DOOM-3-BFG

TraceModel.cpp (40446B)

---

 /*
 ===========================================================================
 
 Doom 3 BFG Edition GPL Source Code
 Copyright (C) 1993-2012 id Software LLC, a ZeniMax Media company. 
 
 This file is part of the Doom 3 BFG Edition GPL Source Code ("Doom 3 BFG Edition Source Code").  
 
 Doom 3 BFG Edition 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 3 of the License, or
 (at your option) any later version.
 
 Doom 3 BFG Edition 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 Doom 3 BFG Edition Source Code.  If not, see <http://www.gnu.org/licenses/>.
 
 In addition, the Doom 3 BFG Edition Source Code is also subject to certain additional terms. You should have received a copy of these additional terms immediately following the terms and conditions of the GNU General Public License which accompanied the Doom 3 BFG Edition Source Code.  If not, please request a copy in writing from id Software at the address below.
 
 If you have questions concerning this license or the applicable additional terms, you may contact in writing id Software LLC, c/o ZeniMax Media Inc., Suite 120, Rockville, Maryland 20850 USA.
 
 ===========================================================================
 */
 
 #pragma hdrstop
 #include "../../idlib/precompiled.h"
 #include "TraceModel.h"
 
 /*
 ============
 idTraceModel::SetupBox
 ============
 */
 void idTraceModel::SetupBox( const idBounds &boxBounds ) {
 	int i;
 
 	if ( type != TRM_BOX ) {
 		InitBox();
 	}
 	// offset to center
 	offset = ( boxBounds[0] + boxBounds[1] ) * 0.5f;
 	// set box vertices
 	for ( i = 0; i < 8; i++ ) {
 		verts[i][0] = boxBounds[(i^(i>>1))&1][0];
 		verts[i][1] = boxBounds[(i>>1)&1][1];
 		verts[i][2] = boxBounds[(i>>2)&1][2];
 	}
 	// set polygon plane distances
 	polys[0].dist = -boxBounds[0][2];
 	polys[1].dist = boxBounds[1][2];
 	polys[2].dist = -boxBounds[0][1];
 	polys[3].dist = boxBounds[1][0];
 	polys[4].dist = boxBounds[1][1];
 	polys[5].dist = -boxBounds[0][0];
 	// set polygon bounds
 	for ( i = 0; i < 6; i++ ) {
 		polys[i].bounds = boxBounds;
 	}
 	polys[0].bounds[1][2] = boxBounds[0][2];
 	polys[1].bounds[0][2] = boxBounds[1][2];
 	polys[2].bounds[1][1] = boxBounds[0][1];
 	polys[3].bounds[0][0] = boxBounds[1][0];
 	polys[4].bounds[0][1] = boxBounds[1][1];
 	polys[5].bounds[1][0] = boxBounds[0][0];
 
 	bounds = boxBounds;
 }
 
 /*
 ============
 idTraceModel::SetupBox
 
   The origin is placed at the center of the cube.
 ============
 */
 void idTraceModel::SetupBox( const float size ) {
 	idBounds boxBounds;
 	float halfSize;
 
 	halfSize = size * 0.5f;
 	boxBounds[0].Set( -halfSize, -halfSize, -halfSize );
 	boxBounds[1].Set( halfSize, halfSize, halfSize );
 	SetupBox( boxBounds );
 }
 
 /*
 ============
 idTraceModel::InitBox
 
   Initialize size independent box.
 ============
 */
 void idTraceModel::InitBox() {
 	int i;
 
 	type = TRM_BOX;
 	numVerts = 8;
 	numEdges = 12;
 	numPolys = 6;
 
 	// set box edges
 	for ( i = 0; i < 4; i++ ) {
 		edges[ i + 1 ].v[0] = i;
 		edges[ i + 1 ].v[1] = (i + 1) & 3;
 		edges[ i + 5 ].v[0] = 4 + i;
 		edges[ i + 5 ].v[1] = 4 + ((i + 1) & 3);
 		edges[ i + 9 ].v[0] = i;
 		edges[ i + 9 ].v[1] = 4 + i;
 	}
 
 	// all edges of a polygon go counter clockwise
 	polys[0].numEdges = 4;
 	polys[0].edges[0] = -4;
 	polys[0].edges[1] = -3;
 	polys[0].edges[2] = -2;
 	polys[0].edges[3] = -1;
 	polys[0].normal.Set( 0.0f, 0.0f, -1.0f );
 
 	polys[1].numEdges = 4;
 	polys[1].edges[0] = 5;
 	polys[1].edges[1] = 6;
 	polys[1].edges[2] = 7;
 	polys[1].edges[3] = 8;
 	polys[1].normal.Set( 0.0f, 0.0f, 1.0f );
 
 	polys[2].numEdges = 4;
 	polys[2].edges[0] = 1;
 	polys[2].edges[1] = 10;
 	polys[2].edges[2] = -5;
 	polys[2].edges[3] = -9;
 	polys[2].normal.Set( 0.0f, -1.0f,  0.0f );
 
 	polys[3].numEdges = 4;
 	polys[3].edges[0] = 2;
 	polys[3].edges[1] = 11;
 	polys[3].edges[2] = -6;
 	polys[3].edges[3] = -10;
 	polys[3].normal.Set( 1.0f,  0.0f,  0.0f );
 
 	polys[4].numEdges = 4;
 	polys[4].edges[0] = 3;
 	polys[4].edges[1] = 12;
 	polys[4].edges[2] = -7;
 	polys[4].edges[3] = -11;
 	polys[4].normal.Set( 0.0f,  1.0f,  0.0f );
 
 	polys[5].numEdges = 4;
 	polys[5].edges[0] = 4;
 	polys[5].edges[1] = 9;
 	polys[5].edges[2] = -8;
 	polys[5].edges[3] = -12;
 	polys[5].normal.Set( -1.0f,  0.0f,  0.0f );
 
 	// convex model
 	isConvex = true;
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::SetupOctahedron
 ============
 */
 void idTraceModel::SetupOctahedron( const idBounds &octBounds ) {
 	int i, e0, e1, v0, v1, v2;
 	idVec3 v;
 
 	if ( type != TRM_OCTAHEDRON ) {
 		InitOctahedron();
 	}
 
 	offset = ( octBounds[0] + octBounds[1] ) * 0.5f;
 	v[0] = octBounds[1][0] - offset[0];
 	v[1] = octBounds[1][1] - offset[1];
 	v[2] = octBounds[1][2] - offset[2];
 
 	// set vertices
 	verts[0].Set( offset.x + v[0], offset.y, offset.z );
 	verts[1].Set( offset.x - v[0], offset.y, offset.z );
 	verts[2].Set( offset.x, offset.y + v[1], offset.z );
 	verts[3].Set( offset.x, offset.y - v[1], offset.z );
 	verts[4].Set( offset.x, offset.y, offset.z + v[2] );
 	verts[5].Set( offset.x, offset.y, offset.z - v[2] );
 
 	// set polygons
 	for ( i = 0; i < numPolys; i++ ) {
 		e0 = polys[i].edges[0];
 		e1 = polys[i].edges[1];
 		v0 = edges[abs(e0)].v[INT32_SIGNBITSET(e0)];
 		v1 = edges[abs(e0)].v[INT32_SIGNBITNOTSET(e0)];
 		v2 = edges[abs(e1)].v[INT32_SIGNBITNOTSET(e1)];
 		// polygon plane
 		polys[i].normal = ( verts[v1] - verts[v0] ).Cross( verts[v2] - verts[v0] );
 		polys[i].normal.Normalize();
 		polys[i].dist = polys[i].normal * verts[v0];
 		// polygon bounds
 		polys[i].bounds[0] = polys[i].bounds[1] = verts[v0];
 		polys[i].bounds.AddPoint( verts[v1] );
 		polys[i].bounds.AddPoint( verts[v2] );
 	}
 
 	// trm bounds
 	bounds = octBounds;
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::SetupOctahedron
 
   The origin is placed at the center of the octahedron.
 ============
 */
 void idTraceModel::SetupOctahedron( const float size ) {
 	idBounds octBounds;
 	float halfSize;
 
 	halfSize = size * 0.5f;
 	octBounds[0].Set( -halfSize, -halfSize, -halfSize );
 	octBounds[1].Set( halfSize, halfSize, halfSize );
 	SetupOctahedron( octBounds );
 }
 
 /*
 ============
 idTraceModel::InitOctahedron
 
   Initialize size independent octahedron.
 ============
 */
 void idTraceModel::InitOctahedron() {
 
 	type = TRM_OCTAHEDRON;
 	numVerts = 6;
 	numEdges = 12;
 	numPolys = 8;
 
 	// set edges
 	edges[ 1].v[0] =  4; edges[ 1].v[1] =  0;
 	edges[ 2].v[0] =  0; edges[ 2].v[1] =  2;
 	edges[ 3].v[0] =  2; edges[ 3].v[1] =  4;
 	edges[ 4].v[0] =  2; edges[ 4].v[1] =  1;
 	edges[ 5].v[0] =  1; edges[ 5].v[1] =  4;
 	edges[ 6].v[0] =  1; edges[ 6].v[1] =  3;
 	edges[ 7].v[0] =  3; edges[ 7].v[1] =  4;
 	edges[ 8].v[0] =  3; edges[ 8].v[1] =  0;
 	edges[ 9].v[0] =  5; edges[ 9].v[1] =  2;
 	edges[10].v[0] =  0; edges[10].v[1] =  5;
 	edges[11].v[0] =  5; edges[11].v[1] =  1;
 	edges[12].v[0] =  5; edges[12].v[1] =  3;
 
 	// all edges of a polygon go counter clockwise
 	polys[0].numEdges = 3;
 	polys[0].edges[0] = 1;
 	polys[0].edges[1] = 2;
 	polys[0].edges[2] = 3;
 
 	polys[1].numEdges = 3;
 	polys[1].edges[0] = -3;
 	polys[1].edges[1] = 4;
 	polys[1].edges[2] = 5;
 
 	polys[2].numEdges = 3;
 	polys[2].edges[0] = -5;
 	polys[2].edges[1] = 6;
 	polys[2].edges[2] = 7;
 
 	polys[3].numEdges = 3;
 	polys[3].edges[0] = -7;
 	polys[3].edges[1] = 8;
 	polys[3].edges[2] = -1;
 
 	polys[4].numEdges = 3;
 	polys[4].edges[0] = 9;
 	polys[4].edges[1] = -2;
 	polys[4].edges[2] = 10;
 
 	polys[5].numEdges = 3;
 	polys[5].edges[0] = 11;
 	polys[5].edges[1] = -4;
 	polys[5].edges[2] = -9;
 
 	polys[6].numEdges = 3;
 	polys[6].edges[0] = 12;
 	polys[6].edges[1] = -6;
 	polys[6].edges[2] = -11;
 
 	polys[7].numEdges = 3;
 	polys[7].edges[0] = -10;
 	polys[7].edges[1] = -8;
 	polys[7].edges[2] = -12;
 
 	// convex model
 	isConvex = true;
 }
 
 /*
 ============
 idTraceModel::SetupDodecahedron
 ============
 */
 void idTraceModel::SetupDodecahedron( const idBounds &dodBounds ) {
 	int i, e0, e1, e2, e3, v0, v1, v2, v3, v4;
 	float s, d;
 	idVec3 a, b, c;
 
 	if ( type != TRM_DODECAHEDRON ) {
 		InitDodecahedron();
 	}
 
 	a[0] = a[1] = a[2] = 0.5773502691896257f; // 1.0f / ( 3.0f ) ^ 0.5f;
 	b[0] = b[1] = b[2] = 0.3568220897730899f; // ( ( 3.0f - ( 5.0f ) ^ 0.5f ) / 6.0f ) ^ 0.5f;
 	c[0] = c[1] = c[2] = 0.9341723589627156f; // ( ( 3.0f + ( 5.0f ) ^ 0.5f ) / 6.0f ) ^ 0.5f;
 	d = 0.5f / c[0];
 	s = ( dodBounds[1][0] - dodBounds[0][0] ) * d;
 	a[0] *= s;
 	b[0] *= s;
 	c[0] *= s;
 	s = ( dodBounds[1][1] - dodBounds[0][1] ) * d;
 	a[1] *= s;
 	b[1] *= s;
 	c[1] *= s;
 	s = ( dodBounds[1][2] - dodBounds[0][2] ) * d;
 	a[2] *= s;
 	b[2] *= s;
 	c[2] *= s;
 
 	offset = ( dodBounds[0] + dodBounds[1] ) * 0.5f;
 
 	// set vertices
 	verts[ 0].Set( offset.x + a[0], offset.y + a[1], offset.z + a[2] );
 	verts[ 1].Set( offset.x + a[0], offset.y + a[1], offset.z - a[2] );
 	verts[ 2].Set( offset.x + a[0], offset.y - a[1], offset.z + a[2] );
 	verts[ 3].Set( offset.x + a[0], offset.y - a[1], offset.z - a[2] );
 	verts[ 4].Set( offset.x - a[0], offset.y + a[1], offset.z + a[2] );
 	verts[ 5].Set( offset.x - a[0], offset.y + a[1], offset.z - a[2] );
 	verts[ 6].Set( offset.x - a[0], offset.y - a[1], offset.z + a[2] );
 	verts[ 7].Set( offset.x - a[0], offset.y - a[1], offset.z - a[2] );
 	verts[ 8].Set( offset.x + b[0], offset.y + c[1], offset.z        );
 	verts[ 9].Set( offset.x - b[0], offset.y + c[1], offset.z        );
 	verts[10].Set( offset.x + b[0], offset.y - c[1], offset.z        );
 	verts[11].Set( offset.x - b[0], offset.y - c[1], offset.z        );
 	verts[12].Set( offset.x + c[0], offset.y       , offset.z + b[2] );
 	verts[13].Set( offset.x + c[0], offset.y       , offset.z - b[2] );
 	verts[14].Set( offset.x - c[0], offset.y       , offset.z + b[2] );
 	verts[15].Set( offset.x - c[0], offset.y       , offset.z - b[2] );
 	verts[16].Set( offset.x       , offset.y + b[1], offset.z + c[2] );
 	verts[17].Set( offset.x       , offset.y - b[1], offset.z + c[2] );
 	verts[18].Set( offset.x       , offset.y + b[1], offset.z - c[2] );
 	verts[19].Set( offset.x       , offset.y - b[1], offset.z - c[2] );
 
 	// set polygons
 	for ( i = 0; i < numPolys; i++ ) {
 		e0 = polys[i].edges[0];
 		e1 = polys[i].edges[1];
 		e2 = polys[i].edges[2];
 		e3 = polys[i].edges[3];
 		v0 = edges[abs(e0)].v[INT32_SIGNBITSET(e0)];
 		v1 = edges[abs(e0)].v[INT32_SIGNBITNOTSET(e0)];
 		v2 = edges[abs(e1)].v[INT32_SIGNBITNOTSET(e1)];
 		v3 = edges[abs(e2)].v[INT32_SIGNBITNOTSET(e2)];
 		v4 = edges[abs(e3)].v[INT32_SIGNBITNOTSET(e3)];
 		// polygon plane
 		polys[i].normal = ( verts[v1] - verts[v0] ).Cross( verts[v2] - verts[v0] );
 		polys[i].normal.Normalize();
 		polys[i].dist = polys[i].normal * verts[v0];
 		// polygon bounds
 		polys[i].bounds[0] = polys[i].bounds[1] = verts[v0];
 		polys[i].bounds.AddPoint( verts[v1] );
 		polys[i].bounds.AddPoint( verts[v2] );
 		polys[i].bounds.AddPoint( verts[v3] );
 		polys[i].bounds.AddPoint( verts[v4] );
 	}
 
 	// trm bounds
 	bounds = dodBounds;
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::SetupDodecahedron
 
   The origin is placed at the center of the octahedron.
 ============
 */
 void idTraceModel::SetupDodecahedron( const float size ) {
 	idBounds dodBounds;
 	float halfSize;
 
 	halfSize = size * 0.5f;
 	dodBounds[0].Set( -halfSize, -halfSize, -halfSize );
 	dodBounds[1].Set( halfSize, halfSize, halfSize );
 	SetupDodecahedron( dodBounds );
 }
 
 /*
 ============
 idTraceModel::InitDodecahedron
 
   Initialize size independent dodecahedron.
 ============
 */
 void idTraceModel::InitDodecahedron() {
 
 	type = TRM_DODECAHEDRON;
 	numVerts = 20;
 	numEdges = 30;
 	numPolys = 12;
 
 	// set edges
 	edges[ 1].v[0] =  0; edges[ 1].v[1] =  8;
 	edges[ 2].v[0] =  8; edges[ 2].v[1] =  9;
 	edges[ 3].v[0] =  9; edges[ 3].v[1] =  4;
 	edges[ 4].v[0] =  4; edges[ 4].v[1] = 16;
 	edges[ 5].v[0] = 16; edges[ 5].v[1] =  0;
 	edges[ 6].v[0] = 16; edges[ 6].v[1] = 17;
 	edges[ 7].v[0] = 17; edges[ 7].v[1] =  2;
 	edges[ 8].v[0] =  2; edges[ 8].v[1] = 12;
 	edges[ 9].v[0] = 12; edges[ 9].v[1] =  0;
 	edges[10].v[0] =  2; edges[10].v[1] = 10;
 	edges[11].v[0] = 10; edges[11].v[1] =  3;
 	edges[12].v[0] =  3; edges[12].v[1] = 13;
 	edges[13].v[0] = 13; edges[13].v[1] = 12;
 	edges[14].v[0] =  9; edges[14].v[1] =  5;
 	edges[15].v[0] =  5; edges[15].v[1] = 15;
 	edges[16].v[0] = 15; edges[16].v[1] = 14;
 	edges[17].v[0] = 14; edges[17].v[1] =  4;
 	edges[18].v[0] =  3; edges[18].v[1] = 19;
 	edges[19].v[0] = 19; edges[19].v[1] = 18;
 	edges[20].v[0] = 18; edges[20].v[1] =  1;
 	edges[21].v[0] =  1; edges[21].v[1] = 13;
 	edges[22].v[0] =  7; edges[22].v[1] = 11;
 	edges[23].v[0] = 11; edges[23].v[1] =  6;
 	edges[24].v[0] =  6; edges[24].v[1] = 14;
 	edges[25].v[0] = 15; edges[25].v[1] =  7;
 	edges[26].v[0] =  1; edges[26].v[1] =  8;
 	edges[27].v[0] = 18; edges[27].v[1] =  5;
 	edges[28].v[0] =  6; edges[28].v[1] = 17;
 	edges[29].v[0] = 11; edges[29].v[1] = 10;
 	edges[30].v[0] = 19; edges[30].v[1] =  7;
 
 	// all edges of a polygon go counter clockwise
 	polys[0].numEdges = 5;
 	polys[0].edges[0] = 1;
 	polys[0].edges[1] = 2;
 	polys[0].edges[2] = 3;
 	polys[0].edges[3] = 4;
 	polys[0].edges[4] = 5;
 
 	polys[1].numEdges = 5;
 	polys[1].edges[0] = -5;
 	polys[1].edges[1] = 6;
 	polys[1].edges[2] = 7;
 	polys[1].edges[3] = 8;
 	polys[1].edges[4] = 9;
 
 	polys[2].numEdges = 5;
 	polys[2].edges[0] = -8;
 	polys[2].edges[1] = 10;
 	polys[2].edges[2] = 11;
 	polys[2].edges[3] = 12;
 	polys[2].edges[4] = 13;
 
 	polys[3].numEdges = 5;
 	polys[3].edges[0] = 14;
 	polys[3].edges[1] = 15;
 	polys[3].edges[2] = 16;
 	polys[3].edges[3] = 17;
 	polys[3].edges[4] = -3;
 
 	polys[4].numEdges = 5;
 	polys[4].edges[0] = 18;
 	polys[4].edges[1] = 19;
 	polys[4].edges[2] = 20;
 	polys[4].edges[3] = 21;
 	polys[4].edges[4] = -12;
 
 	polys[5].numEdges = 5;
 	polys[5].edges[0] = 22;
 	polys[5].edges[1] = 23;
 	polys[5].edges[2] = 24;
 	polys[5].edges[3] = -16;
 	polys[5].edges[4] = 25;
 
 	polys[6].numEdges = 5;
 	polys[6].edges[0] = -9;
 	polys[6].edges[1] = -13;
 	polys[6].edges[2] = -21;
 	polys[6].edges[3] = 26;
 	polys[6].edges[4] = -1;
 
 	polys[7].numEdges = 5;
 	polys[7].edges[0] = -26;
 	polys[7].edges[1] = -20;
 	polys[7].edges[2] = 27;
 	polys[7].edges[3] = -14;
 	polys[7].edges[4] = -2;
 
 	polys[8].numEdges = 5;
 	polys[8].edges[0] = -4;
 	polys[8].edges[1] = -17;
 	polys[8].edges[2] = -24;
 	polys[8].edges[3] = 28;
 	polys[8].edges[4] = -6;
 
 	polys[9].numEdges = 5;
 	polys[9].edges[0] = -23;
 	polys[9].edges[1] = 29;
 	polys[9].edges[2] = -10;
 	polys[9].edges[3] = -7;
 	polys[9].edges[4] = -28;
 
 	polys[10].numEdges = 5;
 	polys[10].edges[0] = -25;
 	polys[10].edges[1] = -15;
 	polys[10].edges[2] = -27;
 	polys[10].edges[3] = -19;
 	polys[10].edges[4] = 30;
 
 	polys[11].numEdges = 5;
 	polys[11].edges[0] = -30;
 	polys[11].edges[1] = -18;
 	polys[11].edges[2] = -11;
 	polys[11].edges[3] = -29;
 	polys[11].edges[4] = -22;
 
 	// convex model
 	isConvex = true;
 }
 
 /*
 ============
 idTraceModel::SetupCylinder
 ============
 */
 void idTraceModel::SetupCylinder( const idBounds &cylBounds, const int numSides ) {
 	int i, n, ii, n2;
 	float angle;
 	idVec3 halfSize;
 
 	n = numSides;
 	if ( n < 3 ) {
 		n = 3;
 	}
 	if ( n * 2 > MAX_TRACEMODEL_VERTS ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many vertices\n" );
 		n = MAX_TRACEMODEL_VERTS / 2;
 	}
 	if ( n * 3 > MAX_TRACEMODEL_EDGES ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many sides\n" );
 		n = MAX_TRACEMODEL_EDGES / 3;
 	}
 	if ( n + 2 > MAX_TRACEMODEL_POLYS ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCylinder: too many polygons\n" );
 		n = MAX_TRACEMODEL_POLYS - 2;
 	}
 
 	type = TRM_CYLINDER;
 	numVerts = n * 2;
 	numEdges = n * 3;
 	numPolys = n + 2;
 	offset = ( cylBounds[0] + cylBounds[1] ) * 0.5f;
 	halfSize = cylBounds[1] - offset;
 	for ( i = 0; i < n; i++ ) {
 		// verts
 		angle = idMath::TWO_PI * i / n;
 		verts[i].x = cos( angle ) * halfSize.x + offset.x;
 		verts[i].y = sin( angle ) * halfSize.y + offset.y;
 		verts[i].z = -halfSize.z + offset.z;
 		verts[n+i].x = verts[i].x;
 		verts[n+i].y = verts[i].y;
 		verts[n+i].z = halfSize.z + offset.z;
 		// edges
 		ii = i + 1;
 		n2 = n << 1;
 		edges[ii].v[0] = i;
 		edges[ii].v[1] = ii % n;
 		edges[n+ii].v[0] = edges[ii].v[0] + n;
 		edges[n+ii].v[1] = edges[ii].v[1] + n;
 		edges[n2+ii].v[0] = i;
 		edges[n2+ii].v[1] = n + i;
 		// vertical polygon edges
 		polys[i].numEdges = 4;
 		polys[i].edges[0] = ii;
 		polys[i].edges[1] = n2 + (ii % n) + 1;
 		polys[i].edges[2] = -(n + ii);
 		polys[i].edges[3] = -(n2 + ii);
 		// bottom and top polygon edges
 		polys[n].edges[i] = -(n - i);
 		polys[n+1].edges[i] = n + ii;
 	}
 	// bottom and top polygon numEdges
 	polys[n].numEdges = n;
 	polys[n+1].numEdges = n;
 	// polygons
 	for ( i = 0; i < n; i++ ) {
 		// vertical polygon plane
 		polys[i].normal = (verts[(i+1)%n] - verts[i]).Cross( verts[n+i] - verts[i] );
 		polys[i].normal.Normalize();
 		polys[i].dist = polys[i].normal * verts[i];
 		// vertical polygon bounds
 		polys[i].bounds.Clear();
 		polys[i].bounds.AddPoint( verts[i] );
 		polys[i].bounds.AddPoint( verts[(i+1)%n] );
 		polys[i].bounds[0][2] = -halfSize.z + offset.z;
 		polys[i].bounds[1][2] = halfSize.z + offset.z;
 	}
 	// bottom and top polygon plane
 	polys[n].normal.Set( 0.0f, 0.0f, -1.0f );
 	polys[n].dist = -cylBounds[0][2];
 	polys[n+1].normal.Set( 0.0f, 0.0f, 1.0f );
 	polys[n+1].dist = cylBounds[1][2];
 	// trm bounds
 	bounds = cylBounds;
 	// bottom and top polygon bounds
 	polys[n].bounds = bounds;
 	polys[n].bounds[1][2] = bounds[0][2];
 	polys[n+1].bounds = bounds;
 	polys[n+1].bounds[0][2] = bounds[1][2];
 	// convex model
 	isConvex = true;
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::SetupCylinder
 
   The origin is placed at the center of the cylinder.
 ============
 */
 void idTraceModel::SetupCylinder( const float height, const float width, const int numSides ) {
 	idBounds cylBounds;
 	float halfHeight, halfWidth;
 
 	halfHeight = height * 0.5f;
 	halfWidth = width * 0.5f;
 	cylBounds[0].Set( -halfWidth, -halfWidth, -halfHeight );
 	cylBounds[1].Set( halfWidth, halfWidth, halfHeight );
 	SetupCylinder( cylBounds, numSides );
 }
 
 /*
 ============
 idTraceModel::SetupCone
 ============
 */
 void idTraceModel::SetupCone( const idBounds &coneBounds, const int numSides ) {
 	int i, n, ii;
 	float angle;
 	idVec3 halfSize;
 
 	n = numSides;
 	if ( n < 2 ) {
 		n = 3;
 	}
 	if ( n + 1 > MAX_TRACEMODEL_VERTS ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many vertices\n" );
 		n = MAX_TRACEMODEL_VERTS - 1;
 	}
 	if ( n * 2 > MAX_TRACEMODEL_EDGES ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many edges\n" );
 		n = MAX_TRACEMODEL_EDGES / 2;
 	}
 	if ( n + 1 > MAX_TRACEMODEL_POLYS ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupCone: too many polygons\n" );
 		n = MAX_TRACEMODEL_POLYS - 1;
 	}
 
 	type = TRM_CONE;
 	numVerts = n + 1;
 	numEdges = n * 2;
 	numPolys = n + 1;
 	offset = ( coneBounds[0] + coneBounds[1] ) * 0.5f;
 	halfSize = coneBounds[1] - offset;
 	verts[n].Set( 0.0f, 0.0f, halfSize.z + offset.z );
 	for ( i = 0; i < n; i++ ) {
 		// verts
 		angle = idMath::TWO_PI * i / n;
 		verts[i].x = cos( angle ) * halfSize.x + offset.x;
 		verts[i].y = sin( angle ) * halfSize.y + offset.y;
 		verts[i].z = -halfSize.z + offset.z;
 		// edges
 		ii = i + 1;
 		edges[ii].v[0] = i;
 		edges[ii].v[1] = ii % n;
 		edges[n+ii].v[0] = i;
 		edges[n+ii].v[1] = n;
 		// vertical polygon edges
 		polys[i].numEdges = 3;
 		polys[i].edges[0] = ii;
 		polys[i].edges[1] = n + (ii % n) + 1;
 		polys[i].edges[2] = -(n + ii);
 		// bottom polygon edges
 		polys[n].edges[i] = -(n - i);
 	}
 	// bottom polygon numEdges
 	polys[n].numEdges = n;
 
 	// polygons
 	for ( i = 0; i < n; i++ ) {
 		// polygon plane
 		polys[i].normal = (verts[(i+1)%n] - verts[i]).Cross( verts[n] - verts[i] );
 		polys[i].normal.Normalize();
 		polys[i].dist = polys[i].normal * verts[i];
 		// polygon bounds
 		polys[i].bounds.Clear();
 		polys[i].bounds.AddPoint( verts[i] );
 		polys[i].bounds.AddPoint( verts[(i+1)%n] );
 		polys[i].bounds.AddPoint( verts[n] );
 	}
 	// bottom polygon plane
 	polys[n].normal.Set( 0.0f, 0.0f, -1.0f );
 	polys[n].dist = -coneBounds[0][2];
 	// trm bounds
 	bounds = coneBounds;
 	// bottom polygon bounds
 	polys[n].bounds = bounds;
 	polys[n].bounds[1][2] = bounds[0][2];
 	// convex model
 	isConvex = true;
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::SetupCone
 
   The origin is placed at the apex of the cone.
 ============
 */
 void idTraceModel::SetupCone( const float height, const float width, const int numSides ) {
 	idBounds coneBounds;
 	float halfWidth;
 
 	halfWidth = width * 0.5f;
 	coneBounds[0].Set( -halfWidth, -halfWidth, -height );
 	coneBounds[1].Set( halfWidth, halfWidth, 0.0f );
 	SetupCone( coneBounds, numSides );
 }
 
 /*
 ============
 idTraceModel::SetupBone
 
   The origin is placed at the center of the bone.
 ============
 */
 void idTraceModel::SetupBone( const float length, const float width ) {
 	int i, j, edgeNum;
 	float halfLength = length * 0.5f;
 
 	if ( type != TRM_BONE ) {
 		InitBone();
 	}
 	// offset to center
 	offset.Set( 0.0f, 0.0f, 0.0f );
 	// set vertices
 	verts[0].Set( 0.0f, 0.0f, -halfLength );
 	verts[1].Set( 0.0f, width * -0.5f, 0.0f );
 	verts[2].Set( width * 0.5f, width * 0.25f, 0.0f );
 	verts[3].Set( width * -0.5f, width * 0.25f, 0.0f );
 	verts[4].Set( 0.0f, 0.0f, halfLength );
 	// set bounds
 	bounds[0].Set( width * -0.5f, width * -0.5f, -halfLength );
 	bounds[1].Set( width * 0.5f, width * 0.25f, halfLength );
 	// poly plane normals
 	polys[0].normal = ( verts[2] - verts[0] ).Cross( verts[1] - verts[0] );
 	polys[0].normal.Normalize();
 	polys[2].normal.Set( -polys[0].normal[0], polys[0].normal[1], polys[0].normal[2] );
 	polys[3].normal.Set( polys[0].normal[0], polys[0].normal[1], -polys[0].normal[2] );
 	polys[5].normal.Set( -polys[0].normal[0], polys[0].normal[1], -polys[0].normal[2] );
 	polys[1].normal = (verts[3] - verts[0]).Cross(verts[2] - verts[0]);
 	polys[1].normal.Normalize();
 	polys[4].normal.Set( polys[1].normal[0], polys[1].normal[1], -polys[1].normal[2] );
 	// poly plane distances
 	for ( i = 0; i < 6; i++ ) {
 		polys[i].dist = polys[i].normal * verts[ edges[ abs(polys[i].edges[0]) ].v[0] ];
 		polys[i].bounds.Clear();
 		for ( j = 0; j < 3; j++ ) {
 			edgeNum = polys[i].edges[ j ];
 			polys[i].bounds.AddPoint( verts[ edges[abs(edgeNum)].v[edgeNum < 0] ] );
 		}
 	}
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::InitBone
 
   Initialize size independent bone.
 ============
 */
 void idTraceModel::InitBone() {
 	int i;
 
 	type = TRM_BONE;
 	numVerts = 5;
 	numEdges = 9;
 	numPolys = 6;
 
 	// set bone edges
 	for ( i = 0; i < 3; i++ ) {
 		edges[ i + 1 ].v[0] = 0;
 		edges[ i + 1 ].v[1] = i + 1;
 		edges[ i + 4 ].v[0] = 1 + i;
 		edges[ i + 4 ].v[1] = 1 + ((i + 1) % 3);
 		edges[ i + 7 ].v[0] = i + 1;
 		edges[ i + 7 ].v[1] = 4;
 	}
 
 	// all edges of a polygon go counter clockwise
 	polys[0].numEdges = 3;
 	polys[0].edges[0] = 2;
 	polys[0].edges[1] = -4;
 	polys[0].edges[2] = -1;
 
 	polys[1].numEdges = 3;
 	polys[1].edges[0] = 3;
 	polys[1].edges[1] = -5;
 	polys[1].edges[2] = -2;
 
 	polys[2].numEdges = 3;
 	polys[2].edges[0] = 1;
 	polys[2].edges[1] = -6;
 	polys[2].edges[2] = -3;
 
 	polys[3].numEdges = 3;
 	polys[3].edges[0] = 4;
 	polys[3].edges[1] = 8;
 	polys[3].edges[2] = -7;
 
 	polys[4].numEdges = 3;
 	polys[4].edges[0] = 5;
 	polys[4].edges[1] = 9;
 	polys[4].edges[2] = -8;
 
 	polys[5].numEdges = 3;
 	polys[5].edges[0] = 6;
 	polys[5].edges[1] = 7;
 	polys[5].edges[2] = -9;
 
 	// convex model
 	isConvex = true;
 }
 
 /*
 ============
 idTraceModel::SetupPolygon
 ============
 */
 void idTraceModel::SetupPolygon( const idVec3 *v, const int count ) {
 	int i, j;
 	idVec3 mid;
 
 	type = TRM_POLYGON;
 	numVerts = count;
 	// times three because we need to be able to turn the polygon into a volume
 	if ( numVerts * 3 > MAX_TRACEMODEL_EDGES ) {
 		idLib::common->Printf( "WARNING: idTraceModel::SetupPolygon: too many vertices\n" );
 		numVerts = MAX_TRACEMODEL_EDGES / 3;
 	}
 
 	numEdges = numVerts;
 	numPolys = 2;
 	// set polygon planes
 	polys[0].numEdges = numEdges;
 	polys[0].normal = ( v[1] - v[0] ).Cross( v[2] - v[0] );
 	polys[0].normal.Normalize();
 	polys[0].dist = polys[0].normal * v[0];
 	polys[1].numEdges = numEdges;
 	polys[1].normal = -polys[0].normal;
 	polys[1].dist = -polys[0].dist;
 	// setup verts, edges and polygons
 	polys[0].bounds.Clear();
 	mid = vec3_origin;
 	for ( i = 0, j = 1; i < numVerts; i++, j++ ) {
 		if ( j >= numVerts ) {
 			j = 0;
 		}
 		verts[i] = v[i];
 		edges[i+1].v[0] = i;
 		edges[i+1].v[1] = j;
 		edges[i+1].normal = polys[0].normal.Cross( v[i] - v[j] );
 		edges[i+1].normal.Normalize();
 		polys[0].edges[i] = i + 1;
 		polys[1].edges[i] = -(numVerts - i);
 		polys[0].bounds.AddPoint( verts[i] );
 		mid += v[i];
 	}
 	polys[1].bounds = polys[0].bounds;
 	// offset to center
 	offset = mid * (1.0f / numVerts);
 	// total bounds
 	bounds = polys[0].bounds;
 	// considered non convex because the model has no volume
 	isConvex = false;
 }
 
 /*
 ============
 idTraceModel::SetupPolygon
 ============
 */
 void idTraceModel::SetupPolygon( const idWinding &w ) {
 	int i;
 	idVec3 *verts;
 
 	verts = (idVec3 *) _alloca16( w.GetNumPoints() * sizeof( idVec3 ) );
 	for ( i = 0; i < w.GetNumPoints(); i++ ) {
 		verts[i] = w[i].ToVec3();
 	}
 	SetupPolygon( verts, w.GetNumPoints() );
 }
 
 /*
 ============
 idTraceModel::VolumeFromPolygon
 ============
 */
 void idTraceModel::VolumeFromPolygon( idTraceModel &trm, float thickness ) const {
 	int i;
 
 	trm = *this;
 	trm.type = TRM_POLYGONVOLUME;
 	trm.numVerts = numVerts * 2;
 	trm.numEdges = numEdges * 3;
 	trm.numPolys = numEdges + 2;
 	for ( i = 0; i < numEdges; i++ ) {
 		trm.verts[ numVerts + i ] = verts[i] - thickness * polys[0].normal;
 		trm.edges[ numEdges + i + 1 ].v[0] = numVerts + i;
 		trm.edges[ numEdges + i + 1 ].v[1] = numVerts + (i+1) % numVerts;
 		trm.edges[ numEdges * 2 + i + 1 ].v[0] = i;
 		trm.edges[ numEdges * 2 + i + 1 ].v[1] = numVerts + i;
 		trm.polys[1].edges[i] = -(numEdges + i + 1);
 		trm.polys[2+i].numEdges = 4;
 		trm.polys[2+i].edges[0] = -(i + 1);
 		trm.polys[2+i].edges[1] = numEdges*2 + i + 1;
 		trm.polys[2+i].edges[2] = numEdges + i + 1;
 		trm.polys[2+i].edges[3] = -(numEdges*2 + (i+1) % numEdges + 1);
 		trm.polys[2+i].normal = (verts[(i + 1) % numVerts] - verts[i]).Cross( polys[0].normal );
 		trm.polys[2+i].normal.Normalize();
 		trm.polys[2+i].dist = trm.polys[2+i].normal * verts[i];
 	}
 	trm.polys[1].dist = trm.polys[1].normal * trm.verts[ numEdges ];
 
 	trm.GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::GenerateEdgeNormals
 ============
 */
 #define SHARP_EDGE_DOT	-0.7f
 
 int idTraceModel::GenerateEdgeNormals() {
 	int i, j, edgeNum, numSharpEdges;
 	float dot;
 	idVec3 dir;
 	traceModelPoly_t *poly;
 	traceModelEdge_t *edge;
 
 	for ( i = 0; i <= numEdges; i++ ) {
 		edges[i].normal.Zero();
 	}
 
 	numSharpEdges = 0;
 	for ( i = 0; i < numPolys; i++ ) {
 		poly = polys + i;
 		for ( j = 0; j < poly->numEdges; j++ ) {
 			edgeNum = poly->edges[j];
 			edge = edges + abs( edgeNum );
 			if ( edge->normal[0] == 0.0f && edge->normal[1] == 0.0f && edge->normal[2] == 0.0f ) {
 				edge->normal = poly->normal;
 			}
 			else {
 				dot = edge->normal * poly->normal;
 				// if the two planes make a very sharp edge
 				if ( dot < SHARP_EDGE_DOT ) {
 					// max length normal pointing outside both polygons
 					dir = verts[ edge->v[edgeNum > 0]] - verts[ edge->v[edgeNum < 0]];
 					edge->normal = edge->normal.Cross( dir ) + poly->normal.Cross( -dir );
 					edge->normal *= ( 0.5f / ( 0.5f + 0.5f * SHARP_EDGE_DOT ) ) / edge->normal.Length();
 					numSharpEdges++;
 				}
 				else {
 					edge->normal = ( 0.5f / ( 0.5f + 0.5f * dot ) ) * ( edge->normal + poly->normal );
 				}
 			}
 		}
 	}
 	return numSharpEdges;
 }
 
 /*
 ============
 idTraceModel::Translate
 ============
 */
 void idTraceModel::Translate( const idVec3 &translation ) {
 	int i;
 
 	for ( i = 0; i < numVerts; i++ ) {
 		verts[i] += translation;
 	}
 	for ( i = 0; i < numPolys; i++ ) {
 		polys[i].dist += polys[i].normal * translation;
 		polys[i].bounds[0] += translation;
 		polys[i].bounds[1] += translation;
 	}
 	offset += translation;
 	bounds[0] += translation;
 	bounds[1] += translation;
 }
 
 /*
 ============
 idTraceModel::Rotate
 ============
 */
 void idTraceModel::Rotate( const idMat3 &rotation ) {
 	int i, j, edgeNum;
 
 	for ( i = 0; i < numVerts; i++ ) {
 		verts[i] *= rotation;
 	}
 
 	bounds.Clear();
 	for ( i = 0; i < numPolys; i++ ) {
 		polys[i].normal *= rotation;
 		polys[i].bounds.Clear();
 		edgeNum = 0;
 		for ( j = 0; j < polys[i].numEdges; j++ ) {
 			edgeNum = polys[i].edges[j];
 			polys[i].bounds.AddPoint( verts[edges[abs(edgeNum)].v[INT32_SIGNBITSET(edgeNum)]] );
 		}
 		polys[i].dist = polys[i].normal * verts[edges[abs(edgeNum)].v[INT32_SIGNBITSET(edgeNum)]];
 		bounds += polys[i].bounds;
 	}
 
 	GenerateEdgeNormals();
 }
 
 /*
 ============
 idTraceModel::Shrink
 ============
 */
 void idTraceModel::Shrink( const float m ) {
 	int i, j, edgeNum;
 	traceModelEdge_t *edge;
 	idVec3 dir;
 
 	if ( type == TRM_POLYGON ) {
 		for ( i = 0; i < numEdges; i++ ) {
 			edgeNum = polys[0].edges[i];
 			edge = &edges[abs(edgeNum)];
 			dir = verts[ edge->v[ INT32_SIGNBITSET(edgeNum) ] ] - verts[ edge->v[ INT32_SIGNBITNOTSET(edgeNum) ] ];
 			if ( dir.Normalize() < 2.0f * m ) {
 				continue;
 			}
 			dir *= m;
 			verts[ edge->v[ 0 ] ] -= dir;
 			verts[ edge->v[ 1 ] ] += dir;
 		}
 		return;
 	}
 
 	for ( i = 0; i < numPolys; i++ ) {
 		polys[i].dist -= m;
 
 		for ( j = 0; j < polys[i].numEdges; j++ ) {
 			edgeNum = polys[i].edges[j];
 			edge = &edges[abs(edgeNum)];
 			verts[ edge->v[ INT32_SIGNBITSET(edgeNum) ] ] -= polys[i].normal * m;
 		}
 	}
 }
 
 /*
 ============
 idTraceModel::Compare
 ============
 */
 bool idTraceModel::Compare( const idTraceModel &trm ) const {
 	int i;
 
 	if ( type != trm.type || numVerts != trm.numVerts || 
 			numEdges != trm.numEdges || numPolys != trm.numPolys ) {
 		return false;
 	}
 	if ( bounds != trm.bounds || offset != trm.offset ) {
 		return false;
 	}
 
 	switch( type ) {
 		case TRM_INVALID:
 		case TRM_BOX:
 		case TRM_OCTAHEDRON:
 		case TRM_DODECAHEDRON:
 		case TRM_CYLINDER:
 		case TRM_CONE:
 			break;
 		case TRM_BONE:
 		case TRM_POLYGON:
 		case TRM_POLYGONVOLUME:
 		case TRM_CUSTOM:
 			for ( i = 0; i < trm.numVerts; i++ ) {
 				if ( verts[i] != trm.verts[i] ) {
 					return false;
 				}
 			}
 			break;
 	}
 	return true;
 }
 
 /*
 ============
 idTraceModel::GetPolygonArea
 ============
 */
 float idTraceModel::GetPolygonArea( int polyNum ) const {
 	int i;
 	idVec3 base, v1, v2, cross;
 	float total;
 	const traceModelPoly_t *poly;
 
 	if ( polyNum < 0 || polyNum >= numPolys ) {
 		return 0.0f;
 	}
 	poly = &polys[polyNum];
 	total = 0.0f;
 	base = verts[ edges[ abs(poly->edges[0]) ].v[ INT32_SIGNBITSET( poly->edges[0] ) ] ];
 	for ( i = 0; i < poly->numEdges; i++ ) {
 		v1 = verts[ edges[ abs(poly->edges[i]) ].v[ INT32_SIGNBITSET( poly->edges[i] ) ] ] - base;
 		v2 = verts[ edges[ abs(poly->edges[i]) ].v[ INT32_SIGNBITNOTSET( poly->edges[i] ) ] ] - base;
 		cross = v1.Cross( v2 );
 		total += cross.Length();
 	}
 	return total * 0.5f;
 }
 
 /*
 ============
 idTraceModel::GetOrderedSilhouetteEdges
 ============
 */
 int idTraceModel::GetOrderedSilhouetteEdges( const int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1], int silEdges[MAX_TRACEMODEL_EDGES] ) const {
 	int i, j, edgeNum, numSilEdges, nextSilVert;
 	int unsortedSilEdges[MAX_TRACEMODEL_EDGES];
 
 	numSilEdges = 0;
 	for ( i = 1; i <= numEdges; i++ ) {
 		if ( edgeIsSilEdge[i] ) {
 			unsortedSilEdges[numSilEdges++] = i;
 		}
 	}
 
 	silEdges[0] = unsortedSilEdges[0];
 	unsortedSilEdges[0] = -1;
 	nextSilVert = edges[silEdges[0]].v[0];
 	for ( i = 1; i < numSilEdges; i++ ) {
 		for ( j = 1; j < numSilEdges; j++ ) {
 			edgeNum = unsortedSilEdges[j];
 			if ( edgeNum >= 0 ) {
 				if ( edges[edgeNum].v[0] == nextSilVert ) {
 					nextSilVert = edges[edgeNum].v[1];
 					silEdges[i] = edgeNum;
 					break;
 				}
 				if ( edges[edgeNum].v[1] == nextSilVert ) {
 					nextSilVert = edges[edgeNum].v[0];
 					silEdges[i] = -edgeNum;
 					break;
 				}
 			}
 		}
 		if ( j >= numSilEdges ) {
 			silEdges[i] = 1;	// shouldn't happen
 		}
 		unsortedSilEdges[j] = -1;
 	}
 	return numSilEdges;
 }
 
 /*
 ============
 idTraceModel::GetProjectionSilhouetteEdges
 ============
 */
 int idTraceModel::GetProjectionSilhouetteEdges( const idVec3 &projectionOrigin, int silEdges[MAX_TRACEMODEL_EDGES] ) const {
 	int i, j, edgeNum;
 	int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1];
 	const traceModelPoly_t *poly;
 	idVec3 dir;
 
 	memset( edgeIsSilEdge, 0, sizeof( edgeIsSilEdge ) );
 
 	for ( i = 0; i < numPolys; i++ ) {
 		poly = &polys[i];
 		edgeNum = poly->edges[0];
 		dir = verts[ edges[abs(edgeNum)].v[ INT32_SIGNBITSET(edgeNum) ] ] - projectionOrigin;
 		if ( dir * poly->normal < 0.0f ) {
 			for ( j = 0; j < poly->numEdges; j++ ) {
 				edgeNum = poly->edges[j];
 				edgeIsSilEdge[abs(edgeNum)] ^= 1;
 			}
 		}
 	}
 
 	return GetOrderedSilhouetteEdges( edgeIsSilEdge, silEdges );
 }
 
 /*
 ============
 idTraceModel::GetParallelProjectionSilhouetteEdges
 ============
 */
 int idTraceModel::GetParallelProjectionSilhouetteEdges( const idVec3 &projectionDir, int silEdges[MAX_TRACEMODEL_EDGES] ) const {
 	int i, j, edgeNum;
 	int edgeIsSilEdge[MAX_TRACEMODEL_EDGES+1];
 	const traceModelPoly_t *poly;
 
 	memset( edgeIsSilEdge, 0, sizeof( edgeIsSilEdge ) );
 
 	for ( i = 0; i < numPolys; i++ ) {
 		poly = &polys[i];
 		if ( projectionDir * poly->normal < 0.0f ) {
 			for ( j = 0; j < poly->numEdges; j++ ) {
 				edgeNum = poly->edges[j];
 				edgeIsSilEdge[abs(edgeNum)] ^= 1;
 			}
 		}
 	}
 
 	return GetOrderedSilhouetteEdges( edgeIsSilEdge, silEdges );
 }
 
 
 /*
 
   credits to Brian Mirtich for his paper "Fast and Accurate Computation of Polyhedral Mass Properties"
 
 */
 
 typedef struct projectionIntegrals_s {
 	float P1;
 	float Pa, Pb;
 	float Paa, Pab, Pbb;
 	float Paaa, Paab, Pabb, Pbbb;
 } projectionIntegrals_t;
 
 /*
 ============
 idTraceModel::ProjectionIntegrals
 ============
 */
 void idTraceModel::ProjectionIntegrals( int polyNum, int a, int b, struct projectionIntegrals_s &integrals ) const {
 	const traceModelPoly_t *poly;
 	int i, edgeNum;
 	idVec3 v1, v2;
 	float a0, a1, da;
 	float b0, b1, db;
 	float a0_2, a0_3, a0_4, b0_2, b0_3, b0_4;
 	float a1_2, a1_3, b1_2, b1_3;
 	float C1, Ca, Caa, Caaa, Cb, Cbb, Cbbb;
 	float Cab, Kab, Caab, Kaab, Cabb, Kabb;
 
 	memset(&integrals, 0, sizeof(projectionIntegrals_t));
 	poly = &polys[polyNum];
 	for ( i = 0; i < poly->numEdges; i++ ) {
 		edgeNum = poly->edges[i];
 		v1 = verts[ edges[ abs(edgeNum) ].v[ edgeNum < 0 ] ];
 		v2 = verts[ edges[ abs(edgeNum) ].v[ edgeNum > 0 ] ];
 		a0 = v1[a];
 		b0 = v1[b];
 		a1 = v2[a];
 		b1 = v2[b];
 		da = a1 - a0;
 		db = b1 - b0;
 		a0_2 = a0 * a0;
 		a0_3 = a0_2 * a0;
 		a0_4 = a0_3 * a0;
 		b0_2 = b0 * b0;
 		b0_3 = b0_2 * b0;
 		b0_4 = b0_3 * b0;
 		a1_2 = a1 * a1;
 		a1_3 = a1_2 * a1; 
 		b1_2 = b1 * b1;
 		b1_3 = b1_2 * b1;
 
 		C1 = a1 + a0;
 		Ca = a1 * C1 + a0_2;
 		Caa = a1 * Ca + a0_3;
 		Caaa = a1 * Caa + a0_4;
 		Cb = b1 * (b1 + b0) + b0_2;
 		Cbb = b1 * Cb + b0_3;
 		Cbbb = b1 * Cbb + b0_4;
 		Cab = 3 * a1_2 + 2 * a1 * a0 + a0_2;
 		Kab = a1_2 + 2 * a1 * a0 + 3 * a0_2;
 		Caab = a0 * Cab + 4 * a1_3;
 		Kaab = a1 * Kab + 4 * a0_3;
 		Cabb = 4 * b1_3 + 3 * b1_2 * b0 + 2 * b1 * b0_2 + b0_3;
 		Kabb = b1_3 + 2 * b1_2 * b0 + 3 * b1 * b0_2 + 4 * b0_3;
 
 		integrals.P1 += db * C1;
 		integrals.Pa += db * Ca;
 		integrals.Paa += db * Caa;
 		integrals.Paaa += db * Caaa;
 		integrals.Pb += da * Cb;
 		integrals.Pbb += da * Cbb;
 		integrals.Pbbb += da * Cbbb;
 		integrals.Pab += db * (b1 * Cab + b0 * Kab);
 		integrals.Paab += db * (b1 * Caab + b0 * Kaab);
 		integrals.Pabb += da * (a1 * Cabb + a0 * Kabb);
 	}
 
 	integrals.P1 *= (1.0f / 2.0f);
 	integrals.Pa *= (1.0f / 6.0f);
 	integrals.Paa *= (1.0f / 12.0f);
 	integrals.Paaa *= (1.0f / 20.0f);
 	integrals.Pb *= (1.0f / -6.0f);
 	integrals.Pbb *= (1.0f / -12.0f);
 	integrals.Pbbb *= (1.0f / -20.0f);
 	integrals.Pab *= (1.0f / 24.0f);
 	integrals.Paab *= (1.0f / 60.0f);
 	integrals.Pabb *= (1.0f / -60.0f);
 }
 
 typedef struct polygonIntegrals_s {
 	float Fa, Fb, Fc;
 	float Faa, Fbb, Fcc;
 	float Faaa, Fbbb, Fccc;
 	float Faab, Fbbc, Fcca;
 } polygonIntegrals_t;
 
 /*
 ============
 idTraceModel::PolygonIntegrals
 ============
 */
 void idTraceModel::PolygonIntegrals( int polyNum, int a, int b, int c, struct polygonIntegrals_s &integrals ) const {
 	projectionIntegrals_t pi;
 	idVec3 n;
 	float w;
 	float k1, k2, k3, k4;
 
 	ProjectionIntegrals( polyNum, a, b, pi );
 
 	n = polys[polyNum].normal;
 	w = -polys[polyNum].dist;
 	k1 = 1 / n[c];
 	k2 = k1 * k1;
 	k3 = k2 * k1;
 	k4 = k3 * k1;
 
 	integrals.Fa = k1 * pi.Pa;
 	integrals.Fb = k1 * pi.Pb;
 	integrals.Fc = -k2 * (n[a] * pi.Pa + n[b] * pi.Pb + w * pi.P1);
 
 	integrals.Faa = k1 * pi.Paa;
 	integrals.Fbb = k1 * pi.Pbb;
 	integrals.Fcc = k3 * (Square(n[a]) * pi.Paa + 2 * n[a] * n[b] * pi.Pab + Square(n[b]) * pi.Pbb
 			+ w * (2 * (n[a] * pi.Pa + n[b] * pi.Pb) + w * pi.P1));
 
 	integrals.Faaa = k1 * pi.Paaa;
 	integrals.Fbbb = k1 * pi.Pbbb;
 	integrals.Fccc = -k4 * (Cube(n[a]) * pi.Paaa + 3 * Square(n[a]) * n[b] * pi.Paab 
 			+ 3 * n[a] * Square(n[b]) * pi.Pabb + Cube(n[b]) * pi.Pbbb
 			+ 3 * w * (Square(n[a]) * pi.Paa + 2 * n[a] * n[b] * pi.Pab + Square(n[b]) * pi.Pbb)
 			+ w * w * (3 * (n[a] * pi.Pa + n[b] * pi.Pb) + w * pi.P1));
 
 	integrals.Faab = k1 * pi.Paab;
 	integrals.Fbbc = -k2 * (n[a] * pi.Pabb + n[b] * pi.Pbbb + w * pi.Pbb);
 	integrals.Fcca = k3 * (Square(n[a]) * pi.Paaa + 2 * n[a] * n[b] * pi.Paab + Square(n[b]) * pi.Pabb
 			+ w * (2 * (n[a] * pi.Paa + n[b] * pi.Pab) + w * pi.Pa));
 }
 
 typedef struct volumeIntegrals_s {
 	float T0;
 	idVec3 T1;
 	idVec3 T2;
 	idVec3 TP;
 } volumeIntegrals_t;
 
 /*
 ============
 idTraceModel::VolumeIntegrals
 ============
 */
 void idTraceModel::VolumeIntegrals( struct volumeIntegrals_s &integrals ) const {
 	const traceModelPoly_t *poly;
 	polygonIntegrals_t pi;
 	int i, a, b, c;
 	float nx, ny, nz;
 
 	memset( &integrals, 0, sizeof(volumeIntegrals_t) );
 	for ( i = 0; i < numPolys; i++ ) {
 		poly = &polys[i];
 
 		nx = idMath::Fabs( poly->normal[0] );
 		ny = idMath::Fabs( poly->normal[1] );
 		nz = idMath::Fabs( poly->normal[2] );
 		if ( nx > ny && nx > nz ) {
 			c = 0;
 		}
 		else {
 			c = (ny > nz) ? 1 : 2;
 		}
 		a = (c + 1) % 3;
 		b = (a + 1) % 3;
 
 		PolygonIntegrals( i, a, b, c, pi );
 
 		integrals.T0 += poly->normal[0] * ((a == 0) ? pi.Fa : ((b == 0) ? pi.Fb : pi.Fc));
 
 		integrals.T1[a] += poly->normal[a] * pi.Faa;
 		integrals.T1[b] += poly->normal[b] * pi.Fbb;
 		integrals.T1[c] += poly->normal[c] * pi.Fcc;
 		integrals.T2[a] += poly->normal[a] * pi.Faaa;
 		integrals.T2[b] += poly->normal[b] * pi.Fbbb;
 		integrals.T2[c] += poly->normal[c] * pi.Fccc;
 		integrals.TP[a] += poly->normal[a] * pi.Faab;
 		integrals.TP[b] += poly->normal[b] * pi.Fbbc;
 		integrals.TP[c] += poly->normal[c] * pi.Fcca;
 	}
 
 	integrals.T1 *= 0.5f;
 	integrals.T2 *= (1.0f / 3.0f);
 	integrals.TP *= 0.5f;
 }
 
 /*
 ============
 idTraceModel::GetMassProperties
 ============
 */
 void idTraceModel::GetMassProperties( const float density, float &mass, idVec3 &centerOfMass, idMat3 &inertiaTensor ) const {
 	volumeIntegrals_t integrals;
 
 	// if polygon trace model
 	if ( type == TRM_POLYGON ) {
 		idTraceModel trm;
 
 		VolumeFromPolygon( trm, 1.0f );
 		trm.GetMassProperties( density, mass, centerOfMass, inertiaTensor );
 		return;
 	}
 
 	VolumeIntegrals( integrals );
 
 	// if no volume
 	if ( integrals.T0 == 0.0f ) {
 		mass = 1.0f;
 		centerOfMass.Zero();
 		inertiaTensor.Identity();
 		return;
 	}
 
 	// mass of model
 	mass = density * integrals.T0;
 	// center of mass
 	centerOfMass = integrals.T1 / integrals.T0;
 	// compute inertia tensor
 	inertiaTensor[0][0] = density * (integrals.T2[1] + integrals.T2[2]);
 	inertiaTensor[1][1] = density * (integrals.T2[2] + integrals.T2[0]);
 	inertiaTensor[2][2] = density * (integrals.T2[0] + integrals.T2[1]);
 	inertiaTensor[0][1] = inertiaTensor[1][0] = - density * integrals.TP[0];
 	inertiaTensor[1][2] = inertiaTensor[2][1] = - density * integrals.TP[1];
 	inertiaTensor[2][0] = inertiaTensor[0][2] = - density * integrals.TP[2];
 	// translate inertia tensor to center of mass
 	inertiaTensor[0][0] -= mass * (centerOfMass[1]*centerOfMass[1] + centerOfMass[2]*centerOfMass[2]);
 	inertiaTensor[1][1] -= mass * (centerOfMass[2]*centerOfMass[2] + centerOfMass[0]*centerOfMass[0]);
 	inertiaTensor[2][2] -= mass * (centerOfMass[0]*centerOfMass[0] + centerOfMass[1]*centerOfMass[1]);
 	inertiaTensor[0][1] = inertiaTensor[1][0] += mass * centerOfMass[0] * centerOfMass[1];
 	inertiaTensor[1][2] = inertiaTensor[2][1] += mass * centerOfMass[1] * centerOfMass[2];
 	inertiaTensor[2][0] = inertiaTensor[0][2] += mass * centerOfMass[2] * centerOfMass[0];
 }