302 lines
12 KiB
C
302 lines
12 KiB
C
/*
|
|
Copyright (C) 2001-2006, William Joseph.
|
|
All Rights Reserved.
|
|
|
|
This file is part of GtkRadiant.
|
|
|
|
GtkRadiant 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.
|
|
|
|
GtkRadiant 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 GtkRadiant; if not, write to the Free Software
|
|
Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
|
|
*/
|
|
|
|
#if !defined( INCLUDED_MATH_QUATERNION_H )
|
|
#define INCLUDED_MATH_QUATERNION_H
|
|
|
|
/// \file
|
|
/// \brief Quaternion data types and related operations.
|
|
|
|
#include "math/matrix.h"
|
|
|
|
/// \brief A quaternion stored in single-precision floating-point.
|
|
typedef Vector4 Quaternion;
|
|
|
|
const Quaternion c_quaternion_identity( 0, 0, 0, 1 );
|
|
|
|
inline Quaternion quaternion_multiplied_by_quaternion( const Quaternion& quaternion, const Quaternion& other ){
|
|
return Quaternion(
|
|
quaternion[3] * other[0] + quaternion[0] * other[3] + quaternion[1] * other[2] - quaternion[2] * other[1],
|
|
quaternion[3] * other[1] + quaternion[1] * other[3] + quaternion[2] * other[0] - quaternion[0] * other[2],
|
|
quaternion[3] * other[2] + quaternion[2] * other[3] + quaternion[0] * other[1] - quaternion[1] * other[0],
|
|
quaternion[3] * other[3] - quaternion[0] * other[0] - quaternion[1] * other[1] - quaternion[2] * other[2]
|
|
);
|
|
}
|
|
|
|
inline void quaternion_multiply_by_quaternion( Quaternion& quaternion, const Quaternion& other ){
|
|
quaternion = quaternion_multiplied_by_quaternion( quaternion, other );
|
|
}
|
|
|
|
/// \brief Constructs a quaternion which rotates between two points on the unit-sphere, \p from and \p to.
|
|
inline Quaternion quaternion_for_unit_vectors( const Vector3& from, const Vector3& to ){
|
|
return Quaternion( vector3_cross( from, to ), static_cast<float>( vector3_dot( from, to ) ) );
|
|
}
|
|
|
|
inline Quaternion quaternion_for_axisangle( const Vector3& axis, double angle ){
|
|
angle *= 0.5;
|
|
float sa = static_cast<float>( sin( angle ) );
|
|
return Quaternion( axis[0] * sa, axis[1] * sa, axis[2] * sa, static_cast<float>( cos( angle ) ) );
|
|
}
|
|
|
|
inline Quaternion quaternion_for_x( double angle ){
|
|
angle *= 0.5;
|
|
return Quaternion( static_cast<float>( sin( angle ) ), 0, 0, static_cast<float>( cos( angle ) ) );
|
|
}
|
|
|
|
inline Quaternion quaternion_for_y( double angle ){
|
|
angle *= 0.5;
|
|
return Quaternion( 0, static_cast<float>( sin( angle ) ), 0, static_cast<float>( cos( angle ) ) );
|
|
}
|
|
|
|
inline Quaternion quaternion_for_z( double angle ){
|
|
angle *= 0.5;
|
|
return Quaternion( 0, 0, static_cast<float>( sin( angle ) ), static_cast<float>( cos( angle ) ) );
|
|
}
|
|
|
|
inline Quaternion quaternion_inverse( const Quaternion& quaternion ){
|
|
return Quaternion( vector3_negated( vector4_to_vector3( quaternion ) ), quaternion[3] );
|
|
}
|
|
|
|
inline void quaternion_conjugate( Quaternion& quaternion ){
|
|
quaternion = quaternion_inverse( quaternion );
|
|
}
|
|
|
|
inline Quaternion quaternion_normalised( const Quaternion& quaternion ){
|
|
const double n = ( 1.0 / ( quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3] ) );
|
|
return Quaternion(
|
|
static_cast<float>( quaternion[0] * n ),
|
|
static_cast<float>( quaternion[1] * n ),
|
|
static_cast<float>( quaternion[2] * n ),
|
|
static_cast<float>( quaternion[3] * n )
|
|
);
|
|
}
|
|
|
|
inline void quaternion_normalise( Quaternion& quaternion ){
|
|
quaternion = quaternion_normalised( quaternion );
|
|
}
|
|
|
|
/// \brief Constructs a pure-rotation matrix from \p quaternion.
|
|
inline Matrix4 matrix4_rotation_for_quaternion( const Quaternion& quaternion ){
|
|
#if 0
|
|
const double xx = quaternion[0] * quaternion[0];
|
|
const double xy = quaternion[0] * quaternion[1];
|
|
const double xz = quaternion[0] * quaternion[2];
|
|
const double xw = quaternion[0] * quaternion[3];
|
|
|
|
const double yy = quaternion[1] * quaternion[1];
|
|
const double yz = quaternion[1] * quaternion[2];
|
|
const double yw = quaternion[1] * quaternion[3];
|
|
|
|
const double zz = quaternion[2] * quaternion[2];
|
|
const double zw = quaternion[2] * quaternion[3];
|
|
|
|
return Matrix4(
|
|
static_cast<float>( 1 - 2 * ( yy + zz ) ),
|
|
static_cast<float>( 2 * ( xy + zw ) ),
|
|
static_cast<float>( 2 * ( xz - yw ) ),
|
|
0,
|
|
static_cast<float>( 2 * ( xy - zw ) ),
|
|
static_cast<float>( 1 - 2 * ( xx + zz ) ),
|
|
static_cast<float>( 2 * ( yz + xw ) ),
|
|
0,
|
|
static_cast<float>( 2 * ( xz + yw ) ),
|
|
static_cast<float>( 2 * ( yz - xw ) ),
|
|
static_cast<float>( 1 - 2 * ( xx + yy ) ),
|
|
0,
|
|
0,
|
|
0,
|
|
0,
|
|
1
|
|
);
|
|
|
|
#else
|
|
const double x2 = quaternion[0] + quaternion[0];
|
|
const double y2 = quaternion[1] + quaternion[1];
|
|
const double z2 = quaternion[2] + quaternion[2];
|
|
const double xx = quaternion[0] * x2;
|
|
const double xy = quaternion[0] * y2;
|
|
const double xz = quaternion[0] * z2;
|
|
const double yy = quaternion[1] * y2;
|
|
const double yz = quaternion[1] * z2;
|
|
const double zz = quaternion[2] * z2;
|
|
const double wx = quaternion[3] * x2;
|
|
const double wy = quaternion[3] * y2;
|
|
const double wz = quaternion[3] * z2;
|
|
|
|
return Matrix4(
|
|
static_cast<float>( 1.0 - ( yy + zz ) ),
|
|
static_cast<float>( xy + wz ),
|
|
static_cast<float>( xz - wy ),
|
|
0,
|
|
static_cast<float>( xy - wz ),
|
|
static_cast<float>( 1.0 - ( xx + zz ) ),
|
|
static_cast<float>( yz + wx ),
|
|
0,
|
|
static_cast<float>( xz + wy ),
|
|
static_cast<float>( yz - wx ),
|
|
static_cast<float>( 1.0 - ( xx + yy ) ),
|
|
0,
|
|
0,
|
|
0,
|
|
0,
|
|
1
|
|
);
|
|
|
|
#endif
|
|
}
|
|
|
|
const double c_half_sqrt2 = 0.70710678118654752440084436210485;
|
|
const float c_half_sqrt2f = static_cast<float>( c_half_sqrt2 );
|
|
|
|
inline bool quaternion_component_is_90( float component ){
|
|
return ( fabs( component ) - c_half_sqrt2 ) < 0.001;
|
|
}
|
|
|
|
inline Matrix4 matrix4_rotation_for_quaternion_quantised( const Quaternion& quaternion ){
|
|
if ( quaternion.y() == 0
|
|
&& quaternion.z() == 0
|
|
&& quaternion_component_is_90( quaternion.x() )
|
|
&& quaternion_component_is_90( quaternion.w() ) ) {
|
|
return matrix4_rotation_for_sincos_x( ( quaternion.x() > 0 ) ? 1.f : -1.f, 0 );
|
|
}
|
|
|
|
if ( quaternion.x() == 0
|
|
&& quaternion.z() == 0
|
|
&& quaternion_component_is_90( quaternion.y() )
|
|
&& quaternion_component_is_90( quaternion.w() ) ) {
|
|
return matrix4_rotation_for_sincos_y( ( quaternion.y() > 0 ) ? 1.f : -1.f, 0 );
|
|
}
|
|
|
|
if ( quaternion.x() == 0
|
|
&& quaternion.y() == 0
|
|
&& quaternion_component_is_90( quaternion.z() )
|
|
&& quaternion_component_is_90( quaternion.w() ) ) {
|
|
return matrix4_rotation_for_sincos_z( ( quaternion.z() > 0 ) ? 1.f : -1.f, 0 );
|
|
}
|
|
|
|
return matrix4_rotation_for_quaternion( quaternion );
|
|
}
|
|
|
|
inline Quaternion quaternion_for_matrix4_rotation( const Matrix4& matrix4 ){
|
|
Quaternion out;
|
|
Matrix4 transposed = matrix4_transposed( matrix4 );
|
|
|
|
/* the monkeys added 1.0 to this for some reason. hint: it's WRONG - eukara */
|
|
double trace = transposed[0] + transposed[5] + transposed[10] + 1.0f;
|
|
|
|
if ( trace > 0.0 ) {
|
|
double S = 0.5 / sqrt( trace );
|
|
return Quaternion(
|
|
static_cast<float>( ( transposed[9] - transposed[6] ) * S ),
|
|
static_cast<float>( ( transposed[2] - transposed[8] ) * S ),
|
|
static_cast<float>( ( transposed[4] - transposed[1] ) * S ),
|
|
static_cast<float>( 0.25 / S )
|
|
);
|
|
}
|
|
|
|
if ( transposed[0] >= transposed[5] && transposed[0] >= transposed[10] ) {
|
|
double S = 2.0 * sqrt( 1.0 + transposed[0] - transposed[5] - transposed[10] );
|
|
return Quaternion(
|
|
static_cast<float>( 0.25 / S ),
|
|
static_cast<float>( ( transposed[1] + transposed[4] ) / S ),
|
|
static_cast<float>( ( transposed[2] + transposed[8] ) / S ),
|
|
static_cast<float>( ( transposed[6] + transposed[9] ) / S )
|
|
);
|
|
}
|
|
|
|
if ( transposed[5] >= transposed[0] && transposed[5] >= transposed[10] ) {
|
|
double S = 2.0 * sqrt( 1.0 + transposed[5] - transposed[0] - transposed[10] );
|
|
return Quaternion(
|
|
static_cast<float>( ( transposed[1] + transposed[4] ) / S ),
|
|
static_cast<float>( 0.25 / S ),
|
|
static_cast<float>( ( transposed[6] + transposed[9] ) / S ),
|
|
static_cast<float>( ( transposed[2] + transposed[8] ) / S )
|
|
);
|
|
}
|
|
|
|
double S = 2.0 * sqrt( 1.0 + transposed[10] - transposed[0] - transposed[5] );
|
|
return Quaternion(
|
|
static_cast<float>( ( transposed[2] + transposed[8] ) / S ),
|
|
static_cast<float>( ( transposed[6] + transposed[9] ) / S ),
|
|
static_cast<float>( 0.25 / S ),
|
|
static_cast<float>( ( transposed[1] + transposed[4] ) / S )
|
|
);
|
|
}
|
|
|
|
/// \brief Returns \p self concatenated with the rotation transform produced by \p rotation.
|
|
/// The concatenated rotation occurs before \p self.
|
|
inline Matrix4 matrix4_rotated_by_quaternion( const Matrix4& self, const Quaternion& rotation ){
|
|
return matrix4_multiplied_by_matrix4( self, matrix4_rotation_for_quaternion( rotation ) );
|
|
}
|
|
|
|
/// \brief Concatenates \p self with the rotation transform produced by \p rotation.
|
|
/// The concatenated rotation occurs before \p self.
|
|
inline void matrix4_rotate_by_quaternion( Matrix4& self, const Quaternion& rotation ){
|
|
self = matrix4_rotated_by_quaternion( self, rotation );
|
|
}
|
|
|
|
/// \brief Rotates \p self by \p rotation, using \p pivotpoint.
|
|
inline void matrix4_pivoted_rotate_by_quaternion( Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint ){
|
|
matrix4_translate_by_vec3( self, pivotpoint );
|
|
matrix4_rotate_by_quaternion( self, rotation );
|
|
matrix4_translate_by_vec3( self, vector3_negated( pivotpoint ) );
|
|
}
|
|
|
|
inline Vector3 quaternion_transformed_point( const Quaternion& quaternion, const Vector3& point ){
|
|
double xx = quaternion.x() * quaternion.x();
|
|
double yy = quaternion.y() * quaternion.y();
|
|
double zz = quaternion.z() * quaternion.z();
|
|
double ww = quaternion.w() * quaternion.w();
|
|
|
|
double xy2 = quaternion.x() * quaternion.y() * 2;
|
|
double xz2 = quaternion.x() * quaternion.z() * 2;
|
|
double xw2 = quaternion.x() * quaternion.w() * 2;
|
|
double yz2 = quaternion.y() * quaternion.z() * 2;
|
|
double yw2 = quaternion.y() * quaternion.w() * 2;
|
|
double zw2 = quaternion.z() * quaternion.w() * 2;
|
|
|
|
return Vector3(
|
|
static_cast<float>( ww * point.x() + yw2 * point.z() - zw2 * point.y() + xx * point.x() + xy2 * point.y() + xz2 * point.z() - zz * point.x() - yy * point.x() ),
|
|
static_cast<float>( xy2 * point.x() + yy * point.y() + yz2 * point.z() + zw2 * point.x() - zz * point.y() + ww * point.y() - xw2 * point.z() - xx * point.y() ),
|
|
static_cast<float>( xz2 * point.x() + yz2 * point.y() + zz * point.z() - yw2 * point.x() - yy * point.z() + xw2 * point.y() - xx * point.z() + ww * point.z() )
|
|
);
|
|
}
|
|
|
|
/// \brief Constructs a pure-rotation transform from \p axis and \p angle (radians).
|
|
inline Matrix4 matrix4_rotation_for_axisangle( const Vector3& axis, double angle ){
|
|
return matrix4_rotation_for_quaternion( quaternion_for_axisangle( axis, angle ) );
|
|
}
|
|
|
|
/// \brief Rotates \p self about \p axis by \p angle.
|
|
inline void matrix4_rotate_by_axisangle( Matrix4& self, const Vector3& axis, double angle ){
|
|
matrix4_multiply_by_matrix4( self, matrix4_rotation_for_axisangle( axis, angle ) );
|
|
}
|
|
|
|
/// \brief Rotates \p self about \p axis by \p angle using \p pivotpoint.
|
|
inline void matrix4_pivoted_rotate_by_axisangle( Matrix4& self, const Vector3& axis, double angle, const Vector3& pivotpoint ){
|
|
matrix4_translate_by_vec3( self, pivotpoint );
|
|
matrix4_rotate_by_axisangle( self, axis, angle );
|
|
matrix4_translate_by_vec3( self, vector3_negated( pivotpoint ) );
|
|
}
|
|
|
|
|
|
#endif
|