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quadrilateralcowboy/idlib/math/Pluecker.h
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/*
===========================================================================
Doom 3 GPL Source Code
Copyright (C) 1999-2011 id Software LLC, a ZeniMax Media company.
This file is part of the Doom 3 GPL Source Code (?Doom 3 Source Code?).
Doom 3 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 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 Source Code. If not, see <http://www.gnu.org/licenses/>.
In addition, the Doom 3 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 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.
===========================================================================
*/
#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 );
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 void idPluecker::FromLine( const idVec3 &start, const idVec3 &end ) {
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];
}
ID_INLINE void idPluecker::FromRay( const idVec3 &start, const idVec3 &dir ) {
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];
}
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 {
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 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__ */
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