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etqw-sdk/source/idlib/bv/Box.cpp

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as released 2008-05-29
2008-05-29 00:00:00 +00:00
// Copyright (C) 2007 Id Software, Inc.
//
#include "../precompiled.h"
#pragma hdrstop
idBox box_zero( vec3_zero, vec3_zero, mat3_identity );
/*
4---{4}---5
+ /| /|
Z {7} {8} {5} |
- / | / {9}
7--{6}----6 |
| | | |
{11} 0---|-{0}-1
| / | / -
| {3} {10} {1} Y
|/ |/ +
3---{2}---2
- X +
plane bits:
0 = min x
1 = max x
2 = min y
3 = max y
4 = min z
5 = max z
*/
static int boxVertPlanes[8] = {
( (1<<0) | (1<<2) | (1<<4) ),
( (1<<1) | (1<<2) | (1<<4) ),
( (1<<1) | (1<<3) | (1<<4) ),
( (1<<0) | (1<<3) | (1<<4) ),
( (1<<0) | (1<<2) | (1<<5) ),
( (1<<1) | (1<<2) | (1<<5) ),
( (1<<1) | (1<<3) | (1<<5) ),
( (1<<0) | (1<<3) | (1<<5) )
};
static int boxVertEdges[8][3] = {
// bottom
{ 3, 0, 8 },
{ 0, 1, 9 },
{ 1, 2, 10 },
{ 2, 3, 11 },
// top
{ 7, 4, 8 },
{ 4, 5, 9 },
{ 5, 6, 10 },
{ 6, 7, 11 }
};
static int boxEdgePlanes[12][2] = {
// bottom
{ 4, 2 },
{ 4, 1 },
{ 4, 3 },
{ 4, 0 },
// top
{ 5, 2 },
{ 5, 1 },
{ 5, 3 },
{ 5, 0 },
// sides
{ 0, 2 },
{ 2, 1 },
{ 1, 3 },
{ 3, 0 }
};
static int boxEdgeVerts[12][2] = {
// bottom
{ 0, 1 },
{ 1, 2 },
{ 2, 3 },
{ 3, 0 },
// top
{ 4, 5 },
{ 5, 6 },
{ 6, 7 },
{ 7, 4 },
// sides
{ 0, 4 },
{ 1, 5 },
{ 2, 6 },
{ 3, 7 }
};
#define POS_EDGE( e ) ( e + 1 )
#define NEG_EDGE( e ) -( e + 1 )
static int boxPlaneEdges[6][4] = {
{ NEG_EDGE( 3 ), POS_EDGE( 11 ), POS_EDGE( 7 ), NEG_EDGE( 8 ) }, // min x
{ POS_EDGE( 9 ), POS_EDGE( 5 ), NEG_EDGE( 10 ), NEG_EDGE( 1 ) }, // max x
{ NEG_EDGE( 0 ), POS_EDGE( 8 ), POS_EDGE( 4 ), NEG_EDGE( 9 ) }, // min y
{ NEG_EDGE( 2 ), POS_EDGE( 10 ), POS_EDGE( 6 ), NEG_EDGE( 11 ) }, // max y
{ POS_EDGE( 0 ), POS_EDGE( 1 ), POS_EDGE( 2 ), POS_EDGE( 3 ) }, // min z
{ NEG_EDGE( 7 ), NEG_EDGE( 6 ), NEG_EDGE( 5 ), NEG_EDGE( 4 ) } // max z
};
static int boxPlaneBitsSilVerts[64][7] = {
{ 0, 0, 0, 0, 0, 0, 0 }, // 000000 = 0
{ 4, 7, 4, 0, 3, 0, 0 }, // 000001 = 1
{ 4, 5, 6, 2, 1, 0, 0 }, // 000010 = 2
{ 0, 0, 0, 0, 0, 0, 0 }, // 000011 = 3
{ 4, 4, 5, 1, 0, 0, 0 }, // 000100 = 4
{ 6, 3, 7, 4, 5, 1, 0 }, // 000101 = 5
{ 6, 4, 5, 6, 2, 1, 0 }, // 000110 = 6
{ 0, 0, 0, 0, 0, 0, 0 }, // 000111 = 7
{ 4, 6, 7, 3, 2, 0, 0 }, // 001000 = 8
{ 6, 6, 7, 4, 0, 3, 2 }, // 001001 = 9
{ 6, 5, 6, 7, 3, 2, 1 }, // 001010 = 10
{ 0, 0, 0, 0, 0, 0, 0 }, // 001011 = 11
{ 0, 0, 0, 0, 0, 0, 0 }, // 001100 = 12
{ 0, 0, 0, 0, 0, 0, 0 }, // 001101 = 13
{ 0, 0, 0, 0, 0, 0, 0 }, // 001110 = 14
{ 0, 0, 0, 0, 0, 0, 0 }, // 001111 = 15
{ 4, 0, 1, 2, 3, 0, 0 }, // 010000 = 16
{ 6, 0, 1, 2, 3, 7, 4 }, // 010001 = 17
{ 6, 3, 2, 6, 5, 1, 0 }, // 010010 = 18
{ 0, 0, 0, 0, 0, 0, 0 }, // 010011 = 19
{ 6, 1, 2, 3, 0, 4, 5 }, // 010100 = 20
{ 6, 1, 2, 3, 7, 4, 5 }, // 010101 = 21
{ 6, 2, 3, 0, 4, 5, 6 }, // 010110 = 22
{ 0, 0, 0, 0, 0, 0, 0 }, // 010111 = 23
{ 6, 0, 1, 2, 6, 7, 3 }, // 011000 = 24
{ 6, 0, 1, 2, 6, 7, 4 }, // 011001 = 25
{ 6, 0, 1, 5, 6, 7, 3 }, // 011010 = 26
{ 0, 0, 0, 0, 0, 0, 0 }, // 011011 = 27
{ 0, 0, 0, 0, 0, 0, 0 }, // 011100 = 28
{ 0, 0, 0, 0, 0, 0, 0 }, // 011101 = 29
{ 0, 0, 0, 0, 0, 0, 0 }, // 011110 = 30
{ 0, 0, 0, 0, 0, 0, 0 }, // 011111 = 31
{ 4, 7, 6, 5, 4, 0, 0 }, // 100000 = 32
{ 6, 7, 6, 5, 4, 0, 3 }, // 100001 = 33
{ 6, 5, 4, 7, 6, 2, 1 }, // 100010 = 34
{ 0, 0, 0, 0, 0, 0, 0 }, // 100011 = 35
{ 6, 4, 7, 6, 5, 1, 0 }, // 100100 = 36
{ 6, 3, 7, 6, 5, 1, 0 }, // 100101 = 37
{ 6, 4, 7, 6, 2, 1, 0 }, // 100110 = 38
{ 0, 0, 0, 0, 0, 0, 0 }, // 100111 = 39
{ 6, 6, 5, 4, 7, 3, 2 }, // 101000 = 40
{ 6, 6, 5, 4, 0, 3, 2 }, // 101001 = 41
{ 6, 5, 4, 7, 3, 2, 1 }, // 101010 = 42
{ 0, 0, 0, 0, 0, 0, 0 }, // 101011 = 43
{ 0, 0, 0, 0, 0, 0, 0 }, // 101100 = 44
{ 0, 0, 0, 0, 0, 0, 0 }, // 101101 = 45
{ 0, 0, 0, 0, 0, 0, 0 }, // 101110 = 46
{ 0, 0, 0, 0, 0, 0, 0 }, // 101111 = 47
{ 0, 0, 0, 0, 0, 0, 0 }, // 110000 = 48
{ 0, 0, 0, 0, 0, 0, 0 }, // 110001 = 49
{ 0, 0, 0, 0, 0, 0, 0 }, // 110010 = 50
{ 0, 0, 0, 0, 0, 0, 0 }, // 110011 = 51
{ 0, 0, 0, 0, 0, 0, 0 }, // 110100 = 52
{ 0, 0, 0, 0, 0, 0, 0 }, // 110101 = 53
{ 0, 0, 0, 0, 0, 0, 0 }, // 110110 = 54
{ 0, 0, 0, 0, 0, 0, 0 }, // 110111 = 55
{ 0, 0, 0, 0, 0, 0, 0 }, // 111000 = 56
{ 0, 0, 0, 0, 0, 0, 0 }, // 111001 = 57
{ 0, 0, 0, 0, 0, 0, 0 }, // 111010 = 58
{ 0, 0, 0, 0, 0, 0, 0 }, // 111011 = 59
{ 0, 0, 0, 0, 0, 0, 0 }, // 111100 = 60
{ 0, 0, 0, 0, 0, 0, 0 }, // 111101 = 61
{ 0, 0, 0, 0, 0, 0, 0 }, // 111110 = 62
{ 0, 0, 0, 0, 0, 0, 0 }, // 111111 = 63
};
/*
============
idBox::AddPoint
============
*/
bool idBox::AddPoint( const idVec3 &v ) {
idMat3 axis2;
idBounds bounds1, bounds2;
if ( extents[0] < 0.0f ) {
extents.Zero();
center = v;
axis.Identity();
return true;
}
bounds1[0][0] = bounds1[1][0] = center * axis[0];
bounds1[0][1] = bounds1[1][1] = center * axis[1];
bounds1[0][2] = bounds1[1][2] = center * axis[2];
bounds1[0] -= extents;
bounds1[1] += extents;
if ( !bounds1.AddPointExpanded( idVec3( v * axis[0], v * axis[1], v * axis[2] ) ) ) {
// point is contained in the box
return false;
}
axis2[0] = v - center;
axis2[0].Normalize();
axis2[1] = axis[ Min3Index( axis2[0] * axis[0], axis2[0] * axis[1], axis2[0] * axis[2] ) ];
axis2[1] = axis2[1] - ( axis2[1] * axis2[0] ) * axis2[0];
axis2[1].Normalize();
axis2[2].Cross( axis2[0], axis2[1] );
AxisProjection( axis2, bounds2 );
bounds2.AddPoint( idVec3( v * axis2[0], v * axis2[1], v * axis2[2] ) );
// create new box based on the smallest bounds
if ( bounds1.GetVolume() < bounds2.GetVolume() ) {
center = ( bounds1[0] + bounds1[1] ) * 0.5f;
extents = bounds1[1] - center;
center *= axis;
}
else {
center = ( bounds2[0] + bounds2[1] ) * 0.5f;
extents = bounds2[1] - center;
center *= axis2;
axis = axis2;
}
return true;
}
/*
============
idBox::AddBox
============
*/
bool idBox::AddBox( const idBox &a ) {
int i;
int besti = 0;
float v, bestv;
idVec3 dir;
idMat3 ax[4];
idBounds bounds[4], b;
if ( a.extents[0] < 0.0f ) {
return false;
}
if ( extents[0] < 0.0f ) {
center = a.center;
extents = a.extents;
axis = a.axis;
return true;
}
// test axis of this box
ax[0] = axis;
bounds[0][0][0] = bounds[0][1][0] = center * ax[0][0];
bounds[0][0][1] = bounds[0][1][1] = center * ax[0][1];
bounds[0][0][2] = bounds[0][1][2] = center * ax[0][2];
bounds[0][0] -= extents;
bounds[0][1] += extents;
a.AxisProjection( ax[0], b );
if ( !bounds[0].AddBoundsExpanded( b ) ) {
// the other box is contained in this box
return false;
}
// test axis of other box
ax[1] = a.axis;
bounds[1][0][0] = bounds[1][1][0] = a.center * ax[1][0];
bounds[1][0][1] = bounds[1][1][1] = a.center * ax[1][1];
bounds[1][0][2] = bounds[1][1][2] = a.center * ax[1][2];
bounds[1][0] -= a.extents;
bounds[1][1] += a.extents;
AxisProjection( ax[1], b );
if ( !bounds[1].AddBoundsExpanded( b ) ) {
// this box is contained in the other box
center = a.center;
extents = a.extents;
axis = a.axis;
return true;
}
// test axes aligned with the vector between the box centers and one of the box axis
dir = a.center - center;
dir.Normalize();
for ( i = 2; i < 4; i++ ) {
ax[i][0] = dir;
ax[i][1] = ax[i-2][ Min3Index( dir * ax[i-2][0], dir * ax[i-2][1], dir * ax[i-2][2] ) ];
ax[i][1] = ax[i][1] - ( ax[i][1] * dir ) * dir;
ax[i][1].Normalize();
ax[i][2].Cross( dir, ax[i][1] );
AxisProjection( ax[i], bounds[i] );
a.AxisProjection( ax[i], b );
bounds[i].AddBounds( b );
}
// get the bounds with the smallest volume
bestv = idMath::INFINITY;
besti = 0;
for ( i = 0; i < 4; i++ ) {
v = bounds[i].GetVolume();
if ( v < bestv ) {
bestv = v;
besti = i;
}
}
// create a box from the smallest bounds axis pair
center = ( bounds[besti][0] + bounds[besti][1] ) * 0.5f;
extents = bounds[besti][1] - center;
center *= ax[besti];
axis = ax[besti];
return false;
}
/*
================
idBox::PlaneDistance
================
*/
float idBox::PlaneDistance( const idPlane &plane ) const {
float d1, d2;
d1 = plane.Distance( center );
d2 = idMath::Fabs( extents[0] * ( plane.Normal() * axis[0] ) ) +
idMath::Fabs( extents[1] * ( plane.Normal() * axis[1] ) ) +
idMath::Fabs( extents[2] * ( plane.Normal() * axis[2] ) );
if ( d1 - d2 > 0.0f ) {
return d1 - d2;
}
if ( d1 + d2 < 0.0f ) {
return d1 + d2;
}
return 0.0f;
}
/*
================
idBox::PlaneSide
================
*/
int idBox::PlaneSide( const idPlane &plane, const float epsilon ) const {
float d1, d2;
d1 = plane.Distance( center );
d2 = idMath::Fabs( extents[0] * ( plane.Normal() * axis[0] ) ) +
idMath::Fabs( extents[1] * ( plane.Normal() * axis[1] ) ) +
idMath::Fabs( extents[2] * ( plane.Normal() * axis[2] ) );
if ( d1 - d2 > epsilon ) {
return PLANESIDE_FRONT;
}
if ( d1 + d2 < -epsilon ) {
return PLANESIDE_BACK;
}
return PLANESIDE_CROSS;
}
/*
============
idBox::IntersectsBox
============
*/
bool idBox::IntersectsBox( const idBox &a ) const {
idVec3 dir; // vector between centers
float c[3][3]; // matrix c = axis.Transpose() * a.axis
float ac[3][3]; // absolute values of c
float axisdir[3]; // axis[i] * dir
float d, e0, e1; // distance between centers and projected extents
dir = a.center - center;
// axis C0 + t * A0
c[0][0] = axis[0] * a.axis[0];
c[0][1] = axis[0] * a.axis[1];
c[0][2] = axis[0] * a.axis[2];
axisdir[0] = axis[0] * dir;
ac[0][0] = idMath::Fabs( c[0][0] );
ac[0][1] = idMath::Fabs( c[0][1] );
ac[0][2] = idMath::Fabs( c[0][2] );
d = idMath::Fabs( axisdir[0] );
e0 = extents[0];
e1 = a.extents[0] * ac[0][0] + a.extents[1] * ac[0][1] + a.extents[2] * ac[0][2];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A1
c[1][0] = axis[1] * a.axis[0];
c[1][1] = axis[1] * a.axis[1];
c[1][2] = axis[1] * a.axis[2];
axisdir[1] = axis[1] * dir;
ac[1][0] = idMath::Fabs( c[1][0] );
ac[1][1] = idMath::Fabs( c[1][1] );
ac[1][2] = idMath::Fabs( c[1][2] );
d = idMath::Fabs( axisdir[1] );
e0 = extents[1];
e1 = a.extents[0] * ac[1][0] + a.extents[1] * ac[1][1] + a.extents[2] * ac[1][2];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A2
c[2][0] = axis[2] * a.axis[0];
c[2][1] = axis[2] * a.axis[1];
c[2][2] = axis[2] * a.axis[2];
axisdir[2] = axis[2] * dir;
ac[2][0] = idMath::Fabs( c[2][0] );
ac[2][1] = idMath::Fabs( c[2][1] );
ac[2][2] = idMath::Fabs( c[2][2] );
d = idMath::Fabs( axisdir[2] );
e0 = extents[2];
e1 = a.extents[0] * ac[2][0] + a.extents[1] * ac[2][1] + a.extents[2] * ac[2][2];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * B0
d = idMath::Fabs( a.axis[0] * dir );
e0 = extents[0] * ac[0][0] + extents[1] * ac[1][0] + extents[2] * ac[2][0];
e1 = a.extents[0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * B1
d = idMath::Fabs( a.axis[1] * dir );
e0 = extents[0] * ac[0][1] + extents[1] * ac[1][1] + extents[2] * ac[2][1];
e1 = a.extents[1];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * B2
d = idMath::Fabs( a.axis[2] * dir );
e0 = extents[0] * ac[0][2] + extents[1] * ac[1][2] + extents[2] * ac[2][2];
e1 = a.extents[2];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A0xB0
d = idMath::Fabs( axisdir[2] * c[1][0] - axisdir[1] * c[2][0] );
e0 = extents[1] * ac[2][0] + extents[2] * ac[1][0];
e1 = a.extents[1] * ac[0][2] + a.extents[2] * ac[0][1];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A0xB1
d = idMath::Fabs( axisdir[2] * c[1][1] - axisdir[1] * c[2][1] );
e0 = extents[1] * ac[2][1] + extents[2] * ac[1][1];
e1 = a.extents[0] * ac[0][2] + a.extents[2] * ac[0][0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A0xB2
d = idMath::Fabs( axisdir[2] * c[1][2] - axisdir[1] * c[2][2] );
e0 = extents[1] * ac[2][2] + extents[2] * ac[1][2];
e1 = a.extents[0] * ac[0][1] + a.extents[1] * ac[0][0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A1xB0
d = idMath::Fabs( axisdir[0] * c[2][0] - axisdir[2] * c[0][0] );
e0 = extents[0] * ac[2][0] + extents[2] * ac[0][0];
e1 = a.extents[1] * ac[1][2] + a.extents[2] * ac[1][1];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A1xB1
d = idMath::Fabs( axisdir[0] * c[2][1] - axisdir[2] * c[0][1] );
e0 = extents[0] * ac[2][1] + extents[2] * ac[0][1];
e1 = a.extents[0] * ac[1][2] + a.extents[2] * ac[1][0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A1xB2
d = idMath::Fabs( axisdir[0] * c[2][2] - axisdir[2] * c[0][2] );
e0 = extents[0] * ac[2][2] + extents[2] * ac[0][2];
e1 = a.extents[0] * ac[1][1] + a.extents[1] * ac[1][0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A2xB0
d = idMath::Fabs( axisdir[1] * c[0][0] - axisdir[0] * c[1][0] );
e0 = extents[0] * ac[1][0] + extents[1] * ac[0][0];
e1 = a.extents[1] * ac[2][2] + a.extents[2] * ac[2][1];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A2xB1
d = idMath::Fabs( axisdir[1] * c[0][1] - axisdir[0] * c[1][1] );
e0 = extents[0] * ac[1][1] + extents[1] * ac[0][1];
e1 = a.extents[0] * ac[2][2] + a.extents[2] * ac[2][0];
if ( d > e0 + e1 ) {
return false;
}
// axis C0 + t * A2xB2
d = idMath::Fabs( axisdir[1] * c[0][2] - axisdir[0] * c[1][2] );
e0 = extents[0] * ac[1][2] + extents[1] * ac[0][2];
e1 = a.extents[0] * ac[2][1] + a.extents[1] * ac[2][0];
if ( d > e0 + e1 ) {
return false;
}
return true;
}
/*
============
idBox::LineIntersection
Returns true if the line intersects the box between the start and end point.
============
*/
bool idBox::LineIntersection( const idVec3 &start, const idVec3 &end ) const {
float ld[3];
idVec3 lineDir = 0.5f * ( end - start );
idVec3 lineCenter = start + lineDir;
idVec3 dir = lineCenter - center;
ld[0] = idMath::Fabs( lineDir * axis[0] );
if ( idMath::Fabs( dir * axis[0] ) > extents[0] + ld[0] ) {
return false;
}
ld[1] = idMath::Fabs( lineDir * axis[1] );
if ( idMath::Fabs( dir * axis[1] ) > extents[1] + ld[1] ) {
return false;
}
ld[2] = idMath::Fabs( lineDir * axis[2] );
if ( idMath::Fabs( dir * axis[2] ) > extents[2] + ld[2] ) {
return false;
}
idVec3 cross = lineDir.Cross( dir );
if ( idMath::Fabs( cross * axis[0] ) > extents[1] * ld[2] + extents[2] * ld[1] ) {
return false;
}
if ( idMath::Fabs( cross * axis[1] ) > extents[0] * ld[2] + extents[2] * ld[0] ) {
return false;
}
if ( idMath::Fabs( cross * axis[2] ) > extents[0] * ld[1] + extents[1] * ld[0] ) {
return false;
}
return true;
}
/*
============
BoxPlaneClip
============
*/
static bool BoxPlaneClip( const float denom, const float numer, float &scale0, float &scale1 ) {
if ( denom > 0.0f ) {
if ( numer > denom * scale1 ) {
return false;
}
if ( numer > denom * scale0 ) {
scale0 = numer / denom;
}
return true;
}
else if ( denom < 0.0f ) {
if ( numer > denom * scale0 ) {
return false;
}
if ( numer > denom * scale1 ) {
scale1 = numer / denom;
}
return true;
}
else {
return ( numer <= 0.0f );
}
}
/*
============
idBox::RayIntersection
Returns true if the ray intersects the box.
The ray can intersect the box in both directions from the start point.
If start is inside the box then scale1 < 0 and scale2 > 0.
============
*/
bool idBox::RayIntersection( const idVec3 &start, const idVec3 &dir, float &scale1, float &scale2 ) const {
idVec3 localStart, localDir;
localStart = ( start - center ) * axis.Transpose();
localDir = dir * axis.Transpose();
scale1 = -idMath::INFINITY;
scale2 = idMath::INFINITY;
return BoxPlaneClip( localDir.x, -localStart.x - extents[0], scale1, scale2 ) &&
BoxPlaneClip( -localDir.x, localStart.x - extents[0], scale1, scale2 ) &&
BoxPlaneClip( localDir.y, -localStart.y - extents[1], scale1, scale2 ) &&
BoxPlaneClip( -localDir.y, localStart.y - extents[1], scale1, scale2 ) &&
BoxPlaneClip( localDir.z, -localStart.z - extents[2], scale1, scale2 ) &&
BoxPlaneClip( -localDir.z, localStart.z - extents[2], scale1, scale2 );
}
/*
============
idBox::FromPoints
Tight box for a collection of points.
============
*/
void idBox::FromPoints( const idVec3 *points, const int numPoints ) {
int i;
float invNumPoints, sumXX, sumXY, sumXZ, sumYY, sumYZ, sumZZ;
idVec3 dir;
idBounds bounds;
idMatX eigenVectors;
idVecX eigenValues;
// compute mean of points
center = points[0];
for ( i = 1; i < numPoints; i++ ) {
center += points[i];
}
invNumPoints = 1.0f / numPoints;
center *= invNumPoints;
// compute covariances of points
sumXX = 0.0f; sumXY = 0.0f; sumXZ = 0.0f;
sumYY = 0.0f; sumYZ = 0.0f; sumZZ = 0.0f;
for ( i = 0; i < numPoints; i++ ) {
dir = points[i] - center;
sumXX += dir.x * dir.x;
sumXY += dir.x * dir.y;
sumXZ += dir.x * dir.z;
sumYY += dir.y * dir.y;
sumYZ += dir.y * dir.z;
sumZZ += dir.z * dir.z;
}
sumXX *= invNumPoints;
sumXY *= invNumPoints;
sumXZ *= invNumPoints;
sumYY *= invNumPoints;
sumYZ *= invNumPoints;
sumZZ *= invNumPoints;
// compute eigenvectors for covariance matrix
eigenValues.SetData( 3, VECX_ALLOCA( 3 ) );
eigenVectors.SetData( 3, 3, MATX_ALLOCA( 3 * 3 ) );
eigenVectors[0][0] = sumXX;
eigenVectors[0][1] = sumXY;
eigenVectors[0][2] = sumXZ;
eigenVectors[1][0] = sumXY;
eigenVectors[1][1] = sumYY;
eigenVectors[1][2] = sumYZ;
eigenVectors[2][0] = sumXZ;
eigenVectors[2][1] = sumYZ;
eigenVectors[2][2] = sumZZ;
eigenVectors.Eigen_SolveSymmetric( eigenValues );
eigenVectors.Eigen_SortIncreasing( eigenValues );
axis[1][0] = eigenVectors[0][1];
axis[1][1] = eigenVectors[1][1];
axis[1][2] = eigenVectors[2][1];
axis[2][0] = eigenVectors[0][2];
axis[2][1] = eigenVectors[1][2];
axis[2][2] = eigenVectors[2][2];
axis[0].Cross( axis[1], axis[2] );
// if two eigenValues are the same then we need to search rotations to get the smallest volume box
const float epsilon = 0.1f;
int rotationAxis = -1;
if ( idMath::Fabs( eigenValues[0] - eigenValues[1] ) < epsilon ) {
rotationAxis = 2;
} else if ( idMath::Fabs( eigenValues[0] - eigenValues[2] ) < epsilon ) {
rotationAxis = 1;
} else if ( idMath::Fabs( eigenValues[1] - eigenValues[2] ) < epsilon ) {
rotationAxis = 0;
}
if ( rotationAxis >= 0 ) {
idRotation rot;
rot.SetVec( axis[rotationAxis] );
bounds.Clear();
for ( i = 0; i < numPoints; i++ ) {
bounds.AddPoint( idVec3( points[i] * axis[0], points[i] * axis[1], points[i] * axis[2] ) );
}
float bestVolume = bounds.GetVolume();
float bestAngle = 0.0f;
float angleStep = 30.0f;
for ( int iteration = 0; iteration < 8; iteration++ ) {
float startAngle = bestAngle;
for ( int a = -1; a <= 1; a += 2 ) {
rot.SetAngle( startAngle + ( a * angleStep ) );
idMat3 a2 = axis * rot.ToMat3();
bounds.Clear();
for ( i = 0; i < numPoints; i++ ) {
bounds.AddPoint( idVec3( points[i] * a2[0], points[i] * a2[1], points[i] * a2[2] ) );
}
float volume = bounds.GetVolume();
if ( volume < bestVolume ) {
bestVolume = volume;
bestAngle = rot.GetAngle();
}
}
angleStep *= 0.5f;
}
rot.SetAngle( bestAngle );
axis *= rot.ToMat3();
}
// refine by calculating the bounds of the points projected onto the axis and adjusting the center and extents
bounds.Clear();
for ( i = 0; i < numPoints; i++ ) {
bounds.AddPoint( idVec3( points[i] * axis[0], points[i] * axis[1], points[i] * axis[2] ) );
}
center = ( bounds[0] + bounds[1] ) * 0.5f;
extents = bounds[1] - center;
center *= axis;
}
/*
============
idBox::FromPointTranslation
Most tight box for the translational movement of the given point.
============
*/
void idBox::FromPointTranslation( const idVec3 &point, const idVec3 &translation ) {
// FIXME: implement
}
/*
============
idBox::FromBoxTranslation
Most tight box for the translational movement of the given box.
============
*/
void idBox::FromBoxTranslation( const idBox &box, const idVec3 &translation ) {
// FIXME: implement
}
/*
============
idBox::FromPointRotation
Most tight bounds for the rotational movement of the given point.
============
*/
void idBox::FromPointRotation( const idVec3 &point, const idRotation &rotation ) {
// FIXME: implement
}
/*
============
idBox::FromBoxRotation
Most tight box for the rotational movement of the given box.
============
*/
void idBox::FromBoxRotation( const idBox &box, const idRotation &rotation ) {
// FIXME: implement
}
/*
============
idBox::ToPoints
============
*/
void idBox::ToPoints( idVec3 points[8] ) const {
idMat3 ax;
idVec3 temp[4];
ax[0] = extents[0] * axis[0];
ax[1] = extents[1] * axis[1];
ax[2] = extents[2] * axis[2];
temp[0] = center - ax[0];
temp[1] = center + ax[0];
temp[2] = ax[1] - ax[2];
temp[3] = ax[1] + ax[2];
points[0] = temp[0] - temp[3];
points[1] = temp[1] - temp[3];
points[2] = temp[1] + temp[2];
points[3] = temp[0] + temp[2];
points[4] = temp[0] - temp[2];
points[5] = temp[1] - temp[2];
points[6] = temp[1] + temp[3];
points[7] = temp[0] + temp[3];
}
/*
============
idBox::GetProjectionSilhouetteVerts
============
*/
int idBox::GetProjectionSilhouetteVerts( const idVec3 &projectionOrigin, idVec3 silVerts[6] ) const {
float f;
int i, planeBits, *index;
idVec3 points[8], dir1, dir2;
ToPoints( points );
dir1 = points[0] - projectionOrigin;
dir2 = points[6] - projectionOrigin;
f = dir1 * axis[0];
planeBits = FLOATSIGNBITNOTSET( f );
f = dir2 * axis[0];
planeBits |= FLOATSIGNBITSET( f ) << 1;
f = dir1 * axis[1];
planeBits |= FLOATSIGNBITNOTSET( f ) << 2;
f = dir2 * axis[1];
planeBits |= FLOATSIGNBITSET( f ) << 3;
f = dir1 * axis[2];
planeBits |= FLOATSIGNBITNOTSET( f ) << 4;
f = dir2 * axis[2];
planeBits |= FLOATSIGNBITSET( f ) << 5;
index = boxPlaneBitsSilVerts[planeBits];
for ( i = 0; i < index[0]; i++ ) {
silVerts[i] = points[index[i+1]];
}
return index[0];
}
/*
============
idBox::GetParallelProjectionSilhouetteVerts
============
*/
int idBox::GetParallelProjectionSilhouetteVerts( const idVec3 &projectionDir, idVec3 silVerts[6] ) const {
float f;
int i, planeBits, *index;
idVec3 points[8];
ToPoints( points );
planeBits = 0;
f = projectionDir * axis[0];
if ( FLOATNOTZERO( f ) ) {
planeBits = 1 << FLOATSIGNBITSET( f );
}
f = projectionDir * axis[1];
if ( FLOATNOTZERO( f ) ) {
planeBits |= 4 << FLOATSIGNBITSET( f );
}
f = projectionDir * axis[2];
if ( FLOATNOTZERO( f ) ) {
planeBits |= 16 << FLOATSIGNBITSET( f );
}
index = boxPlaneBitsSilVerts[planeBits];
for ( i = 0; i < index[0]; i++ ) {
silVerts[i] = points[index[i+1]];
}
return index[0];
}
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