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_inverse(const Quaternion& quaternion)
65 return Quaternion(vector3_negated(vector4_to_vector3(quaternion)), quaternion[3]);
68 inline void quaternion_conjugate(Quaternion& quaternion)
70 quaternion = quaternion_inverse(quaternion);
73 inline Quaternion quaternion_normalised(const Quaternion& quaternion)
75 const double n = (1.0 / (quaternion[0] * quaternion[0] + quaternion[1] * quaternion[1] + quaternion[2] * quaternion[2] + quaternion[3] * quaternion[3]));
77 static_cast<float>(quaternion[0] * n),
78 static_cast<float>(quaternion[1] * n),
79 static_cast<float>(quaternion[2] * n),
80 static_cast<float>(quaternion[3] * n)
84 inline void quaternion_normalise(Quaternion& quaternion)
86 quaternion = quaternion_normalised(quaternion);
89 /// \brief Constructs a pure-rotation matrix from \p quaternion.
90 inline Matrix4 matrix4_rotation_for_quaternion(const Quaternion& quaternion)
93 const double xx = quaternion[0] * quaternion[0];
94 const double xy = quaternion[0] * quaternion[1];
95 const double xz = quaternion[0] * quaternion[2];
96 const double xw = quaternion[0] * quaternion[3];
98 const double yy = quaternion[1] * quaternion[1];
99 const double yz = quaternion[1] * quaternion[2];
100 const double yw = quaternion[1] * quaternion[3];
102 const double zz = quaternion[2] * quaternion[2];
103 const double zw = quaternion[2] * quaternion[3];
106 static_cast<float>( 1 - 2 * ( yy + zz ) ),
107 static_cast<float>( 2 * ( xy + zw ) ),
108 static_cast<float>( 2 * ( xz - yw ) ),
110 static_cast<float>( 2 * ( xy - zw ) ),
111 static_cast<float>( 1 - 2 * ( xx + zz ) ),
112 static_cast<float>( 2 * ( yz + xw ) ),
114 static_cast<float>( 2 * ( xz + yw ) ),
115 static_cast<float>( 2 * ( yz - xw ) ),
116 static_cast<float>( 1 - 2 * ( xx + yy ) ),
125 const double x2 = quaternion[0] + quaternion[0];
126 const double y2 = quaternion[1] + quaternion[1];
127 const double z2 = quaternion[2] + quaternion[2];
128 const double xx = quaternion[0] * x2;
129 const double xy = quaternion[0] * y2;
130 const double xz = quaternion[0] * z2;
131 const double yy = quaternion[1] * y2;
132 const double yz = quaternion[1] * z2;
133 const double zz = quaternion[2] * z2;
134 const double wx = quaternion[3] * x2;
135 const double wy = quaternion[3] * y2;
136 const double wz = quaternion[3] * z2;
139 static_cast<float>( 1.0 - (yy + zz) ),
140 static_cast<float>(xy + wz),
141 static_cast<float>(xz - wy),
143 static_cast<float>(xy - wz),
144 static_cast<float>( 1.0 - (xx + zz) ),
145 static_cast<float>(yz + wx),
147 static_cast<float>(xz + wy),
148 static_cast<float>(yz - wx),
149 static_cast<float>( 1.0 - (xx + yy) ),
160 const double c_half_sqrt2 = 0.70710678118654752440084436210485;
161 const float c_half_sqrt2f = static_cast<float>(c_half_sqrt2);
163 inline bool quaternion_component_is_90(float component)
165 return (fabs(component) - c_half_sqrt2) < 0.001;
168 inline Matrix4 matrix4_rotation_for_quaternion_quantised(const Quaternion& quaternion)
170 if(quaternion.y() == 0
171 && quaternion.z() == 0
172 && quaternion_component_is_90(quaternion.x())
173 && quaternion_component_is_90(quaternion.w()))
175 return matrix4_rotation_for_sincos_x((quaternion.x() > 0) ? 1.f : -1.f, 0);
178 if(quaternion.x() == 0
179 && quaternion.z() == 0
180 && quaternion_component_is_90(quaternion.y())
181 && quaternion_component_is_90(quaternion.w()))
183 return matrix4_rotation_for_sincos_y((quaternion.y() > 0) ? 1.f : -1.f, 0);
186 if(quaternion.x() == 0
187 && quaternion.y() == 0
188 && quaternion_component_is_90(quaternion.z())
189 && quaternion_component_is_90(quaternion.w()))
191 return matrix4_rotation_for_sincos_z((quaternion.z() > 0) ? 1.f : -1.f, 0);
194 return matrix4_rotation_for_quaternion(quaternion);
197 inline Quaternion quaternion_for_matrix4_rotation(const Matrix4& matrix4)
199 Matrix4 transposed = matrix4_transposed(matrix4);
201 double trace = transposed[0] + transposed[5] + transposed[10] + 1.0;
205 double S = 0.5 / sqrt(trace);
207 static_cast<float>((transposed[9] - transposed[6]) * S),
208 static_cast<float>((transposed[2] - transposed[8]) * S),
209 static_cast<float>((transposed[4] - transposed[1]) * S),
210 static_cast<float>(0.25 / S)
214 if(transposed[0] >= transposed[5] && transposed[0] >= transposed[10])
216 double S = 2.0 * sqrt(1.0 + transposed[0] - transposed[5] - transposed[10]);
218 static_cast<float>(0.25 / S),
219 static_cast<float>((transposed[1] + transposed[4]) / S),
220 static_cast<float>((transposed[2] + transposed[8]) / S),
221 static_cast<float>((transposed[6] + transposed[9]) / S)
225 if(transposed[5] >= transposed[0] && transposed[5] >= transposed[10])
227 double S = 2.0 * sqrt(1.0 + transposed[5] - transposed[0] - transposed[10]);
229 static_cast<float>((transposed[1] + transposed[4]) / S),
230 static_cast<float>(0.25 / S),
231 static_cast<float>((transposed[6] + transposed[9]) / S),
232 static_cast<float>((transposed[2] + transposed[8]) / S)
236 double S = 2.0 * sqrt(1.0 + transposed[10] - transposed[0] - transposed[5]);
238 static_cast<float>((transposed[2] + transposed[8]) / S),
239 static_cast<float>((transposed[6] + transposed[9]) / S),
240 static_cast<float>(0.25 / S),
241 static_cast<float>((transposed[1] + transposed[4]) / S)
245 /// \brief Returns \p self concatenated with the rotation transform produced by \p rotation.
246 /// The concatenated rotation occurs before \p self.
247 inline Matrix4 matrix4_rotated_by_quaternion(const Matrix4& self, const Quaternion& rotation)
249 return matrix4_multiplied_by_matrix4(self, matrix4_rotation_for_quaternion(rotation));
252 /// \brief Concatenates \p self with the rotation transform produced by \p rotation.
253 /// The concatenated rotation occurs before \p self.
254 inline void matrix4_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation)
256 self = matrix4_rotated_by_quaternion(self, rotation);
259 /// \brief Rotates \p self by \p rotation, using \p pivotpoint.
260 inline void matrix4_pivoted_rotate_by_quaternion(Matrix4& self, const Quaternion& rotation, const Vector3& pivotpoint)
262 matrix4_translate_by_vec3(self, pivotpoint);
263 matrix4_rotate_by_quaternion(self, rotation);
264 matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));
267 inline Vector3 quaternion_transformed_point(const Quaternion& quaternion, const Vector3& point)
269 double xx = quaternion.x() * quaternion.x();
270 double yy = quaternion.y() * quaternion.y();
271 double zz = quaternion.z() * quaternion.z();
272 double ww = quaternion.w() * quaternion.w();
274 double xy2 = quaternion.x() * quaternion.y() * 2;
275 double xz2 = quaternion.x() * quaternion.z() * 2;
276 double xw2 = quaternion.x() * quaternion.w() * 2;
277 double yz2 = quaternion.y() * quaternion.z() * 2;
278 double yw2 = quaternion.y() * quaternion.w() * 2;
279 double zw2 = quaternion.z() * quaternion.w() * 2;
282 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()),
283 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()),
284 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())
288 /// \brief Constructs a pure-rotation transform from \p axis and \p angle (radians).
289 inline Matrix4 matrix4_rotation_for_axisangle(const Vector3& axis, double angle)
291 return matrix4_rotation_for_quaternion(quaternion_for_axisangle(axis, angle));
294 /// \brief Rotates \p self about \p axis by \p angle.
295 inline void matrix4_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle)
297 matrix4_multiply_by_matrix4(self, matrix4_rotation_for_axisangle(axis, angle));
300 /// \brief Rotates \p self about \p axis by \p angle using \p pivotpoint.
301 inline void matrix4_pivoted_rotate_by_axisangle(Matrix4& self, const Vector3& axis, double angle, const Vector3& pivotpoint)
303 matrix4_translate_by_vec3(self, pivotpoint);
304 matrix4_rotate_by_axisangle(self, axis, angle);
305 matrix4_translate_by_vec3(self, vector3_negated(pivotpoint));