433 lines
13 KiB
C
433 lines
13 KiB
C
|
// Copyright (C) 2007 Id Software, Inc.
|
||
|
|
//
|
||
|
|
|
||
|
|
#ifndef __MATH_PLUECKER_H__
|
||
|
|
#define __MATH_PLUECKER_H__
|
||
|
|
|
||
|
|
/*
|
||
|
|
===============================================================================
|
||
|
|
|
||
|
|
Pluecker coordinate
|
||
|
|
|
||
|
|
===============================================================================
|
||
|
|
*/
|
||
|
|
|
||
|
|
class idPluecker {
|
||
|
|
public:
|
||
|
|
idPluecker( void );
|
||
|
|
explicit idPluecker( const float *a );
|
||
|
|
explicit idPluecker( const idVec3 &start, const idVec3 &end );
|
||
|
|
explicit idPluecker( const float a1, const float a2, const float a3, const float a4, const float a5, const float a6 );
|
||
|
|
|
||
|
|
float operator[]( const int index ) const;
|
||
|
|
float & operator[]( const int index );
|
||
|
|
idPluecker operator-() const; // flips the direction
|
||
|
|
idPluecker operator*( const float a ) const;
|
||
|
|
idPluecker operator/( const float a ) const;
|
||
|
|
float operator*( const idPluecker &a ) const; // permuted inner product
|
||
|
|
idPluecker operator-( const idPluecker &a ) const;
|
||
|
|
idPluecker operator+( const idPluecker &a ) const;
|
||
|
|
idPluecker & operator*=( const float a );
|
||
|
|
idPluecker & operator/=( const float a );
|
||
|
|
idPluecker & operator+=( const idPluecker &a );
|
||
|
|
idPluecker & operator-=( const idPluecker &a );
|
||
|
|
|
||
|
|
bool Compare( const idPluecker &a ) const; // exact compare, no epsilon
|
||
|
|
bool Compare( const idPluecker &a, const float epsilon ) const; // compare with epsilon
|
||
|
|
bool operator==( const idPluecker &a ) const; // exact compare, no epsilon
|
||
|
|
bool operator!=( const idPluecker &a ) const; // exact compare, no epsilon
|
||
|
|
|
||
|
|
void Set( const float a1, const float a2, const float a3, const float a4, const float a5, const float a6 );
|
||
|
|
void Zero( void );
|
||
|
|
|
||
|
|
idPluecker Rotate( const idMat3 &rotation ) const;
|
||
|
|
idPluecker Translate( const idVec3 &translation ) const;
|
||
|
|
idPluecker TranslateAndRotate( const idVec3 &translation, const idMat3 &rotation ) const;
|
||
|
|
|
||
|
|
void FromLine( const idVec3 &start, const idVec3 &end ); // pluecker from line
|
||
|
|
void FromRay( const idVec3 &start, const idVec3 &dir ); // pluecker from ray
|
||
|
|
bool FromPlanes( const idPlane &p1, const idPlane &p2 ); // pluecker from intersection of planes
|
||
|
|
bool ToLine( idVec3 &start, idVec3 &end ) const; // pluecker to line
|
||
|
|
bool ToRay( idVec3 &start, idVec3 &dir ) const; // pluecker to ray
|
||
|
|
void ToDir( idVec3 &dir ) const; // pluecker to direction
|
||
|
|
float PermutedInnerProduct( const idPluecker &a ) const; // pluecker permuted inner product
|
||
|
|
float Distance3DSqr( const idPluecker &a ) const; // pluecker line distance
|
||
|
|
|
||
|
|
float Length( void ) const; // pluecker length
|
||
|
|
float LengthSqr( void ) const; // pluecker squared length
|
||
|
|
idPluecker Normalize( void ) const; // pluecker normalize
|
||
|
|
float NormalizeSelf( void ); // pluecker normalize
|
||
|
|
|
||
|
|
int GetDimension( void ) const;
|
||
|
|
|
||
|
|
const float * ToFloatPtr( void ) const;
|
||
|
|
float * ToFloatPtr( void );
|
||
|
|
const char * ToString( int precision = 2 ) const;
|
||
|
|
|
||
|
|
private:
|
||
|
|
float p[6];
|
||
|
|
};
|
||
|
|
|
||
|
|
extern idPluecker pluecker_origin;
|
||
|
|
#define pluecker_zero pluecker_origin
|
||
|
|
|
||
|
|
ID_INLINE idPluecker::idPluecker( void ) {
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker::idPluecker( const float *a ) {
|
||
|
|
memcpy( p, a, 6 * sizeof( float ) );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker::idPluecker( const idVec3 &start, const idVec3 &end ) {
|
||
|
|
FromLine( start, end );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker::idPluecker( const float a1, const float a2, const float a3, const float a4, const float a5, const float a6 ) {
|
||
|
|
p[0] = a1;
|
||
|
|
p[1] = a2;
|
||
|
|
p[2] = a3;
|
||
|
|
p[3] = a4;
|
||
|
|
p[4] = a5;
|
||
|
|
p[5] = a6;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::operator-() const {
|
||
|
|
return idPluecker( -p[0], -p[1], -p[2], -p[3], -p[4], -p[5] );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::operator[]( const int index ) const {
|
||
|
|
return p[index];
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float &idPluecker::operator[]( const int index ) {
|
||
|
|
return p[index];
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::operator*( const float a ) const {
|
||
|
|
return idPluecker( p[0]*a, p[1]*a, p[2]*a, p[3]*a, p[4]*a, p[5]*a );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::operator*( const idPluecker &a ) const {
|
||
|
|
return p[0] * a.p[4] + p[1] * a.p[5] + p[2] * a.p[3] + p[4] * a.p[0] + p[5] * a.p[1] + p[3] * a.p[2];
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::operator/( const float a ) const {
|
||
|
|
float inva;
|
||
|
|
|
||
|
|
assert( a != 0.0f );
|
||
|
|
inva = 1.0f / a;
|
||
|
|
return idPluecker( p[0]*inva, p[1]*inva, p[2]*inva, p[3]*inva, p[4]*inva, p[5]*inva );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::operator+( const idPluecker &a ) const {
|
||
|
|
return idPluecker( p[0] + a[0], p[1] + a[1], p[2] + a[2], p[3] + a[3], p[4] + a[4], p[5] + a[5] );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::operator-( const idPluecker &a ) const {
|
||
|
|
return idPluecker( p[0] - a[0], p[1] - a[1], p[2] - a[2], p[3] - a[3], p[4] - a[4], p[5] - a[5] );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker &idPluecker::operator*=( const float a ) {
|
||
|
|
p[0] *= a;
|
||
|
|
p[1] *= a;
|
||
|
|
p[2] *= a;
|
||
|
|
p[3] *= a;
|
||
|
|
p[4] *= a;
|
||
|
|
p[5] *= a;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker &idPluecker::operator/=( const float a ) {
|
||
|
|
float inva;
|
||
|
|
|
||
|
|
assert( a != 0.0f );
|
||
|
|
inva = 1.0f / a;
|
||
|
|
p[0] *= inva;
|
||
|
|
p[1] *= inva;
|
||
|
|
p[2] *= inva;
|
||
|
|
p[3] *= inva;
|
||
|
|
p[4] *= inva;
|
||
|
|
p[5] *= inva;
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker &idPluecker::operator+=( const idPluecker &a ) {
|
||
|
|
p[0] += a[0];
|
||
|
|
p[1] += a[1];
|
||
|
|
p[2] += a[2];
|
||
|
|
p[3] += a[3];
|
||
|
|
p[4] += a[4];
|
||
|
|
p[5] += a[5];
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker &idPluecker::operator-=( const idPluecker &a ) {
|
||
|
|
p[0] -= a[0];
|
||
|
|
p[1] -= a[1];
|
||
|
|
p[2] -= a[2];
|
||
|
|
p[3] -= a[3];
|
||
|
|
p[4] -= a[4];
|
||
|
|
p[5] -= a[5];
|
||
|
|
return *this;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::Compare( const idPluecker &a ) const {
|
||
|
|
return ( ( p[0] == a[0] ) && ( p[1] == a[1] ) && ( p[2] == a[2] ) &&
|
||
|
|
( p[3] == a[3] ) && ( p[4] == a[4] ) && ( p[5] == a[5] ) );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::Compare( const idPluecker &a, const float epsilon ) const {
|
||
|
|
if ( idMath::Fabs( p[0] - a[0] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( idMath::Fabs( p[1] - a[1] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( idMath::Fabs( p[2] - a[2] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( idMath::Fabs( p[3] - a[3] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( idMath::Fabs( p[4] - a[4] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
if ( idMath::Fabs( p[5] - a[5] ) > epsilon ) {
|
||
|
|
return false;
|
||
|
|
}
|
||
|
|
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::operator==( const idPluecker &a ) const {
|
||
|
|
return Compare( a );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::operator!=( const idPluecker &a ) const {
|
||
|
|
return !Compare( a );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE void idPluecker::Set( const float a1, const float a2, const float a3, const float a4, const float a5, const float a6 ) {
|
||
|
|
p[0] = a1;
|
||
|
|
p[1] = a2;
|
||
|
|
p[2] = a3;
|
||
|
|
p[3] = a4;
|
||
|
|
p[4] = a5;
|
||
|
|
p[5] = a6;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE void idPluecker::Zero( void ) {
|
||
|
|
p[0] = p[1] = p[2] = p[3] = p[4] = p[5] = 0.0f;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::Rotate( const idMat3 &rotation ) const {
|
||
|
|
idPluecker result;
|
||
|
|
result[0] = rotation[ 0 ].z * p[3] - rotation[ 1 ].z * p[1] + rotation[ 2 ].z * p[0];
|
||
|
|
result[1] = - rotation[ 0 ].y * p[3] + rotation[ 1 ].y * p[1] - rotation[ 2 ].y * p[0];
|
||
|
|
result[2] = rotation[ 0 ].x * p[2] - rotation[ 1 ].x * p[5] + rotation[ 2 ].x * p[4];
|
||
|
|
result[3] = rotation[ 0 ].x * p[3] - rotation[ 1 ].x * p[1] + rotation[ 2 ].x * p[0];
|
||
|
|
result[4] = rotation[ 0 ].z * p[2] - rotation[ 1 ].z * p[5] + rotation[ 2 ].z * p[4];
|
||
|
|
result[5] = - rotation[ 0 ].y * p[2] + rotation[ 1 ].y * p[5] - rotation[ 2 ].y * p[4];
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::Translate( const idVec3 &translation ) const {
|
||
|
|
idPluecker result;
|
||
|
|
result[0] = p[0] + translation[0] * p[5] + p[2] * translation[1];
|
||
|
|
result[1] = p[1] - translation[0] * p[4] + p[2] * translation[2];
|
||
|
|
result[2] = p[2];
|
||
|
|
result[3] = p[3] - translation[1] * p[4] - p[5] * translation[2];
|
||
|
|
result[4] = p[4];
|
||
|
|
result[5] = p[5];
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::TranslateAndRotate( const idVec3 &translation, const idMat3 &rotation ) const {
|
||
|
|
idVec3 t;
|
||
|
|
idPluecker result;
|
||
|
|
t[0] = p[0] + translation[0] * p[5] + p[2] * translation[1];
|
||
|
|
t[1] = p[1] - translation[0] * p[4] + p[2] * translation[2];
|
||
|
|
t[2] = p[3] - translation[1] * p[4] - p[5] * translation[2];
|
||
|
|
result[0] = rotation[ 0 ].z * t[2] - rotation[ 1 ].z * t[1] + rotation[ 2 ].z * t[0];
|
||
|
|
result[1] = - rotation[ 0 ].y * t[2] + rotation[ 1 ].y * t[1] - rotation[ 2 ].y * t[0];
|
||
|
|
result[2] = rotation[ 0 ].x * p[2] - rotation[ 1 ].x * p[5] + rotation[ 2 ].x * p[4];
|
||
|
|
result[3] = rotation[ 0 ].x * t[2] - rotation[ 1 ].x * t[1] + rotation[ 2 ].x * t[0];
|
||
|
|
result[4] = rotation[ 0 ].z * p[2] - rotation[ 1 ].z * p[5] + rotation[ 2 ].z * p[4];
|
||
|
|
result[5] = - rotation[ 0 ].y * p[2] + rotation[ 1 ].y * p[5] - rotation[ 2 ].y * p[4];
|
||
|
|
return result;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE void idPluecker::FromLine( const idVec3 &start, const idVec3 &end ) {
|
||
|
|
// FIXME: make sure to compile with -fno-unsafe-math-optimizations instead
|
||
|
|
#if 0
|
||
|
|
// #ifdef MACOS_X //DAJ BUGFIX the round off the gcc does
|
||
|
|
double v0, v1, v2, v3, v4, v5;
|
||
|
|
v0 = (double)(start[0]) * (double)(end[1]);
|
||
|
|
v1 = (double)(end[0]) * (double)(start[1]);
|
||
|
|
v2 = (double)(start[0]) * (double)(end[2]);
|
||
|
|
v3 = (double)(end[0]) * (double)(start[2]);
|
||
|
|
v4 = (double)(start[1]) * (double)(end[2]);
|
||
|
|
v5 = (double)(end[1]) * (double)(start[2]);
|
||
|
|
p[0] = v0 - v1;
|
||
|
|
p[1] = v2 - v3;
|
||
|
|
p[2] = start[0] - end[0];
|
||
|
|
p[3] = v4 - v5;
|
||
|
|
p[4] = start[2] - end[2];
|
||
|
|
p[5] = end[1] - start[1];
|
||
|
|
#else
|
||
|
|
p[0] = start[0] * end[1] - end[0] * start[1];
|
||
|
|
p[1] = start[0] * end[2] - end[0] * start[2];
|
||
|
|
p[2] = start[0] - end[0];
|
||
|
|
p[3] = start[1] * end[2] - end[1] * start[2];
|
||
|
|
p[4] = start[2] - end[2];
|
||
|
|
p[5] = end[1] - start[1];
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE void idPluecker::FromRay( const idVec3 &start, const idVec3 &dir ) {
|
||
|
|
#if 0
|
||
|
|
// #ifdef MACOS_X //DAJ BUGFIX the round off the gcc does
|
||
|
|
double v0, v1, v2, v3, v4, v5;
|
||
|
|
v0 = (double)(start[0]) * (double)(dir[1]);
|
||
|
|
v1 = (double)(dir[0]) * (double)(start[1]);
|
||
|
|
v2 = (double)(start[0]) * (double)(dir[2]);
|
||
|
|
v3 = (double)(dir[0]) * (double)(start[2]);
|
||
|
|
v4 = (double)(start[1]) * (double)(dir[2]);
|
||
|
|
v5 = (double)(dir[1]) * (double)(start[2]);
|
||
|
|
p[0] = v0 - v1;
|
||
|
|
p[1] = v2 - v3;
|
||
|
|
p[2] = -dir[0];
|
||
|
|
p[3] = v4 - v5;
|
||
|
|
p[4] = -dir[2];
|
||
|
|
p[5] = dir[1];
|
||
|
|
#else
|
||
|
|
p[0] = start[0] * dir[1] - dir[0] * start[1];
|
||
|
|
p[1] = start[0] * dir[2] - dir[0] * start[2];
|
||
|
|
p[2] = -dir[0];
|
||
|
|
p[3] = start[1] * dir[2] - dir[1] * start[2];
|
||
|
|
p[4] = -dir[2];
|
||
|
|
p[5] = dir[1];
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::ToLine( idVec3 &start, idVec3 &end ) const {
|
||
|
|
idVec3 dir1, dir2;
|
||
|
|
float d;
|
||
|
|
|
||
|
|
dir1[0] = p[3];
|
||
|
|
dir1[1] = -p[1];
|
||
|
|
dir1[2] = p[0];
|
||
|
|
|
||
|
|
dir2[0] = -p[2];
|
||
|
|
dir2[1] = p[5];
|
||
|
|
dir2[2] = -p[4];
|
||
|
|
|
||
|
|
d = dir2 * dir2;
|
||
|
|
if ( d == 0.0f ) {
|
||
|
|
return false; // pluecker coordinate does not represent a line
|
||
|
|
}
|
||
|
|
|
||
|
|
start = dir2.Cross(dir1) * (1.0f / d);
|
||
|
|
end = start + dir2;
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE bool idPluecker::ToRay( idVec3 &start, idVec3 &dir ) const {
|
||
|
|
idVec3 dir1;
|
||
|
|
float d;
|
||
|
|
|
||
|
|
dir1[0] = p[3];
|
||
|
|
dir1[1] = -p[1];
|
||
|
|
dir1[2] = p[0];
|
||
|
|
|
||
|
|
dir[0] = -p[2];
|
||
|
|
dir[1] = p[5];
|
||
|
|
dir[2] = -p[4];
|
||
|
|
|
||
|
|
d = dir * dir;
|
||
|
|
if ( d == 0.0f ) {
|
||
|
|
return false; // pluecker coordinate does not represent a line
|
||
|
|
}
|
||
|
|
|
||
|
|
start = dir.Cross(dir1) * (1.0f / d);
|
||
|
|
return true;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE void idPluecker::ToDir( idVec3 &dir ) const {
|
||
|
|
dir[0] = -p[2];
|
||
|
|
dir[1] = p[5];
|
||
|
|
dir[2] = -p[4];
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::PermutedInnerProduct( const idPluecker &a ) const {
|
||
|
|
#if 0
|
||
|
|
// #ifdef MACOS_X //DAJ BUGFIX lousy gcc floating point
|
||
|
|
double v0, v1, v2, v3, v4, v5, v6;
|
||
|
|
v0 = (double)(p[0]) * (double)(a.p[4]);
|
||
|
|
v1 = (double)(p[1]) * (double)(a.p[5]);
|
||
|
|
v2 = (double)(p[2]) * (double)(a.p[3]);
|
||
|
|
v3 = (double)(p[4]) * (double)(a.p[0]);
|
||
|
|
v4 = (double)(p[5]) * (double)(a.p[1]);
|
||
|
|
v5 = (double)(p[3]) * (double)(a.p[2]);
|
||
|
|
v6 = v0 + v1 + v2 + v3 + v4 + v5;
|
||
|
|
return v6;
|
||
|
|
#else
|
||
|
|
return p[0] * a.p[4] + p[1] * a.p[5] + p[2] * a.p[3] + p[4] * a.p[0] + p[5] * a.p[1] + p[3] * a.p[2];
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::Length( void ) const {
|
||
|
|
return ( float )idMath::Sqrt( p[5] * p[5] + p[4] * p[4] + p[2] * p[2] );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::LengthSqr( void ) const {
|
||
|
|
return ( p[5] * p[5] + p[4] * p[4] + p[2] * p[2] );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float idPluecker::NormalizeSelf( void ) {
|
||
|
|
float l, d;
|
||
|
|
|
||
|
|
l = LengthSqr();
|
||
|
|
if ( l == 0.0f ) {
|
||
|
|
return l; // pluecker coordinate does not represent a line
|
||
|
|
}
|
||
|
|
d = idMath::InvSqrt( l );
|
||
|
|
p[0] *= d;
|
||
|
|
p[1] *= d;
|
||
|
|
p[2] *= d;
|
||
|
|
p[3] *= d;
|
||
|
|
p[4] *= d;
|
||
|
|
p[5] *= d;
|
||
|
|
return d * l;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE idPluecker idPluecker::Normalize( void ) const {
|
||
|
|
float d;
|
||
|
|
|
||
|
|
d = LengthSqr();
|
||
|
|
if ( d == 0.0f ) {
|
||
|
|
return *this; // pluecker coordinate does not represent a line
|
||
|
|
}
|
||
|
|
d = idMath::InvSqrt( d );
|
||
|
|
return idPluecker( p[0]*d, p[1]*d, p[2]*d, p[3]*d, p[4]*d, p[5]*d );
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE int idPluecker::GetDimension( void ) const {
|
||
|
|
return 6;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE const float *idPluecker::ToFloatPtr( void ) const {
|
||
|
|
return p;
|
||
|
|
}
|
||
|
|
|
||
|
|
ID_INLINE float *idPluecker::ToFloatPtr( void ) {
|
||
|
|
return p;
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif /* !__MATH_PLUECKER_H__ */
|