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cm_trace.c
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/*
===========================================================================
Copyright (C) 1999-2005 Id Software, Inc.
This file is part of Quake III Arena source code.
Quake III Arena source code is free software; you can redistribute it
and/or modify it under the terms of the GNU General Public License as
published by the Free Software Foundation; either version 2 of the License,
or (at your option) any later version.
Quake III Arena source code 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with Quake III Arena source code; if not, write to the Free Software
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
===========================================================================
*/
#include "cm_local.h"
// always use bbox vs. bbox collision and never capsule vs. bbox or vice versa
//#define ALWAYS_BBOX_VS_BBOX
// always use capsule vs. capsule collision and never capsule vs. bbox or vice versa
//#define ALWAYS_CAPSULE_VS_CAPSULE
//#define CAPSULE_DEBUG
/*
===============================================================================
BASIC MATH
===============================================================================
*/
/*
================
RotatePoint
================
*/
static void RotatePoint( vec3_t point, /*const*/ vec3_t matrix[3] ) {
vec3_t tvec;
VectorCopy(point, tvec);
point[0] = DotProduct(matrix[0], tvec);
point[1] = DotProduct(matrix[1], tvec);
point[2] = DotProduct(matrix[2], tvec);
}
/*
================
TransposeMatrix
================
*/
static void TransposeMatrix( /*const*/ vec3_t matrix[3], vec3_t transpose[3] ) {
int i, j;
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
transpose[i][j] = matrix[j][i];
}
}
}
/*
================
CreateRotationMatrix
================
*/
static void CreateRotationMatrix( const vec3_t angles, vec3_t matrix[3] ) {
AngleVectors(angles, matrix[0], matrix[1], matrix[2]);
VectorInverse(matrix[1]);
}
/*
================
CM_ProjectPointOntoVector
================
*/
static void CM_ProjectPointOntoVector( const vec3_t point, const vec3_t vStart, const vec3_t vDir, vec3_t vProj )
{
vec3_t pVec;
VectorSubtract( point, vStart, pVec );
// project onto the directional vector for this segment
VectorMA( vStart, DotProduct( pVec, vDir ), vDir, vProj );
}
/*
================
CM_DistanceFromLineSquared
================
*/
static float CM_DistanceFromLineSquared( const vec3_t p, const vec3_t lp1, const vec3_t lp2, const vec3_t dir ) {
vec3_t proj, t;
int j;
CM_ProjectPointOntoVector(p, lp1, dir, proj);
for (j = 0; j < 3; j++)
if ((proj[j] > lp1[j] && proj[j] > lp2[j]) ||
(proj[j] < lp1[j] && proj[j] < lp2[j]))
break;
if (j < 3) {
if (fabs(proj[j] - lp1[j]) < fabs(proj[j] - lp2[j]))
VectorSubtract(p, lp1, t);
else
VectorSubtract(p, lp2, t);
return VectorLengthSquared(t);
}
VectorSubtract(p, proj, t);
return VectorLengthSquared(t);
}
/*
================
SquareRootFloat
================
*/
static float SquareRootFloat(float number) {
floatint_t t;
float x, y;
const float f = 1.5F;
x = number * 0.5F;
t.f = number;
t.i = 0x5f3759df - ( t.i >> 1 );
y = t.f;
y = y * ( f - ( x * y * y ) );
y = y * ( f - ( x * y * y ) );
return number * y;
}
/*
===============================================================================
POSITION TESTING
===============================================================================
*/
/*
================
CM_TestBoxInBrush
================
*/
static void CM_TestBoxInBrush( traceWork_t *tw, const cbrush_t *brush ) {
int i;
cplane_t *plane;
double dist;
double d1;
cbrushside_t *side;
double t;
vec3_t startp;
if (!brush->numsides) {
return;
}
// special test for axial
if ( tw->bounds[0][0] > brush->bounds[1][0]
|| tw->bounds[0][1] > brush->bounds[1][1]
|| tw->bounds[0][2] > brush->bounds[1][2]
|| tw->bounds[1][0] < brush->bounds[0][0]
|| tw->bounds[1][1] < brush->bounds[0][1]
|| tw->bounds[1][2] < brush->bounds[0][2]
) {
return;
}
if ( tw->sphere.use ) {
// the first six planes are the axial planes, so we only
// need to test the remainder
for ( i = 6 ; i < brush->numsides ; i++ ) {
side = brush->sides + i;
plane = side->plane;
// adjust the plane distance appropriately for radius
dist = plane->dist + tw->sphere.radius;
// find the closest point on the capsule to the plane
t = DotProductDP( plane->normal, tw->sphere.offset );
if ( t > 0 )
{
VectorSubtractDP( tw->start, tw->sphere.offset, startp );
}
else
{
VectorAddDP( tw->start, tw->sphere.offset, startp );
}
d1 = DotProductDP( startp, plane->normal ) - dist;
// if completely in front of face, no intersection
if ( d1 > 0 ) {
return;
}
}
} else {
// the first six planes are the axial planes, so we only
// need to test the remainder
for ( i = 6 ; i < brush->numsides ; i++ ) {
side = brush->sides + i;
plane = side->plane;
// adjust the plane distance appropriately for mins/maxs
dist = plane->dist - DotProduct( tw->offsets[ plane->signbits ], plane->normal );
d1 = DotProductDP( tw->start, plane->normal ) - dist;
// if completely in front of face, no intersection
if ( d1 > 0 ) {
return;
}
}
}
// inside this brush
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
tw->trace.contents = brush->contents;
}
/*
================
CM_TestInLeaf
================
*/
static void CM_TestInLeaf( traceWork_t *tw, const cLeaf_t *leaf ) {
int k;
int brushnum;
cbrush_t *b;
cPatch_t *patch;
// test box position against all brushes in the leaf
for (k=0 ; k<leaf->numLeafBrushes ; k++) {
brushnum = cm.leafbrushes[leaf->firstLeafBrush+k];
b = &cm.brushes[brushnum];
if (b->checkcount == cm.checkcount) {
continue; // already checked this brush in another leaf
}
b->checkcount = cm.checkcount;
if ( !(b->contents & tw->contents)) {
continue;
}
CM_TestBoxInBrush( tw, b );
if ( tw->trace.allsolid ) {
return;
}
}
// test against all patches
#ifdef BSPC
if (1) {
#else
if ( !cm_noCurves->integer ) {
#endif //BSPC
for ( k = 0 ; k < leaf->numLeafSurfaces ; k++ ) {
patch = cm.surfaces[ cm.leafsurfaces[ leaf->firstLeafSurface + k ] ];
if ( !patch ) {
continue;
}
if ( patch->checkcount == cm.checkcount ) {
continue; // already checked this brush in another leaf
}
patch->checkcount = cm.checkcount;
if ( !(patch->contents & tw->contents)) {
continue;
}
if ( CM_PositionTestInPatchCollide( tw, patch->pc ) ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
tw->trace.contents = patch->contents;
return;
}
}
}
}
/*
==================
CM_TestCapsuleInCapsule
capsule inside capsule check
==================
*/
static void CM_TestCapsuleInCapsule( traceWork_t *tw, clipHandle_t model ) {
int i;
vec3_t mins, maxs;
vec3_t top, bottom;
vec3_t p1, p2, tmp;
vec3_t offset, symetricSize[2];
float radius, halfwidth, halfheight, offs, r;
CM_ModelBounds(model, mins, maxs);
VectorAdd(tw->start, tw->sphere.offset, top);
VectorSubtract(tw->start, tw->sphere.offset, bottom);
for ( i = 0 ; i < 3 ; i++ ) {
offset[i] = ( mins[i] + maxs[i] ) * 0.5;
symetricSize[0][i] = mins[i] - offset[i];
symetricSize[1][i] = maxs[i] - offset[i];
}
halfwidth = symetricSize[ 1 ][ 0 ];
halfheight = symetricSize[ 1 ][ 2 ];
radius = ( halfwidth > halfheight ) ? halfheight : halfwidth;
offs = halfheight - radius;
r = Square(tw->sphere.radius + radius);
// check if any of the spheres overlap
VectorCopy(offset, p1);
p1[2] += offs;
VectorSubtract(p1, top, tmp);
if ( VectorLengthSquared(tmp) < r ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
}
VectorSubtract(p1, bottom, tmp);
if ( VectorLengthSquared(tmp) < r ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
}
VectorCopy(offset, p2);
p2[2] -= offs;
VectorSubtract(p2, top, tmp);
if ( VectorLengthSquared(tmp) < r ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
}
VectorSubtract(p2, bottom, tmp);
if ( VectorLengthSquared(tmp) < r ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
}
// if between cylinder up and lower bounds
if ( (top[2] >= p1[2] && top[2] <= p2[2]) ||
(bottom[2] >= p1[2] && bottom[2] <= p2[2]) ) {
// 2d coordinates
top[2] = p1[2] = 0;
// if the cylinders overlap
VectorSubtract(top, p1, tmp);
if ( VectorLengthSquared(tmp) < r ) {
tw->trace.startsolid = tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
}
}
}
/*
==================
CM_TestBoundingBoxInCapsule
bounding box inside capsule check
==================
*/
static void CM_TestBoundingBoxInCapsule( traceWork_t *tw, clipHandle_t model ) {
vec3_t mins, maxs, offset, size[2];
clipHandle_t h;
cmodel_t *cmod;
int i;
// mins maxs of the capsule
CM_ModelBounds(model, mins, maxs);
// offset for capsule center
for ( i = 0 ; i < 3 ; i++ ) {
offset[i] = ( mins[i] + maxs[i] ) * 0.5;
size[0][i] = mins[i] - offset[i];
size[1][i] = maxs[i] - offset[i];
tw->start[i] -= offset[i];
tw->end[i] -= offset[i];
}
// replace the bounding box with the capsule
tw->sphere.use = qtrue;
tw->sphere.radius = ( size[1][0] > size[1][2] ) ? size[1][2]: size[1][0];
tw->sphere.halfheight = size[1][2];
VectorSet( tw->sphere.offset, 0, 0, size[1][2] - tw->sphere.radius );
// replace the capsule with the bounding box
h = CM_TempBoxModel(tw->size[0], tw->size[1], qfalse);
// calculate collision
cmod = CM_ClipHandleToModel( h );
CM_TestInLeaf( tw, &cmod->leaf );
}
/*
==================
CM_PositionTest
==================
*/
#define MAX_POSITION_LEAFS 1024
static void CM_PositionTest( traceWork_t *tw ) {
int leafs[MAX_POSITION_LEAFS];
int i;
leafList_t ll;
// identify the leafs we are touching
VectorAdd( tw->start, tw->size[0], ll.bounds[0] );
VectorAdd( tw->start, tw->size[1], ll.bounds[1] );
for (i=0 ; i<3 ; i++) {
ll.bounds[0][i] -= 1;
ll.bounds[1][i] += 1;
}
ll.count = 0;
ll.maxcount = MAX_POSITION_LEAFS;
ll.list = leafs;
ll.storeLeafs = CM_StoreLeafs;
ll.lastLeaf = 0;
ll.overflowed = qfalse;
cm.checkcount++;
CM_BoxLeafnums_r( &ll, 0 );
cm.checkcount++;
// test the contents of the leafs
for (i=0 ; i < ll.count ; i++) {
CM_TestInLeaf( tw, &cm.leafs[leafs[i]] );
if ( tw->trace.allsolid ) {
break;
}
}
}
/*
===============================================================================
TRACING
===============================================================================
*/
/*
================
CM_TraceThroughPatch
================
*/
static void CM_TraceThroughPatch( traceWork_t *tw, const cPatch_t *patch ) {
float oldFrac;
c_patch_traces++;
oldFrac = tw->trace.fraction;
CM_TraceThroughPatchCollide( tw, patch->pc );
if ( tw->trace.fraction < oldFrac ) {
tw->trace.surfaceFlags = patch->surfaceFlags;
tw->trace.contents = patch->contents;
}
}
/*
================
CM_TraceThroughBrush
================
*/
static void CM_TraceThroughBrush( traceWork_t *tw, const cbrush_t *brush ) {
int i;
cplane_t *plane, *clipplane;
double dist;
float enterFrac, leaveFrac;
double d1, d2;
qboolean getout, startout;
float f;
cbrushside_t *side, *leadside;
double t;
vec3_t startp;
vec3_t endp;
enterFrac = -1.0;
leaveFrac = 1.0;
clipplane = NULL;
if ( !brush->numsides ) {
return;
}
c_brush_traces++;
getout = qfalse;
startout = qfalse;
leadside = NULL;
if ( tw->sphere.use ) {
//
// compare the trace against all planes of the brush
// find the latest time the trace crosses a plane towards the interior
// and the earliest time the trace crosses a plane towards the exterior
//
for (i = 0; i < brush->numsides; i++) {
side = brush->sides + i;
plane = side->plane;
// adjust the plane distance appropriately for radius
dist = plane->dist + tw->sphere.radius;
// find the closest point on the capsule to the plane
t = DotProductDP( plane->normal, tw->sphere.offset );
if ( t > 0 )
{
VectorSubtractDP( tw->start, tw->sphere.offset, startp );
VectorSubtractDP( tw->end, tw->sphere.offset, endp );
}
else
{
VectorAddDP( tw->start, tw->sphere.offset, startp );
VectorAddDP( tw->end, tw->sphere.offset, endp );
}
d1 = DotProductDP( startp, plane->normal ) - dist;
d2 = DotProductDP( endp, plane->normal ) - dist;
if (d2 > 0) {
getout = qtrue; // endpoint is not in solid
}
if (d1 > 0) {
startout = qtrue;
}
// if completely in front of face, no intersection with the entire brush
if (d1 > 0 && ( d2 >= SURFACE_CLIP_EPSILON || d2 >= d1 ) ) {
return;
}
// if it doesn't cross the plane, the plane isn't relevant
if (d1 <= 0 && d2 <= 0 ) {
continue;
}
// crosses face
if (d1 > d2) { // enter
f = (d1-SURFACE_CLIP_EPSILON) / (d1-d2);
if ( f < 0 ) {
f = 0;
}
if (f > enterFrac) {
enterFrac = f;
clipplane = plane;
leadside = side;
}
} else { // leave
f = (d1+SURFACE_CLIP_EPSILON) / (d1-d2);
if ( f > 1 ) {
f = 1;
}
if (f < leaveFrac) {
leaveFrac = f;
}
}
}
} else {
//
// compare the trace against all planes of the brush
// find the latest time the trace crosses a plane towards the interior
// and the earliest time the trace crosses a plane towards the exterior
//
for (i = 0; i < brush->numsides; i++) {
side = brush->sides + i;
plane = side->plane;
// adjust the plane distance appropriately for mins/maxs
dist = plane->dist - DotProductDP( tw->offsets[ plane->signbits ], plane->normal );
d1 = DotProductDP( tw->start, plane->normal ) - dist;
d2 = DotProductDP( tw->end, plane->normal ) - dist;
if (d2 > 0) {
getout = qtrue; // endpoint is not in solid
}
if (d1 > 0) {
startout = qtrue;
}
// if completely in front of face, no intersection with the entire brush
if (d1 > 0 && ( d2 >= SURFACE_CLIP_EPSILON || d2 >= d1 ) ) {
return;
}
// if it doesn't cross the plane, the plane isn't relevant
if (d1 <= 0 && d2 <= 0 ) {
continue;
}
// crosses face
if (d1 > d2) { // enter
f = (d1-SURFACE_CLIP_EPSILON) / (d1-d2);
if ( f < 0 ) {
f = 0;
}
if (f > enterFrac) {
enterFrac = f;
clipplane = plane;
leadside = side;
}
} else { // leave
f = (d1+SURFACE_CLIP_EPSILON) / (d1-d2);
if ( f > 1 ) {
f = 1;
}
if (f < leaveFrac) {
leaveFrac = f;
}
}
}
}
//
// all planes have been checked, and the trace was not
// completely outside the brush
//
if (!startout) { // original point was inside brush
tw->trace.startsolid = qtrue;
if (!getout) {
tw->trace.allsolid = qtrue;
tw->trace.fraction = 0;
tw->trace.contents = brush->contents;
}
return;
}
if (enterFrac < leaveFrac) {
if (enterFrac > -1 && enterFrac < tw->trace.fraction) {
if (enterFrac < 0) {
enterFrac = 0;
}
tw->trace.fraction = enterFrac;
if ( clipplane != NULL ) {
tw->trace.plane = *clipplane;
}
if ( leadside != NULL ) {
tw->trace.surfaceFlags = leadside->surfaceFlags;
}
tw->trace.contents = brush->contents;
}
}
}
/*
================
CM_TraceThroughLeaf
================
*/
static void CM_TraceThroughLeaf( traceWork_t *tw, const cLeaf_t *leaf ) {
int k;
int brushnum;
cbrush_t *b;
cPatch_t *patch;
// trace line against all brushes in the leaf
for ( k = 0 ; k < leaf->numLeafBrushes ; k++ ) {
brushnum = cm.leafbrushes[leaf->firstLeafBrush+k];
b = &cm.brushes[brushnum];
if ( b->checkcount == cm.checkcount ) {
continue; // already checked this brush in another leaf
}
b->checkcount = cm.checkcount;
if ( !(b->contents & tw->contents) ) {
continue;
}
if ( !CM_BoundsIntersect( tw->bounds[0], tw->bounds[1],
b->bounds[0], b->bounds[1] ) ) {
continue;
}
CM_TraceThroughBrush( tw, b );
if ( !tw->trace.fraction ) {
return;
}
}
// trace line against all patches in the leaf
#ifdef BSPC
if (1) {
#else
if ( !cm_noCurves->integer ) {
#endif
for ( k = 0 ; k < leaf->numLeafSurfaces ; k++ ) {
patch = cm.surfaces[ cm.leafsurfaces[ leaf->firstLeafSurface + k ] ];
if ( !patch ) {
continue;
}
if ( patch->checkcount == cm.checkcount ) {
continue; // already checked this patch in another leaf
}
patch->checkcount = cm.checkcount;
if ( !(patch->contents & tw->contents) ) {
continue;
}
CM_TraceThroughPatch( tw, patch );
if ( !tw->trace.fraction ) {
return;
}
}
}
}
#define RADIUS_EPSILON 1.0f
/*
================
CM_TraceThroughSphere
get the first intersection of the ray with the sphere
================
*/
static void CM_TraceThroughSphere( traceWork_t *tw, const vec3_t origin, float radius, const vec3_t start, const vec3_t end ) {
float l1, l2, length, scale, fraction;
//float a;
float b, c, d, sqrtd;
vec3_t v1, dir, intersection;
// if inside the sphere
VectorSubtract(start, origin, dir);
l1 = VectorLengthSquared(dir);
if (l1 < Square(radius)) {
tw->trace.fraction = 0;
tw->trace.startsolid = qtrue;
// test for allsolid
VectorSubtract(end, origin, dir);
l1 = VectorLengthSquared(dir);
if (l1 < Square(radius)) {
tw->trace.allsolid = qtrue;
}
return;
}
//
VectorSubtract(end, start, dir);
length = VectorNormalize(dir);
//
l1 = CM_DistanceFromLineSquared(origin, start, end, dir);
VectorSubtract(end, origin, v1);
l2 = VectorLengthSquared(v1);
// if no intersection with the sphere and the end point is at least an epsilon away
if (l1 >= Square(radius) && l2 > Square(radius+SURFACE_CLIP_EPSILON)) {
return;
}
//
// | origin - (start + t * dir) | = radius
// a = dir[0]^2 + dir[1]^2 + dir[2]^2;
// b = 2 * (dir[0] * (start[0] - origin[0]) + dir[1] * (start[1] - origin[1]) + dir[2] * (start[2] - origin[2]));
// c = (start[0] - origin[0])^2 + (start[1] - origin[1])^2 + (start[2] - origin[2])^2 - radius^2;
//
VectorSubtract(start, origin, v1);
// dir is normalized so a = 1
//a = 1.0f;//dir[0] * dir[0] + dir[1] * dir[1] + dir[2] * dir[2];
b = 2.0f * (dir[0] * v1[0] + dir[1] * v1[1] + dir[2] * v1[2]);
c = v1[0] * v1[0] + v1[1] * v1[1] + v1[2] * v1[2] - (radius+RADIUS_EPSILON) * (radius+RADIUS_EPSILON);
d = b * b - 4.0f * c;// * a;
if (d > 0) {
sqrtd = SquareRootFloat(d);
// = (- b + sqrtd) * 0.5f; // / (2.0f * a);
fraction = (- b - sqrtd) * 0.5f; // / (2.0f * a);
//
if (fraction < 0) {
fraction = 0;
}
else {
fraction /= length;
}
if ( fraction < tw->trace.fraction ) {
tw->trace.fraction = fraction;
VectorSubtract(end, start, dir);
VectorMA(start, fraction, dir, intersection);
VectorSubtract(intersection, origin, dir);
#ifdef CAPSULE_DEBUG
l2 = VectorLength(dir);
if (l2 < radius) {
int bah = 1;
}
#endif
scale = 1 / (radius+RADIUS_EPSILON);
VectorScale(dir, scale, dir);
VectorCopy(dir, tw->trace.plane.normal);
VectorAdd( tw->modelOrigin, intersection, intersection);
tw->trace.plane.dist = DotProduct(tw->trace.plane.normal, intersection);
tw->trace.contents = CONTENTS_BODY;
}
}
else if (d == 0) {
//t1 = (- b ) / 2;
// slide along the sphere
}
// no intersection at all
}
/*
================
CM_TraceThroughVerticalCylinder
get the first intersection of the ray with the cylinder
the cylinder extends halfheight above and below the origin
================
*/
static void CM_TraceThroughVerticalCylinder( traceWork_t *tw, const vec3_t origin, float radius, float halfheight, const vec3_t start, const vec3_t end ) {
float length, scale, fraction, l1, l2;
//float a;
float b, c, d, sqrtd;
vec3_t v1, dir, start2d, end2d, org2d, intersection;
// 2d coordinates
VectorSet(start2d, start[0], start[1], 0);
VectorSet(end2d, end[0], end[1], 0);
VectorSet(org2d, origin[0], origin[1], 0);
// if start is between lower and upper cylinder bounds
if (start[2] <= origin[2] + halfheight &&
start[2] >= origin[2] - halfheight) {
// if inside the cylinder
VectorSubtract(start2d, org2d, dir);
l1 = VectorLengthSquared(dir);
if (l1 < Square(radius)) {
tw->trace.fraction = 0;
tw->trace.startsolid = qtrue;
VectorSubtract(end2d, org2d, dir);
l1 = VectorLengthSquared(dir);
if (l1 < Square(radius)) {
tw->trace.allsolid = qtrue;
}
return;
}
}
//
VectorSubtract(end2d, start2d, dir);
length = VectorNormalize(dir);
//
l1 = CM_DistanceFromLineSquared(org2d, start2d, end2d, dir);
VectorSubtract(end2d, org2d, v1);
l2 = VectorLengthSquared(v1);
// if no intersection with the cylinder and the end point is at least an epsilon away
if (l1 >= Square(radius) && l2 > Square(radius+SURFACE_CLIP_EPSILON)) {
return;
}
//
//
// (start[0] - origin[0] - t * dir[0]) ^ 2 + (start[1] - origin[1] - t * dir[1]) ^ 2 = radius ^ 2
// (v1[0] + t * dir[0]) ^ 2 + (v1[1] + t * dir[1]) ^ 2 = radius ^ 2;
// v1[0] ^ 2 + 2 * v1[0] * t * dir[0] + (t * dir[0]) ^ 2 +
// v1[1] ^ 2 + 2 * v1[1] * t * dir[1] + (t * dir[1]) ^ 2 = radius ^ 2
// t ^ 2 * (dir[0] ^ 2 + dir[1] ^ 2) + t * (2 * v1[0] * dir[0] + 2 * v1[1] * dir[1]) +
// v1[0] ^ 2 + v1[1] ^ 2 - radius ^ 2 = 0
//
VectorSubtract(start, origin, v1);
// dir is normalized so we can use a = 1
//a = 1.0f;// * (dir[0] * dir[0] + dir[1] * dir[1]);
b = 2.0f * (v1[0] * dir[0] + v1[1] * dir[1]);
c = v1[0] * v1[0] + v1[1] * v1[1] - (radius+RADIUS_EPSILON) * (radius+RADIUS_EPSILON);
d = b * b - 4.0f * c;// * a;
if (d > 0) {
sqrtd = SquareRootFloat(d);
// = (- b + sqrtd) * 0.5f;// / (2.0f * a);
fraction = (- b - sqrtd) * 0.5f;// / (2.0f * a);
//
if (fraction < 0) {
fraction = 0;
}
else {
fraction /= length;
}
if ( fraction < tw->trace.fraction ) {
VectorSubtract(end, start, dir);
VectorMA(start, fraction, dir, intersection);
// if the intersection is between the cylinder lower and upper bound
if (intersection[2] <= origin[2] + halfheight &&
intersection[2] >= origin[2] - halfheight) {
//
tw->trace.fraction = fraction;
VectorSubtract(intersection, origin, dir);
dir[2] = 0;
#ifdef CAPSULE_DEBUG
l2 = VectorLength(dir);
if (l2 <= radius) {
int bah = 1;
}
#endif
scale = 1 / (radius+RADIUS_EPSILON);
VectorScale(dir, scale, dir);
VectorCopy(dir, tw->trace.plane.normal);
VectorAdd( tw->modelOrigin, intersection, intersection);
tw->trace.plane.dist = DotProduct(tw->trace.plane.normal, intersection);
tw->trace.contents = CONTENTS_BODY;
}
}
}
else if (d == 0) {
//t[0] = (- b ) / 2 * a;
// slide along the cylinder
}
// no intersection at all
}
/*
================
CM_TraceCapsuleThroughCapsule
capsule vs. capsule collision (not rotated)
================
*/
static void CM_TraceCapsuleThroughCapsule( traceWork_t *tw, clipHandle_t model ) {
int i;
vec3_t mins, maxs;
vec3_t top, bottom, starttop, startbottom, endtop, endbottom;
vec3_t offset, symetricSize[2];
float radius, halfwidth, halfheight, offs, h;
CM_ModelBounds(model, mins, maxs);
// test trace bounds vs. capsule bounds
if ( tw->bounds[0][0] > maxs[0] + RADIUS_EPSILON
|| tw->bounds[0][1] > maxs[1] + RADIUS_EPSILON
|| tw->bounds[0][2] > maxs[2] + RADIUS_EPSILON
|| tw->bounds[1][0] < mins[0] - RADIUS_EPSILON
|| tw->bounds[1][1] < mins[1] - RADIUS_EPSILON
|| tw->bounds[1][2] < mins[2] - RADIUS_EPSILON
) {
return;
}
// top origin and bottom origin of each sphere at start and end of trace
VectorAdd(tw->start, tw->sphere.offset, starttop);
VectorSubtract(tw->start, tw->sphere.offset, startbottom);
VectorAdd(tw->end, tw->sphere.offset, endtop);
VectorSubtract(tw->end, tw->sphere.offset, endbottom);
// calculate top and bottom of the capsule spheres to collide with
for ( i = 0 ; i < 3 ; i++ ) {
offset[i] = ( mins[i] + maxs[i] ) * 0.5;
symetricSize[0][i] = mins[i] - offset[i];
symetricSize[1][i] = maxs[i] - offset[i];
}
halfwidth = symetricSize[ 1 ][ 0 ];
halfheight = symetricSize[ 1 ][ 2 ];
radius = ( halfwidth > halfheight ) ? halfheight : halfwidth;
offs = halfheight - radius;
VectorCopy(offset, top);
top[2] += offs;
VectorCopy(offset, bottom);
bottom[2] -= offs;
// expand radius of spheres
radius += tw->sphere.radius;
// if there is horizontal movement
if ( tw->start[0] != tw->end[0] || tw->start[1] != tw->end[1] ) {
// height of the expanded cylinder is the height of both cylinders minus the radius of both spheres
h = halfheight + tw->sphere.halfheight - radius;
// if the cylinder has a height
if ( h > 0 ) {
// test for collisions between the cylinders
CM_TraceThroughVerticalCylinder(tw, offset, radius, h, tw->start, tw->end);
}
}
// test for collision between the spheres
CM_TraceThroughSphere(tw, top, radius, startbottom, endbottom);
CM_TraceThroughSphere(tw, bottom, radius, starttop, endtop);
}
/*
================
CM_TraceBoundingBoxThroughCapsule
bounding box vs. capsule collision
================
*/
static void CM_TraceBoundingBoxThroughCapsule( traceWork_t *tw, clipHandle_t model ) {
vec3_t mins, maxs, offset, size[2];
clipHandle_t h;
cmodel_t *cmod;
int i;
// mins maxs of the capsule
CM_ModelBounds(model, mins, maxs);
// offset for capsule center