2 Copyright (C) 2001-2006, William Joseph.
5 This file is part of GtkRadiant.
7 GtkRadiant is free software; you can redistribute it and/or modify
8 it under the terms of the GNU General Public License as published by
9 the Free Software Foundation; either version 2 of the License, or
10 (at your option) any later version.
12 GtkRadiant is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
15 GNU General Public License for more details.
17 You should have received a copy of the GNU General Public License
18 along with GtkRadiant; if not, write to the Free Software
19 Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
22 #if !defined(INCLUDED_MATH_QUATERNION_H)
23 #define INCLUDED_MATH_QUATERNION_H
26 /// \brief Quaternion data types and related operations.
28 #include "math/matrix.h"
30 /// \brief A quaternion stored in single-precision floating-point.
31 typedef Vector4 Quaternion;
33 const Quaternion c_quaternion_identity(0, 0, 0, 1);
35 inline Quaternion quaternion_multiplied_by_quaternion(const Quaternion& quaternion, const Quaternion& other)
38 quaternion[3]*other[0] + quaternion[0]*other[3] + quaternion[1]*other[2] - quaternion[2]*other[1],
39 quaternion[3]*other[1] + quaternion[1]*other[3] + quaternion[2]*other[0] - quaternion[0]*other[2],
40 quaternion[3]*other[2] + quaternion[2]*other[3] + quaternion[0]*other[1] - quaternion[1]*other[0],
41 quaternion[3]*other[3] - quaternion[0]*other[0] - quaternion[1]*other[1] - quaternion[2]*other[2]
45 inline void quaternion_multiply_by_quaternion(Quaternion& quaternion, const Quaternion& other)
47 quaternion = quaternion_multiplied_by_quaternion(quaternion, other);
50 /// \brief Constructs a quaternion which rotates between two points on the unit-sphere, \p from and \p to.
51 inline Quaternion quaternion_for_unit_vectors(const Vector3& from, const Vector3& to)
53 return Quaternion(vector3_cross(from, to), static_cast<float>(vector3_dot(from, to)));
56 inline Quaternion quaternion_for_axisangle(const Vector3& axis, double angle)
59 float sa = static_cast<float>(sin(angle));
60 return Quaternion(axis[0] * sa, axis[1] * sa, axis[2] * sa, static_cast<float>(cos(angle)));
63 inline Quaternion quaternion_for_x(double angle)
66 return Quaternion(static_cast<float>(sin(angle)), 0, 0, static_cast<float>(cos(angle)));
69 inline Quaternion quaternion_for_y(double angle)
72 return Quaternion(0, static_cast<float>(sin(angle)), 0, static_cast<float>(cos(angle)));
75 inline Quaternion quaternion_for_z(double angle)
78 return Quaternion(0, 0, static_cast<float>(sin(angle)), static_cast<float>(cos(angle)));
81 inline Quaternion quaternion_inverse(const Quaternion& quaternion)
83 return Quaternion(vector3_negated(vector4_to_vector3(quaternion)), quaternion[3]);
86 inline void quaternion_conjugate(Quaternion& quaternion)
88 quaternion = quaternion_inverse(quaternion);
91 inline Quaternion quaternion_normalised(const Quaternion& quaternion)
93 const double n = (1.0 / (quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3]));
95 static_cast<float>(quaternion[0] * n),
96 static_cast<float>(quaternion[1] * n),
97 static_cast<float>(quaternion[2] * n),
98 static_cast<float>(quaternion[3] * n)
102 inline void quaternion_normalise(Quaternion& quaternion)
104 quaternion = quaternion_normalised(quaternion);
107 /// \brief Constructs a pure-rotation matrix from \p quaternion.
108 inline Matrix4 matrix4_rotation_for_quaternion(const Quaternion& quaternion)
111 const double xx = quaternion[0] * quaternion[0];
112 const double xy = quaternion[0] * quaternion[1];
113 const double xz = quaternion[0] * quaternion[2];
114 const double xw = quaternion[0] * quaternion[3];
116 const double yy = quaternion[1] * quaternion[1];
117 const double yz = quaternion[1] * quaternion[2];
118 const double yw = quaternion[1] * quaternion[3];
120 const double zz = quaternion[2] * quaternion[2];
121 const double zw = quaternion[2] * quaternion[3];
124 static_cast<float>( 1 - 2 * ( yy + zz ) ),
125 static_cast<float>( 2 * ( xy + zw ) ),
126 static_cast<float>( 2 * ( xz - yw ) ),
128 static_cast<float>( 2 * ( xy - zw ) ),
129 static_cast<float>( 1 - 2 * ( xx + zz ) ),
130 static_cast<float>( 2 * ( yz + xw ) ),
132 static_cast<float>( 2 * ( xz + yw ) ),
133 static_cast<float>( 2 * ( yz - xw ) ),
134 static_cast<float>( 1 - 2 * ( xx + yy ) ),
143 const double x2 = quaternion[0] + quaternion[0];
144 const double y2 = quaternion[1] + quaternion[1];
145 const double z2 = quaternion[2] + quaternion[2];
146 const double xx = quaternion[0] * x2;
147 const double xy = quaternion[0] * y2;
148 const double xz = quaternion[0] * z2;
149 const double yy = quaternion[1] * y2;
150 const double yz = quaternion[1] * z2;
151 const double zz = quaternion[2] * z2;
152 const double wx = quaternion[3] * x2;
153 const double wy = quaternion[3] * y2;
154 const double wz = quaternion[3] * z2;
157 static_cast<float>( 1.0 - (yy + zz) ),
158 static_cast<float>(xy + wz),
159 static_cast<float>(xz - wy),
161 static_cast<float>(xy - wz),
162 static_cast<float>( 1.0 - (xx + zz) ),
163 static_cast<float>(yz + wx),
165 static_cast<float>(xz + wy),
166 static_cast<float>(yz - wx),
167 static_cast<float>( 1.0 - (xx + yy) ),
178 const double c_half_sqrt2 = 0.70710678118654752440084436210485;
179 const float c_half_sqrt2f = static_cast<float>(c_half_sqrt2);
181 inline bool quaternion_component_is_90(float component)
183 return (fabs(component) - c_half_sqrt2) < 0.001;
186 inline Matrix4 matrix4_rotation_for_quaternion_quantised(const Quaternion& quaternion)
188 if(quaternion.y() == 0
189 && quaternion.z() == 0
190 && quaternion_component_is_90(quaternion.x())
191 && quaternion_component_is_90(quaternion.w()))
193 return matrix4_rotation_for_sincos_x((quaternion.x() > 0) ? 1.f : -1.f, 0);
196 if(quaternion.x() == 0
197 && quaternion.z() == 0
198 && quaternion_component_is_90(quaternion.y())
199 && quaternion_component_is_90(quaternion.w()))
201 return matrix4_rotation_for_sincos_y((quaternion.y() > 0) ? 1.f : -1.f, 0);
204 if(quaternion.x() == 0
205 && quaternion.y() == 0
206 && quaternion_component_is_90(quaternion.z())
207 && quaternion_component_is_90(quaternion.w()))
209 return matrix4_rotation_for_sincos_z((quaternion.z() > 0) ? 1.f : -1.f, 0);
212 return matrix4_rotation_for_quaternion(quaternion);
215 inline Quaternion quaternion_for_matrix4_rotation(const Matrix4& matrix4)
217 Matrix4 transposed = matrix4_transposed(matrix4);
219 double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;
223 double S = 0.5 / sqrt(trace);
225 static_cast<float>((transposed[9] - transposed[6]) * S),
226 static_cast<float>((transposed[2] - transposed[8]) * S),
227 static_cast<float>((transposed[4] - transposed[1]) * S),
228 static_cast<float>(0.25 / S)
232 if(transposed[0] >= transposed[5] && transposed[0] >= transposed[10])
234 double S = 2.0 * sqrt(1.0 + transposed[0] - transposed[5] - transposed[10]);
236 static_cast<float>(0.25 / S),
237 static_cast<float>((transposed[1] + transposed[4]) / S),
238 static_cast<float>((transposed[2] + transposed[8]) / S),
239 static_cast<float>((transposed[6] + transposed[9]) / S)
243 if(transposed[5] >= transposed[0] && transposed[5] >= transposed[10])
245 double S = 2.0 * sqrt(1.0 + transposed[5] - transposed[0] - transposed[10]);
247 static_cast<float>((transposed[1] + transposed[4]) / S),
248 static_cast<float>(0.25 / S),
249 static_cast<float>((transposed[6] + transposed[9]) / S),
250 static_cast<float>((transposed[2] + transposed[8]) / S)
254 double S = 2.0 * sqrt(1.0 + transposed[10] - transposed[0] - transposed[5]);
256 static_cast<float>((transposed[2] + transposed[8]) / S),
257 static_cast<float>((transposed[6] + transposed[9]) / S),
258 static_cast<float>(0.25 / S),
259 static_cast<float>((transposed[1] + transposed[4]) / S)
263 /// \brief Returns \p self concatenated with the rotation transform produced by \p rotation.
264 /// The concatenated rotation occurs before \p self.
265 inline Matrix4 matrix4_rotated_by_quaternion(const Matrix4& self, const Quaternion& rotation)
267 return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_quaternion(rotation));
270 /// \brief Concatenates \p self with the rotation transform produced by \p rotation.
271 /// The concatenated rotation occurs before \p self.
272 inline void matrix4_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation)
274 self = matrix4_rotated_by_quaternion(self, rotation);
277 /// \brief Rotates \p self by \p rotation, using \p pivotpoint.
278 inline void matrix4_pivoted_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint)
280 matrix4_translate_by_vec3(self, pivotpoint);
281 matrix4_rotate_by_quaternion(self, rotation);
282 matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
285 inline Vector3 quaternion_transformed_point(const Quaternion& quaternion, const Vector3& point)
287 double xx = quaternion.x() * quaternion.x();
288 double yy = quaternion.y() * quaternion.y();
289 double zz = quaternion.z() * quaternion.z();
290 double ww = quaternion.w() * quaternion.w();
292 double xy2 = quaternion.x() * quaternion.y() * 2;
293 double xz2 = quaternion.x() * quaternion.z() * 2;
294 double xw2 = quaternion.x() * quaternion.w() * 2;
295 double yz2 = quaternion.y() * quaternion.z() * 2;
296 double yw2 = quaternion.y() * quaternion.w() * 2;
297 double zw2 = quaternion.z() * quaternion.w() * 2;
300 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()),
301 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()),
302 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())
306 /// \brief Constructs a pure-rotation transform from \p axis and \p angle (radians).
307 inline Matrix4 matrix4_rotation_for_axisangle(const Vector3& axis, double angle)
309 return matrix4_rotation_for_quaternion(quaternion_for_axisangle(axis, angle));
312 /// \brief Rotates \p self about \p axis by \p angle.
313 inline void matrix4_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle)
315 matrix4_multiply_by_matrix4(self, matrix4_rotation_for_axisangle(axis, angle));
318 /// \brief Rotates \p self about \p axis by \p angle using \p pivotpoint.
319 inline void matrix4_pivoted_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle, const Vector3& pivotpoint)
321 matrix4_translate_by_vec3(self, pivotpoint);
322 matrix4_rotate_by_axisangle(self, axis, angle);
323 matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));