.mV[VZ] > -boxZ )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(-1.0f, 0.0f, 0.0f) * box_rotation;
                                return BACK_SIDE;
                        }
                }
        
                // left
                if (pointY > 0.0f  &&  dirY < 0.0f)
                {
                        // plane_normal                = [0, 1, 0]
                        // plane_normal*line_point     = pointY 
                        // plane_normal*line_direction = dirY
                        // D                           = -boxY
                        // alpha                       = - (-boxY + pointY) / dirY
                        line_plane_intersection = line_point + ((boxY - pointY)/dirY) * line_direction;

                        if (line_plane_intersection.mV[VX] <  boxX &&
                                line_plane_intersection.mV[VX] > -boxX &&
                                line_plane_intersection.mV[VZ] <  boxZ &&
                                line_plane_intersection.mV[VZ] > -boxZ )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(0.0f, 1.0f, 0.0f) * box_rotation;
                                return LEFT_SIDE;
                        }
                }
        
                // right
                if (pointY < 0.0f  &&  dirY > 0.0f)
                {
                        // plane_normal                = [0, -1, 0]
                        // plane_normal*line_point     = -pointY 
                        // plane_normal*line_direction = -dirY
                        // D                           = -boxY
                        // alpha                       = - (-boxY - pointY) / (-dirY)
                        line_plane_intersection = line_point - ((boxY + pointY)/dirY) * line_direction;
                        if (line_plane_intersection.mV[VX] <  boxX &&
                                line_plane_intersection.mV[VX] > -boxX &&
                                line_plane_intersection.mV[VZ] <  boxZ &&
                                line_plane_intersection.mV[VZ] > -boxZ )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(0.0f, -1.0f, 0.0f) * box_rotation;
                                return RIGHT_SIDE;
                        }
                }
        
                // top
                if (pointZ > 0.0f  &&  dirZ < 0.0f)
                {
                        // plane_normal                = [0, 0, 1]
                        // plane_normal*line_point     = pointZ 
                        // plane_normal*line_direction = dirZ
                        // D                           = -boxZ
                        // alpha                       = - (-boxZ + pointZ) / dirZ
                        line_plane_intersection = line_point - ((pointZ - boxZ)/dirZ) * line_direction;
                        if (line_plane_intersection.mV[VX] <  boxX &&
                                line_plane_intersection.mV[VX] > -boxX &&
                                line_plane_intersection.mV[VY] <  boxY &&
                                line_plane_intersection.mV[VY] > -boxY )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(0.0f, 0.0f, 1.0f) * box_rotation;
                                return TOP_SIDE;
                        }
                }
        
                // bottom
                if (pointZ < 0.0f  &&  dirZ > 0.0f)
                {
                        // plane_normal                = [0, 0, -1]
                        // plane_normal*line_point     = -pointZ 
                        // plane_normal*line_direction = -dirZ
                        // D                           = -boxZ
                        // alpha                       = - (-boxZ - pointZ) / (-dirZ)
                        line_plane_intersection = line_point - ((boxZ + pointZ)/dirZ) * line_direction;
                        if (line_plane_intersection.mV[VX] <  boxX &&
                                line_plane_intersection.mV[VX] > -boxX &&
                                line_plane_intersection.mV[VY] <  boxY &&
                                line_plane_intersection.mV[VY] > -boxY )
                        {
                                intersection = (line_plane_intersection * box_rotation) + box_center;
                                intersection_normal = LLVector3(0.0f, 0.0f, -1.0f) * box_rotation;
                                return BOTTOM_SIDE;
                        }
                }
                return NO_SIDE;
        }

        // -------------- point is INSIDE the box ----------------

        // front
        if (dirX > 0.0f)
        {
                // plane_normal                = [ 1, 0, 0]
                // plane_normal*line_point     = pointX
                // plane_normal*line_direction = dirX
                // D                           = -boxX
                // alpha                       = - (-boxX + pointX) / dirX
                line_plane_intersection = line_point - ((pointX - boxX) / dirX) * line_direction;
                if (line_plane_intersection.mV[VY] <  boxY &&
                        line_plane_intersection.mV[VY] > -boxY &&
                        line_plane_intersection.mV[VZ] <  boxZ &&
                        line_plane_intersection.mV[VZ] > -boxZ )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(1.0f, 0.0f, 0.0f) * box_rotation;
                        return FRONT_SIDE;
                }
        }

        // back
        if (dirX < 0.0f)
        {
                // plane_normal                = [ -1, 0, 0]
                // plane_normal*line_point     = -pX 
                // plane_normal*line_direction = -direction.mV[VX]
                // D                           = -bX
                // alpha                       = - (-bX - pX) / (-dirX)
                line_plane_intersection = line_point - ((boxX + pointX)/ dirX) * line_direction;
                if (line_plane_intersection.mV[VY] <  boxY &&
                        line_plane_intersection.mV[VY] > -boxY &&
                        line_plane_intersection.mV[VZ] <  boxZ &&
                        line_plane_intersection.mV[VZ] > -boxZ )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(-1.0f, 0.0f, 0.0f) * box_rotation;
                        return BACK_SIDE;
                }
        }

        // left
        if (dirY > 0.0f)
        {
                // plane_normal                = [0, 1, 0]
                // plane_normal*line_point     = pointY 
                // plane_normal*line_direction = dirY
                // D                           = -boxY
                // alpha                       = - (-boxY + pointY) / dirY
                line_plane_intersection = line_point + ((boxY - pointY)/dirY) * line_direction;

                if (line_plane_intersection.mV[VX] <  boxX &&
                        line_plane_intersection.mV[VX] > -boxX &&
                        line_plane_intersection.mV[VZ] <  boxZ &&
                        line_plane_intersection.mV[VZ] > -boxZ )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(0.0f, 1.0f, 0.0f) * box_rotation;
                        return LEFT_SIDE;
                }
        }

        // right
        if (dirY < 0.0f)
        {
                // plane_normal                = [0, -1, 0]
                // plane_normal*line_point     = -pointY 
                // plane_normal*line_direction = -dirY
                // D                           = -boxY
                // alpha                       = - (-boxY - pointY) / (-dirY)
                line_plane_intersection = line_point - ((boxY + pointY)/dirY) * line_direction;
                if (line_plane_intersection.mV[VX] <  boxX &&
                        line_plane_intersection.mV[VX] > -boxX &&
                        line_plane_intersection.mV[VZ] <  boxZ &&
                        line_plane_intersection.mV[VZ] > -boxZ )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(0.0f, -1.0f, 0.0f) * box_rotation;
                        return RIGHT_SIDE;
                }
        }

        // top
        if (dirZ > 0.0f)
        {
                // plane_normal                = [0, 0, 1]
                // plane_normal*line_point     = pointZ 
                // plane_normal*line_direction = dirZ
                // D                           = -boxZ
                // alpha                       = - (-boxZ + pointZ) / dirZ
                line_plane_intersection = line_point - ((pointZ - boxZ)/dirZ) * line_direction;
                if (line_plane_intersection.mV[VX] <  boxX &&
                        line_plane_intersection.mV[VX] > -boxX &&
                        line_plane_intersection.mV[VY] <  boxY &&
                        line_plane_intersection.mV[VY] > -boxY )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(0.0f, 0.0f, 1.0f) * box_rotation;
                        return TOP_SIDE;
                }
        }

        // bottom
        if (dirZ < 0.0f)
        {
                // plane_normal                = [0, 0, -1]
                // plane_normal*line_point     = -pointZ 
                // plane_normal*line_direction = -dirZ
                // D                           = -boxZ
                // alpha                       = - (-boxZ - pointZ) / (-dirZ)
                line_plane_intersection = line_point - ((boxZ + pointZ)/dirZ) * line_direction;
                if (line_plane_intersection.mV[VX] <  boxX &&
                        line_plane_intersection.mV[VX] > -boxX &&
                        line_plane_intersection.mV[VY] <  boxY &&
                        line_plane_intersection.mV[VY] > -boxY )
                {
                        intersection = (line_plane_intersection * box_rotation) + box_center;
                        intersection_normal = LLVector3(0.0f, 0.0f, -1.0f) * box_rotation;
                        return BOTTOM_SIDE;
                }
        }

        // should never get here unless line instersects at tangent point on edge or corner
        // however such cases will be EXTREMELY rare
        return NO_SIDE;
}


BOOL ray_prism(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                           const LLVector3 &prism_center, const LLVector3 &prism_scale, const LLQuaternion &prism_rotation,
                           LLVector3 &intersection, LLVector3 &intersection_normal)
{
        //      (0)              Z  
        //      /| \             .  
        //    (1)|  \           /|\  _.Y
        //     | \   \           |   /|
        //     | |\   \          |  /
        //     | | \(0)\         | / 
        //     | |  \   \        |/
        //     | |   \   \      (*)----> X  
        //     |(3)---\---(2)      
        //     |/      \  /        
        //    (4)-------(5)        

        // need to calculate the points of the prism so we can run ray tests with each face
        F32 x = prism_scale.mV[VX];
        F32 y = prism_scale.mV[VY];
        F32 z = prism_scale.mV[VZ];

        F32 tx = x * 2.0f / 3.0f;
        F32 ty = y * 0.5f;
        F32 tz = z * 2.0f / 3.0f;

        LLVector3 point0(tx-x,  ty, tz);
        LLVector3 point1(tx-x, -ty, tz);
        LLVector3 point2(tx,    ty, tz-z);
        LLVector3 point3(tx-x,  ty, tz-z);
        LLVector3 point4(tx-x, -ty, tz-z);
        LLVector3 point5(tx,   -ty, tz-z);

        // transform these points into absolute frame
        point0 = (point0 * prism_rotation) + prism_center;
        point1 = (point1 * prism_rotation) + prism_center;
        point2 = (point2 * prism_rotation) + prism_center;
        point3 = (point3 * prism_rotation) + prism_center;
        point4 = (point4 * prism_rotation) + prism_center;
        point5 = (point5 * prism_rotation) + prism_center;

        // test ray intersection for each face
        BOOL b_hit = FALSE;
        LLVector3 face_intersection, face_normal;
        F32 distance_squared = 0.0f;
        F32 temp;

        // face 0
        if (ray_direction * ( (point0 - point2) % (point5 - point2)) < 0.0f  && 
                ray_quadrangle(ray_point, ray_direction, point5, point2, point0, intersection, intersection_normal))
        {
                distance_squared = (ray_point - intersection).magVecSquared();
                b_hit = TRUE;
        }

        // face 1
        if (ray_direction * ( (point0 - point3) % (point2 - point3)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point2, point3, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 2
        if (ray_direction * ( (point1 - point4) % (point3 - point4)) < 0.0f  &&
                ray_quadrangle(ray_point, ray_direction, point3, point4, point1, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 3
        if (ray_direction * ( (point5 - point4) % (point1 - point4)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point1, point4, point5, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }

        // face 4
        if (ray_direction * ( (point4 - point5) % (point2 - point5)) < 0.0f  &&
                ray_quadrangle(ray_point, ray_direction, point2, point5, point4, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }

        return b_hit;
}


BOOL ray_tetrahedron(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                         const LLVector3 &t_center, const LLVector3 &t_scale, const LLQuaternion &t_rotation,
                                         LLVector3 &intersection, LLVector3 &intersection_normal)
{
        F32 a = 0.5f * F_SQRT3;                         // height of unit triangle
        F32 b = 1.0f / F_SQRT3;                         // distance of center of unit triangle to each point
        F32 c = F_SQRT2 / F_SQRT3;                      // height of unit tetrahedron
        F32 d = 0.5f * F_SQRT3 / F_SQRT2;       // distance of center of tetrahedron to each point

        // if we want the tetrahedron to have unit height (c = 1.0) then we need to divide
        // each constant by hieght of a unit tetrahedron
        F32 oo_c = 1.0f / c;
        a = a * oo_c;
        b = b * oo_c;
        c = 1.0f;
        d = d * oo_c;
        F32 e = 0.5f * oo_c;

        LLVector3 point0(                          0.0f,                                        0.0f,  t_scale.mV[VZ] * d);
        LLVector3 point1(t_scale.mV[VX] * b,                                    0.0f,  t_scale.mV[VZ] * (d-c));
        LLVector3 point2(t_scale.mV[VX] * (b-a),  e * t_scale.mV[VY],  t_scale.mV[VZ] * (d-c));
        LLVector3 point3(t_scale.mV[VX] * (b-a), -e * t_scale.mV[VY],  t_scale.mV[VZ] * (d-c));

        // transform these points into absolute frame
        point0 = (point0 * t_rotation) + t_center;
        point1 = (point1 * t_rotation) + t_center;
        point2 = (point2 * t_rotation) + t_center;
        point3 = (point3 * t_rotation) + t_center;

        // test ray intersection for each face
        BOOL b_hit = FALSE;
        LLVector3 face_intersection, face_normal;
        F32 distance_squared = 1.0e12f;
        F32 temp;

        // face 0
        if (ray_direction * ( (point2 - point1) % (point0 - point1)) < 0.0f  && 
                ray_triangle(ray_point, ray_direction, point1, point2, point0, intersection, intersection_normal))
        {
                distance_squared = (ray_point - intersection).magVecSquared();
                b_hit = TRUE;
        }

        // face 1
        if (ray_direction * ( (point3 - point2) % (point0 - point2)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point2, point3, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 2
        if (ray_direction * ( (point1 - point3) % (point0 - point3)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point3, point1, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 3
        if (ray_direction * ( (point2 - point3) % (point1 - point3)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point3, point2, point1, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }

        return b_hit;
}


BOOL ray_pyramid(const LLVector3 &ray_point, const LLVector3 &ray_direction,
                                 const LLVector3 &p_center, const LLVector3 &p_scale, const LLQuaternion &p_rotation,
                                 LLVector3 &intersection, LLVector3 &intersection_normal)
{
        // center of mass of pyramid is located 1/4 its height from the base
        F32 x = 0.5f * p_scale.mV[VX];
        F32 y = 0.5f * p_scale.mV[VY];
        F32 z = 0.25f * p_scale.mV[VZ];

        LLVector3 point0(0.0f, 0.0f,  p_scale.mV[VZ] - z);
        LLVector3 point1( x,  y, -z);
        LLVector3 point2(-x,  y, -z);
        LLVector3 point3(-x, -y, -z);
        LLVector3 point4( x, -y, -z);

        // transform these points into absolute frame
        point0 = (point0 * p_rotation) + p_center;
        point1 = (point1 * p_rotation) + p_center;
        point2 = (point2 * p_rotation) + p_center;
        point3 = (point3 * p_rotation) + p_center;
        point4 = (point4 * p_rotation) + p_center;

        // test ray intersection for each face
        BOOL b_hit = FALSE;
        LLVector3 face_intersection, face_normal;
        F32 distance_squared = 1.0e12f;
        F32 temp;

        // face 0
        if (ray_direction * ( (point1 - point4) % (point0 - point4)) < 0.0f  && 
                ray_triangle(ray_point, ray_direction, point4, point1, point0, intersection, intersection_normal))
        {
                distance_squared = (ray_point - intersection).magVecSquared();
                b_hit = TRUE;
        }

        // face 1
        if (ray_direction * ( (point2 - point1) % (point0 - point1)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point1, point2, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 2
        if (ray_direction * ( (point3 - point2) % (point0 - point2)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point2, point3, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }

        // face 3
        if (ray_direction * ( (point4 - point3) % (point0 - point3)) < 0.0f  &&
                ray_triangle(ray_point, ray_direction, point3, point4, point0, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                distance_squared = temp;
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        distance_squared = (ray_point - face_intersection).magVecSquared();
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }
        
        // face 4
        if (ray_direction * ( (point3 - point4) % (point2 - point4)) < 0.0f  &&
                ray_quadrangle(ray_point, ray_direction, point4, point3, point2, face_intersection, face_normal))
        {
                if (TRUE == b_hit)
                {
                        temp = (ray_point - face_intersection).magVecSquared();
                        if (temp < distance_squared)
                        {
                                intersection = face_intersection;
                                intersection_normal = face_normal;
                        }
                }
                else 
                {
                        intersection = face_intersection;
                        intersection_normal = face_normal;
                        b_hit = TRUE;
                }
        }

        return b_hit;
}


BOOL linesegment_circle(const LLVector3 &point_a, const LLVector3 &point_b,
                                                const LLVector3 &circle_center, const LLVector3 plane_normal, F32 circle_radius,
                                                LLVector3 &intersection)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_circle(point_a, ray_direction, circle_center, plane_normal, circle_radius, intersection))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_triangle(const LLVector3 &point_a, const LLVector3 &point_b,
                                                  const LLVector3 &point_0, const LLVector3 &point_1, const LLVector3 &point_2,
                                                  LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_triangle(point_a, ray_direction, point_0, point_1, point_2, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_quadrangle(const LLVector3 &point_a, const LLVector3 &point_b,
                                                        const LLVector3 &point_0, const LLVector3 &point_1, const LLVector3 &point_2,
                                                        LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_quadrangle(point_a, ray_direction, point_0, point_1, point_2, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_sphere(const LLVector3 &point_a, const LLVector3 &point_b,
                                const LLVector3 &sphere_center, F32 sphere_radius,
                                LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_sphere(point_a, ray_direction, sphere_center, sphere_radius, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_cylinder(const LLVector3 &point_a, const LLVector3 &point_b,
                                  const LLVector3 &cyl_center, const LLVector3 &cyl_scale, const LLQuaternion &cyl_rotation,
                                  LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_cylinder(point_a, ray_direction, cyl_center, cyl_scale, cyl_rotation, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


U32 linesegment_box(const LLVector3 &point_a, const LLVector3 &point_b, 
                                        const LLVector3 &box_center, const LLVector3 &box_scale, const LLQuaternion &box_rotation,
                                        LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 direction = point_b - point_a;
        if (direction.isNull())
        {
                return NO_SIDE;
        }

        F32 segment_length = direction.normVec();
        U32 box_side = ray_box(point_a, direction, box_center, box_scale, box_rotation, intersection, intersection_normal);
        if (NO_SIDE == box_side  ||  segment_length < (intersection - point_a).magVec())
        {
                return NO_SIDE;
        }

        return box_side;
}


BOOL linesegment_prism(const LLVector3 &point_a, const LLVector3 &point_b,
                                           const LLVector3 &prism_center, const LLVector3 &prism_scale, const LLQuaternion &prism_rotation,
                                           LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_prism(point_a, ray_direction, prism_center, prism_scale, prism_rotation, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_tetrahedron(const LLVector3 &point_a, const LLVector3 &point_b,
                                                         const LLVector3 &t_center, const LLVector3 &t_scale, const LLQuaternion &t_rotation,
                                                         LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_tetrahedron(point_a, ray_direction, t_center, t_scale, t_rotation, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}


BOOL linesegment_pyramid(const LLVector3 &point_a, const LLVector3 &point_b,
                                                 const LLVector3 &p_center, const LLVector3 &p_scale, const LLQuaternion &p_rotation,
                                                 LLVector3 &intersection, LLVector3 &intersection_normal)
{
        LLVector3 ray_direction = point_b - point_a;
        F32 segment_length = ray_direction.normVec();

        if (ray_pyramid(point_a, ray_direction, p_center, p_scale, p_rotation, intersection, intersection_normal))
        {
                if (segment_length >= (point_a - intersection).magVec())
                {
                        return TRUE;
                }
        }
        return FALSE;
}

---