worldspawn/libs/math/quaternion.h

/*
   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