gtkradiant/libs/math/quaternion.h
spog 2a1870f6d6 fixed arbitrary rotation
git-svn-id: svn://svn.icculus.org/gtkradiant/GtkRadiant/trunk@83 8a3a26a2-13c4-0310-b231-cf6edde360e5
2006-06-11 12:45:44 +00:00

327 lines
11 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)
{
Matrix4 transposed = matrix4_transposed(matrix4);
double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;
if(trace > 0.0001)
{
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