path: root/indra/llmath/raytrace.cpp

/**
 * @file raytrace.cpp
 * @brief Functions called by box object scripts.
 *
 * $LicenseInfo:firstyear=2001&license=viewerlgpl$
 * Second Life Viewer Source Code
 * Copyright (C) 2010, Linden Research, Inc.
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation;
 * version 2.1 of the License only.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 *
 * Linden Research, Inc., 945 Battery Street, San Francisco, CA  94111  USA
 * $/LicenseInfo$
 */

#include "linden_common.h"

#include <cmath>
//#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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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 (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;
}