Alan Huchin Herrera / Mbed 2 deprecated Nucleo_MPU_9250_

Quadrirotor

Dependencies:   CommonTypes ESC Matrix PID Servo kalman mbed-rtos mbed

Fork of Nucleo_MPU_9250 by Alan Huchin Herrera

CID10DOF/vector_math.h@0:89cf0851969b, 2018-06-26 (annotated)

Committer:
AlanHuchin
Date:
Tue Jun 26 18:24:45 2018 +0000
Revision:
0:89cf0851969b
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AlanHuchin 0:89cf0851969b 1 /*
AlanHuchin 0:89cf0851969b 2 Copyright (c) 2007, Markus Trenkwalder
AlanHuchin 0:89cf0851969b 3
AlanHuchin 0:89cf0851969b 4 All rights reserved.
AlanHuchin 0:89cf0851969b 5
AlanHuchin 0:89cf0851969b 6 Redistribution and use in source and binary forms, with or without
AlanHuchin 0:89cf0851969b 7 modification, are permitted provided that the following conditions are met:
AlanHuchin 0:89cf0851969b 8
AlanHuchin 0:89cf0851969b 9 * Redistributions of source code must retain the above copyright notice,
AlanHuchin 0:89cf0851969b 10 this list of conditions and the following disclaimer.
AlanHuchin 0:89cf0851969b 11
AlanHuchin 0:89cf0851969b 12 * Redistributions in binary form must reproduce the above copyright notice,
AlanHuchin 0:89cf0851969b 13 this list of conditions and the following disclaimer in the documentation
AlanHuchin 0:89cf0851969b 14 and/or other materials provided with the distribution.
AlanHuchin 0:89cf0851969b 15
AlanHuchin 0:89cf0851969b 16 * Neither the name of the library's copyright owner nor the names of its
AlanHuchin 0:89cf0851969b 17 contributors may be used to endorse or promote products derived from this
AlanHuchin 0:89cf0851969b 18 software without specific prior written permission.
AlanHuchin 0:89cf0851969b 19
AlanHuchin 0:89cf0851969b 20 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
AlanHuchin 0:89cf0851969b 21 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
AlanHuchin 0:89cf0851969b 22 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
AlanHuchin 0:89cf0851969b 23 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
AlanHuchin 0:89cf0851969b 24 CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
AlanHuchin 0:89cf0851969b 25 EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
AlanHuchin 0:89cf0851969b 26 PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
AlanHuchin 0:89cf0851969b 27 PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
AlanHuchin 0:89cf0851969b 28 LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
AlanHuchin 0:89cf0851969b 29 NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
AlanHuchin 0:89cf0851969b 30 SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
AlanHuchin 0:89cf0851969b 31 */
AlanHuchin 0:89cf0851969b 32
AlanHuchin 0:89cf0851969b 33 #ifndef VECTOR_MATH_H
AlanHuchin 0:89cf0851969b 34 #define VECTOR_MATH_H
AlanHuchin 0:89cf0851969b 35
AlanHuchin 0:89cf0851969b 36 //#include <cmath>
AlanHuchin 0:89cf0851969b 37
AlanHuchin 0:89cf0851969b 38 // "minor" can be defined from GCC and can cause problems
AlanHuchin 0:89cf0851969b 39 #undef minor
AlanHuchin 0:89cf0851969b 40
AlanHuchin 0:89cf0851969b 41 #ifndef M_PI
AlanHuchin 0:89cf0851969b 42 #define M_PI 3.14159265358979323846
AlanHuchin 0:89cf0851969b 43 #endif
AlanHuchin 0:89cf0851969b 44
AlanHuchin 0:89cf0851969b 45 namespace vmath {
AlanHuchin 0:89cf0851969b 46
AlanHuchin 0:89cf0851969b 47 //using std::sin;
AlanHuchin 0:89cf0851969b 48 //using std::cos;
AlanHuchin 0:89cf0851969b 49 //using std::acos;
AlanHuchin 0:89cf0851969b 50 //using std::sqrt;
AlanHuchin 0:89cf0851969b 51
AlanHuchin 0:89cf0851969b 52 template <typename T>
AlanHuchin 0:89cf0851969b 53 inline T rsqrt(T x)
AlanHuchin 0:89cf0851969b 54 {
AlanHuchin 0:89cf0851969b 55 return T(1) / sqrt(x);
AlanHuchin 0:89cf0851969b 56 }
AlanHuchin 0:89cf0851969b 57
AlanHuchin 0:89cf0851969b 58 template <typename T>
AlanHuchin 0:89cf0851969b 59 inline T inv(T x)
AlanHuchin 0:89cf0851969b 60 {
AlanHuchin 0:89cf0851969b 61 return T(1) / x;
AlanHuchin 0:89cf0851969b 62 }
AlanHuchin 0:89cf0851969b 63
AlanHuchin 0:89cf0851969b 64 namespace detail {
AlanHuchin 0:89cf0851969b 65 // This function is used heavily in this library. Here is a generic
AlanHuchin 0:89cf0851969b 66 // implementation for it. If you can provide a faster one for your specific
AlanHuchin 0:89cf0851969b 67 // types this can speed up things considerably.
AlanHuchin 0:89cf0851969b 68 template <typename T>
AlanHuchin 0:89cf0851969b 69 inline T multiply_accumulate(int count, const T *a, const T *b)
AlanHuchin 0:89cf0851969b 70 {
AlanHuchin 0:89cf0851969b 71 T result = T(0);
AlanHuchin 0:89cf0851969b 72 for (int i = 0; i < count; ++i)
AlanHuchin 0:89cf0851969b 73 result += a[i] * b[i];
AlanHuchin 0:89cf0851969b 74 return result;
AlanHuchin 0:89cf0851969b 75 }
AlanHuchin 0:89cf0851969b 76 }
AlanHuchin 0:89cf0851969b 77
AlanHuchin 0:89cf0851969b 78 #define MOP_M_CLASS_TEMPLATE(CLASS, OP, COUNT) \
AlanHuchin 0:89cf0851969b 79 CLASS & operator OP (const CLASS& rhs) \
AlanHuchin 0:89cf0851969b 80 { \
AlanHuchin 0:89cf0851969b 81 for (int i = 0; i < (COUNT); ++i ) \
AlanHuchin 0:89cf0851969b 82 (*this)[i] OP rhs[i]; \
AlanHuchin 0:89cf0851969b 83 return *this; \
AlanHuchin 0:89cf0851969b 84 }
AlanHuchin 0:89cf0851969b 85
AlanHuchin 0:89cf0851969b 86 #define MOP_M_TYPE_TEMPLATE(CLASS, OP, COUNT) \
AlanHuchin 0:89cf0851969b 87 CLASS & operator OP (const T & rhs) \
AlanHuchin 0:89cf0851969b 88 { \
AlanHuchin 0:89cf0851969b 89 for (int i = 0; i < (COUNT); ++i ) \
AlanHuchin 0:89cf0851969b 90 (*this)[i] OP rhs; \
AlanHuchin 0:89cf0851969b 91 return *this; \
AlanHuchin 0:89cf0851969b 92 }
AlanHuchin 0:89cf0851969b 93
AlanHuchin 0:89cf0851969b 94 #define MOP_COMP_TEMPLATE(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 95 bool operator == (const CLASS & rhs) \
AlanHuchin 0:89cf0851969b 96 { \
AlanHuchin 0:89cf0851969b 97 bool result = true; \
AlanHuchin 0:89cf0851969b 98 for (int i = 0; i < (COUNT); ++i) \
AlanHuchin 0:89cf0851969b 99 result = result && (*this)[i] == rhs[i]; \
AlanHuchin 0:89cf0851969b 100 return result; \
AlanHuchin 0:89cf0851969b 101 } \
AlanHuchin 0:89cf0851969b 102 bool operator != (const CLASS & rhs) \
AlanHuchin 0:89cf0851969b 103 { return !((*this) == rhs); }
AlanHuchin 0:89cf0851969b 104
AlanHuchin 0:89cf0851969b 105 #define MOP_G_UMINUS_TEMPLATE(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 106 CLASS operator - () const \
AlanHuchin 0:89cf0851969b 107 { \
AlanHuchin 0:89cf0851969b 108 CLASS result; \
AlanHuchin 0:89cf0851969b 109 for (int i = 0; i < (COUNT); ++i) \
AlanHuchin 0:89cf0851969b 110 result[i] = -(*this)[i]; \
AlanHuchin 0:89cf0851969b 111 return result; \
AlanHuchin 0:89cf0851969b 112 }
AlanHuchin 0:89cf0851969b 113
AlanHuchin 0:89cf0851969b 114 #define COMMON_OPERATORS(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 115 MOP_M_CLASS_TEMPLATE(CLASS, +=, COUNT) \
AlanHuchin 0:89cf0851969b 116 MOP_M_CLASS_TEMPLATE(CLASS, -=, COUNT) \
AlanHuchin 0:89cf0851969b 117 /*no *= as this is not the same for vectors and matrices */ \
AlanHuchin 0:89cf0851969b 118 MOP_M_CLASS_TEMPLATE(CLASS, /=, COUNT) \
AlanHuchin 0:89cf0851969b 119 MOP_M_TYPE_TEMPLATE(CLASS, +=, COUNT) \
AlanHuchin 0:89cf0851969b 120 MOP_M_TYPE_TEMPLATE(CLASS, -=, COUNT) \
AlanHuchin 0:89cf0851969b 121 MOP_M_TYPE_TEMPLATE(CLASS, *=, COUNT) \
AlanHuchin 0:89cf0851969b 122 MOP_M_TYPE_TEMPLATE(CLASS, /=, COUNT) \
AlanHuchin 0:89cf0851969b 123 MOP_G_UMINUS_TEMPLATE(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 124 MOP_COMP_TEMPLATE(CLASS, COUNT)
AlanHuchin 0:89cf0851969b 125
AlanHuchin 0:89cf0851969b 126 #define VECTOR_COMMON(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 127 COMMON_OPERATORS(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 128 MOP_M_CLASS_TEMPLATE(CLASS, *=, COUNT) \
AlanHuchin 0:89cf0851969b 129 operator const T* () const { return &x; } \
AlanHuchin 0:89cf0851969b 130 operator T* () { return &x; }
AlanHuchin 0:89cf0851969b 131
AlanHuchin 0:89cf0851969b 132 #define FOP_G_SOURCE_TEMPLATE(OP, CLASS) \
AlanHuchin 0:89cf0851969b 133 { CLASS<T> r = lhs; r OP##= rhs; return r; }
AlanHuchin 0:89cf0851969b 134
AlanHuchin 0:89cf0851969b 135 #define FOP_G_CLASS_TEMPLATE(OP, CLASS) \
AlanHuchin 0:89cf0851969b 136 template <typename T> \
AlanHuchin 0:89cf0851969b 137 inline CLASS<T> operator OP (const CLASS<T> &lhs, const CLASS<T> &rhs) \
AlanHuchin 0:89cf0851969b 138 FOP_G_SOURCE_TEMPLATE(OP, CLASS)
AlanHuchin 0:89cf0851969b 139
AlanHuchin 0:89cf0851969b 140 #define FOP_G_TYPE_TEMPLATE(OP, CLASS) \
AlanHuchin 0:89cf0851969b 141 template <typename T> \
AlanHuchin 0:89cf0851969b 142 inline CLASS<T> operator OP (const CLASS<T> &lhs, const T &rhs) \
AlanHuchin 0:89cf0851969b 143 FOP_G_SOURCE_TEMPLATE(OP, CLASS)
AlanHuchin 0:89cf0851969b 144
AlanHuchin 0:89cf0851969b 145 // forward declarations
AlanHuchin 0:89cf0851969b 146 template <typename T> struct vec2;
AlanHuchin 0:89cf0851969b 147 template <typename T> struct vec3;
AlanHuchin 0:89cf0851969b 148 template <typename T> struct vec4;
AlanHuchin 0:89cf0851969b 149 template <typename T> struct mat2;
AlanHuchin 0:89cf0851969b 150 template <typename T> struct mat3;
AlanHuchin 0:89cf0851969b 151 template <typename T> struct mat4;
AlanHuchin 0:89cf0851969b 152 template <typename T> struct quat;
AlanHuchin 0:89cf0851969b 153
AlanHuchin 0:89cf0851969b 154 #define FREE_MODIFYING_OPERATORS(CLASS) \
AlanHuchin 0:89cf0851969b 155 FOP_G_CLASS_TEMPLATE(+, CLASS) \
AlanHuchin 0:89cf0851969b 156 FOP_G_CLASS_TEMPLATE(-, CLASS) \
AlanHuchin 0:89cf0851969b 157 FOP_G_CLASS_TEMPLATE(*, CLASS) \
AlanHuchin 0:89cf0851969b 158 FOP_G_CLASS_TEMPLATE(/, CLASS) \
AlanHuchin 0:89cf0851969b 159 FOP_G_TYPE_TEMPLATE(+, CLASS) \
AlanHuchin 0:89cf0851969b 160 FOP_G_TYPE_TEMPLATE(-, CLASS) \
AlanHuchin 0:89cf0851969b 161 FOP_G_TYPE_TEMPLATE(*, CLASS) \
AlanHuchin 0:89cf0851969b 162 FOP_G_TYPE_TEMPLATE(/, CLASS)
AlanHuchin 0:89cf0851969b 163
AlanHuchin 0:89cf0851969b 164 FREE_MODIFYING_OPERATORS(vec2)
AlanHuchin 0:89cf0851969b 165 FREE_MODIFYING_OPERATORS(vec3)
AlanHuchin 0:89cf0851969b 166 FREE_MODIFYING_OPERATORS(vec4)
AlanHuchin 0:89cf0851969b 167 FREE_MODIFYING_OPERATORS(mat2)
AlanHuchin 0:89cf0851969b 168 FREE_MODIFYING_OPERATORS(mat3)
AlanHuchin 0:89cf0851969b 169 FREE_MODIFYING_OPERATORS(mat4)
AlanHuchin 0:89cf0851969b 170 FREE_MODIFYING_OPERATORS(quat)
AlanHuchin 0:89cf0851969b 171
AlanHuchin 0:89cf0851969b 172 #define FREE_OPERATORS(CLASS) \
AlanHuchin 0:89cf0851969b 173 template <typename T> \
AlanHuchin 0:89cf0851969b 174 inline CLASS<T> operator + (const T& a, const CLASS<T>& b) \
AlanHuchin 0:89cf0851969b 175 { CLASS<T> r = b; r += a; return r; } \
AlanHuchin 0:89cf0851969b 176 \
AlanHuchin 0:89cf0851969b 177 template <typename T> \
AlanHuchin 0:89cf0851969b 178 inline CLASS<T> operator * (const T& a, const CLASS<T>& b) \
AlanHuchin 0:89cf0851969b 179 { CLASS<T> r = b; r *= a; return r; } \
AlanHuchin 0:89cf0851969b 180 \
AlanHuchin 0:89cf0851969b 181 template <typename T> \
AlanHuchin 0:89cf0851969b 182 inline CLASS<T> operator - (const T& a, const CLASS<T>& b) \
AlanHuchin 0:89cf0851969b 183 { return -b + a; } \
AlanHuchin 0:89cf0851969b 184 \
AlanHuchin 0:89cf0851969b 185 template <typename T> \
AlanHuchin 0:89cf0851969b 186 inline CLASS<T> operator / (const T& a, const CLASS<T>& b) \
AlanHuchin 0:89cf0851969b 187 { CLASS<T> r(a); r /= b; return r; }
AlanHuchin 0:89cf0851969b 188
AlanHuchin 0:89cf0851969b 189 FREE_OPERATORS(vec2)
AlanHuchin 0:89cf0851969b 190 FREE_OPERATORS(vec3)
AlanHuchin 0:89cf0851969b 191 FREE_OPERATORS(vec4)
AlanHuchin 0:89cf0851969b 192 FREE_OPERATORS(mat2)
AlanHuchin 0:89cf0851969b 193 FREE_OPERATORS(mat3)
AlanHuchin 0:89cf0851969b 194 FREE_OPERATORS(mat4)
AlanHuchin 0:89cf0851969b 195 FREE_OPERATORS(quat)
AlanHuchin 0:89cf0851969b 196
AlanHuchin 0:89cf0851969b 197 template <typename T>
AlanHuchin 0:89cf0851969b 198 struct vec2 {
AlanHuchin 0:89cf0851969b 199 T x, y;
AlanHuchin 0:89cf0851969b 200
AlanHuchin 0:89cf0851969b 201 vec2() {};
AlanHuchin 0:89cf0851969b 202 explicit vec2(const T i) : x(i), y(i) {}
AlanHuchin 0:89cf0851969b 203 explicit vec2(const T ix, const T iy) : x(ix), y(iy) {}
AlanHuchin 0:89cf0851969b 204 explicit vec2(const vec3<T>& v);
AlanHuchin 0:89cf0851969b 205 explicit vec2(const vec4<T>& v);
AlanHuchin 0:89cf0851969b 206
AlanHuchin 0:89cf0851969b 207 VECTOR_COMMON(vec2, 2)
AlanHuchin 0:89cf0851969b 208 };
AlanHuchin 0:89cf0851969b 209
AlanHuchin 0:89cf0851969b 210 template <typename T>
AlanHuchin 0:89cf0851969b 211 struct vec3 {
AlanHuchin 0:89cf0851969b 212 T x, y, z;
AlanHuchin 0:89cf0851969b 213
AlanHuchin 0:89cf0851969b 214 vec3() {};
AlanHuchin 0:89cf0851969b 215 explicit vec3(const T i) : x(i), y(i), z(i) {}
AlanHuchin 0:89cf0851969b 216 explicit vec3(const T ix, const T iy, const T iz) : x(ix), y(iy), z(iz) {}
AlanHuchin 0:89cf0851969b 217 explicit vec3(const vec2<T>& xy, const T iz) : x(xy.x), y(xy.y), z(iz) {}
AlanHuchin 0:89cf0851969b 218 explicit vec3(const T ix, const vec2<T>& yz) : x(ix), y(yz.y), z(yz.z) {}
AlanHuchin 0:89cf0851969b 219 explicit vec3(const vec4<T>& v);
AlanHuchin 0:89cf0851969b 220
AlanHuchin 0:89cf0851969b 221 VECTOR_COMMON(vec3, 3)
AlanHuchin 0:89cf0851969b 222 };
AlanHuchin 0:89cf0851969b 223
AlanHuchin 0:89cf0851969b 224 template <typename T>
AlanHuchin 0:89cf0851969b 225 struct vec4 {
AlanHuchin 0:89cf0851969b 226 T x, y, z, w;
AlanHuchin 0:89cf0851969b 227
AlanHuchin 0:89cf0851969b 228 vec4() {};
AlanHuchin 0:89cf0851969b 229 explicit vec4(const T i) : x(i), y(i), z(i), w(i) {}
AlanHuchin 0:89cf0851969b 230 explicit vec4(const T ix, const T iy, const T iz, const T iw) : x(ix), y(iy), z(iz), w(iw) {}
AlanHuchin 0:89cf0851969b 231 explicit vec4(const vec3<T>& xyz,const T iw) : x(xyz.x), y(xyz.y), z(xyz.z), w(iw) {}
AlanHuchin 0:89cf0851969b 232 explicit vec4(const T ix, const vec3<T>& yzw) : x(ix), y(yzw.x), z(yzw.y), w(yzw.z) {}
AlanHuchin 0:89cf0851969b 233 explicit vec4(const vec2<T>& xy, const vec2<T>& zw) : x(xy.x), y(xy.y), z(zw.x), w(zw.y) {}
AlanHuchin 0:89cf0851969b 234
AlanHuchin 0:89cf0851969b 235 VECTOR_COMMON(vec4, 4)
AlanHuchin 0:89cf0851969b 236 };
AlanHuchin 0:89cf0851969b 237
AlanHuchin 0:89cf0851969b 238 // additional constructors that omit the last element
AlanHuchin 0:89cf0851969b 239 template <typename T> inline vec2<T>::vec2(const vec3<T>& v) : x(v.x), y(v.y) {}
AlanHuchin 0:89cf0851969b 240 template <typename T> inline vec2<T>::vec2(const vec4<T>& v) : x(v.x), y(v.y) {}
AlanHuchin 0:89cf0851969b 241 template <typename T> inline vec3<T>::vec3(const vec4<T>& v) : x(v.x), y(v.y), z(v.z) {}
AlanHuchin 0:89cf0851969b 242
AlanHuchin 0:89cf0851969b 243 #define VEC_QUAT_FUNC_TEMPLATE(CLASS, COUNT) \
AlanHuchin 0:89cf0851969b 244 template <typename T> \
AlanHuchin 0:89cf0851969b 245 inline T dot(const CLASS & u, const CLASS & v) \
AlanHuchin 0:89cf0851969b 246 { \
AlanHuchin 0:89cf0851969b 247 const T *a = u; \
AlanHuchin 0:89cf0851969b 248 const T *b = v; \
AlanHuchin 0:89cf0851969b 249 using namespace detail; \
AlanHuchin 0:89cf0851969b 250 return multiply_accumulate(COUNT, a, b); \
AlanHuchin 0:89cf0851969b 251 } \
AlanHuchin 0:89cf0851969b 252 template <typename T> \
AlanHuchin 0:89cf0851969b 253 inline T length(const CLASS & v) \
AlanHuchin 0:89cf0851969b 254 { \
AlanHuchin 0:89cf0851969b 255 return sqrt(dot(v, v)); \
AlanHuchin 0:89cf0851969b 256 } \
AlanHuchin 0:89cf0851969b 257 template <typename T> inline CLASS normalize(const CLASS & v) \
AlanHuchin 0:89cf0851969b 258 { \
AlanHuchin 0:89cf0851969b 259 return v * rsqrt(dot(v, v)); \
AlanHuchin 0:89cf0851969b 260 } \
AlanHuchin 0:89cf0851969b 261 template <typename T> inline CLASS lerp(const CLASS & u, const CLASS & v, const T x) \
AlanHuchin 0:89cf0851969b 262 { \
AlanHuchin 0:89cf0851969b 263 return u * (T(1) - x) + v * x; \
AlanHuchin 0:89cf0851969b 264 }
AlanHuchin 0:89cf0851969b 265
AlanHuchin 0:89cf0851969b 266 VEC_QUAT_FUNC_TEMPLATE(vec2<T>, 2)
AlanHuchin 0:89cf0851969b 267 VEC_QUAT_FUNC_TEMPLATE(vec3<T>, 3)
AlanHuchin 0:89cf0851969b 268 VEC_QUAT_FUNC_TEMPLATE(vec4<T>, 4)
AlanHuchin 0:89cf0851969b 269 VEC_QUAT_FUNC_TEMPLATE(quat<T>, 4)
AlanHuchin 0:89cf0851969b 270
AlanHuchin 0:89cf0851969b 271 #define VEC_FUNC_TEMPLATE(CLASS) \
AlanHuchin 0:89cf0851969b 272 template <typename T> inline CLASS reflect(const CLASS & I, const CLASS & N) \
AlanHuchin 0:89cf0851969b 273 { \
AlanHuchin 0:89cf0851969b 274 return I - T(2) * dot(N, I) * N; \
AlanHuchin 0:89cf0851969b 275 } \
AlanHuchin 0:89cf0851969b 276 template <typename T> inline CLASS refract(const CLASS & I, const CLASS & N, T eta) \
AlanHuchin 0:89cf0851969b 277 { \
AlanHuchin 0:89cf0851969b 278 const T d = dot(N, I); \
AlanHuchin 0:89cf0851969b 279 const T k = T(1) - eta * eta * (T(1) - d * d); \
AlanHuchin 0:89cf0851969b 280 if ( k < T(0) ) \
AlanHuchin 0:89cf0851969b 281 return CLASS(T(0)); \
AlanHuchin 0:89cf0851969b 282 else \
AlanHuchin 0:89cf0851969b 283 return eta * I - (eta * d + static_cast<T>(sqrt(k))) * N; \
AlanHuchin 0:89cf0851969b 284 }
AlanHuchin 0:89cf0851969b 285
AlanHuchin 0:89cf0851969b 286 VEC_FUNC_TEMPLATE(vec2<T>)
AlanHuchin 0:89cf0851969b 287 VEC_FUNC_TEMPLATE(vec3<T>)
AlanHuchin 0:89cf0851969b 288 VEC_FUNC_TEMPLATE(vec4<T>)
AlanHuchin 0:89cf0851969b 289
AlanHuchin 0:89cf0851969b 290 template <typename T> inline T lerp(const T & u, const T & v, const T x)
AlanHuchin 0:89cf0851969b 291 {
AlanHuchin 0:89cf0851969b 292 return dot(vec2<T>(u, v), vec2<T>((T(1) - x), x));
AlanHuchin 0:89cf0851969b 293 }
AlanHuchin 0:89cf0851969b 294
AlanHuchin 0:89cf0851969b 295 template <typename T> inline vec3<T> cross(const vec3<T>& u, const vec3<T>& v)
AlanHuchin 0:89cf0851969b 296 {
AlanHuchin 0:89cf0851969b 297 return vec3<T>(
AlanHuchin 0:89cf0851969b 298 dot(vec2<T>(u.y, -v.y), vec2<T>(v.z, u.z)),
AlanHuchin 0:89cf0851969b 299 dot(vec2<T>(u.z, -v.z), vec2<T>(v.x, u.x)),
AlanHuchin 0:89cf0851969b 300 dot(vec2<T>(u.x, -v.x), vec2<T>(v.y, u.y)));
AlanHuchin 0:89cf0851969b 301 }
AlanHuchin 0:89cf0851969b 302
AlanHuchin 0:89cf0851969b 303
AlanHuchin 0:89cf0851969b 304 #define MATRIX_COL4(SRC, C) \
AlanHuchin 0:89cf0851969b 305 vec4<T>(SRC.elem[0][C], SRC.elem[1][C], SRC.elem[2][C], SRC.elem[3][C])
AlanHuchin 0:89cf0851969b 306
AlanHuchin 0:89cf0851969b 307 #define MATRIX_ROW4(SRC, R) \
AlanHuchin 0:89cf0851969b 308 vec4<T>(SRC.elem[R][0], SRC.elem[R][1], SRC.elem[R][2], SRC.elem[R][3])
AlanHuchin 0:89cf0851969b 309
AlanHuchin 0:89cf0851969b 310 #define MATRIX_COL3(SRC, C) \
AlanHuchin 0:89cf0851969b 311 vec3<T>(SRC.elem[0][C], SRC.elem[1][C], SRC.elem[2][C])
AlanHuchin 0:89cf0851969b 312
AlanHuchin 0:89cf0851969b 313 #define MATRIX_ROW3(SRC, R) \
AlanHuchin 0:89cf0851969b 314 vec3<T>(SRC.elem[R][0], SRC.elem[R][1], SRC.elem[R][2])
AlanHuchin 0:89cf0851969b 315
AlanHuchin 0:89cf0851969b 316 #define MATRIX_COL2(SRC, C) \
AlanHuchin 0:89cf0851969b 317 vec2<T>(SRC.elem[0][C], SRC.elem[1][C])
AlanHuchin 0:89cf0851969b 318
AlanHuchin 0:89cf0851969b 319 #define MATRIX_ROW2(SRC, R) \
AlanHuchin 0:89cf0851969b 320 vec2<T>(SRC.elem[R][0], SRC.elem[R][1])
AlanHuchin 0:89cf0851969b 321
AlanHuchin 0:89cf0851969b 322 #define MOP_M_MATRIX_MULTIPLY(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 323 CLASS & operator *= (const CLASS & rhs) \
AlanHuchin 0:89cf0851969b 324 { \
AlanHuchin 0:89cf0851969b 325 CLASS result; \
AlanHuchin 0:89cf0851969b 326 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 327 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 328 result.elem[r][c] = dot( \
AlanHuchin 0:89cf0851969b 329 MATRIX_ROW ## SIZE((*this), r), \
AlanHuchin 0:89cf0851969b 330 MATRIX_COL ## SIZE(rhs, c)); \
AlanHuchin 0:89cf0851969b 331 return (*this) = result; \
AlanHuchin 0:89cf0851969b 332 }
AlanHuchin 0:89cf0851969b 333
AlanHuchin 0:89cf0851969b 334 #define MATRIX_CONSTRUCTOR_FROM_T(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 335 explicit CLASS(const T v) \
AlanHuchin 0:89cf0851969b 336 { \
AlanHuchin 0:89cf0851969b 337 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 338 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 339 if (r == c) elem[r][c] = v; \
AlanHuchin 0:89cf0851969b 340 else elem[r][c] = T(0); \
AlanHuchin 0:89cf0851969b 341 }
AlanHuchin 0:89cf0851969b 342
AlanHuchin 0:89cf0851969b 343 #define MATRIX_CONSTRUCTOR_FROM_LOWER(CLASS1, CLASS2, SIZE1, SIZE2) \
AlanHuchin 0:89cf0851969b 344 explicit CLASS1(const CLASS2<T>& m) \
AlanHuchin 0:89cf0851969b 345 { \
AlanHuchin 0:89cf0851969b 346 for (int r = 0; r < SIZE1; ++r) \
AlanHuchin 0:89cf0851969b 347 for (int c = 0; c < SIZE1; ++c) \
AlanHuchin 0:89cf0851969b 348 if (r < SIZE2 && c < SIZE2) elem[r][c] = m.elem[r][c]; \
AlanHuchin 0:89cf0851969b 349 else elem[r][c] = r == c ? T(1) : T(0); \
AlanHuchin 0:89cf0851969b 350 }
AlanHuchin 0:89cf0851969b 351
AlanHuchin 0:89cf0851969b 352 #define MATRIX_COMMON(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 353 COMMON_OPERATORS(CLASS, SIZE*SIZE) \
AlanHuchin 0:89cf0851969b 354 MOP_M_MATRIX_MULTIPLY(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 355 MATRIX_CONSTRUCTOR_FROM_T(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 356 operator const T* () const { return (const T*) elem; } \
AlanHuchin 0:89cf0851969b 357 operator T* () { return (T*) elem; }
AlanHuchin 0:89cf0851969b 358
AlanHuchin 0:89cf0851969b 359 template <typename T> struct mat2;
AlanHuchin 0:89cf0851969b 360 template <typename T> struct mat3;
AlanHuchin 0:89cf0851969b 361 template <typename T> struct mat4;
AlanHuchin 0:89cf0851969b 362
AlanHuchin 0:89cf0851969b 363 template <typename T>
AlanHuchin 0:89cf0851969b 364 struct mat2 {
AlanHuchin 0:89cf0851969b 365 T elem[2][2];
AlanHuchin 0:89cf0851969b 366
AlanHuchin 0:89cf0851969b 367 mat2() {}
AlanHuchin 0:89cf0851969b 368
AlanHuchin 0:89cf0851969b 369 explicit mat2(
AlanHuchin 0:89cf0851969b 370 const T m00, const T m01,
AlanHuchin 0:89cf0851969b 371 const T m10, const T m11)
AlanHuchin 0:89cf0851969b 372 {
AlanHuchin 0:89cf0851969b 373 elem[0][0] = m00; elem[0][1] = m01;
AlanHuchin 0:89cf0851969b 374 elem[1][0] = m10; elem[1][1] = m11;
AlanHuchin 0:89cf0851969b 375 }
AlanHuchin 0:89cf0851969b 376
AlanHuchin 0:89cf0851969b 377 explicit mat2(const vec2<T>& v0, const vec2<T>& v1)
AlanHuchin 0:89cf0851969b 378 {
AlanHuchin 0:89cf0851969b 379 elem[0][0] = v0[0];
AlanHuchin 0:89cf0851969b 380 elem[1][0] = v0[1];
AlanHuchin 0:89cf0851969b 381 elem[0][1] = v1[0];
AlanHuchin 0:89cf0851969b 382 elem[1][1] = v1[1];
AlanHuchin 0:89cf0851969b 383 }
AlanHuchin 0:89cf0851969b 384
AlanHuchin 0:89cf0851969b 385 explicit mat2(const mat3<T>& m);
AlanHuchin 0:89cf0851969b 386
AlanHuchin 0:89cf0851969b 387 MATRIX_COMMON(mat2, 2)
AlanHuchin 0:89cf0851969b 388 };
AlanHuchin 0:89cf0851969b 389
AlanHuchin 0:89cf0851969b 390 template <typename T>
AlanHuchin 0:89cf0851969b 391 struct mat3 {
AlanHuchin 0:89cf0851969b 392 T elem[3][3];
AlanHuchin 0:89cf0851969b 393
AlanHuchin 0:89cf0851969b 394 mat3() {}
AlanHuchin 0:89cf0851969b 395
AlanHuchin 0:89cf0851969b 396 explicit mat3(
AlanHuchin 0:89cf0851969b 397 const T m00, const T m01, const T m02,
AlanHuchin 0:89cf0851969b 398 const T m10, const T m11, const T m12,
AlanHuchin 0:89cf0851969b 399 const T m20, const T m21, const T m22)
AlanHuchin 0:89cf0851969b 400 {
AlanHuchin 0:89cf0851969b 401 elem[0][0] = m00; elem[0][1] = m01; elem[0][2] = m02;
AlanHuchin 0:89cf0851969b 402 elem[1][0] = m10; elem[1][1] = m11; elem[1][2] = m12;
AlanHuchin 0:89cf0851969b 403 elem[2][0] = m20; elem[2][1] = m21; elem[2][2] = m22;
AlanHuchin 0:89cf0851969b 404 }
AlanHuchin 0:89cf0851969b 405
AlanHuchin 0:89cf0851969b 406 explicit mat3(const vec3<T>& v0, const vec3<T>& v1, const vec3<T>& v2)
AlanHuchin 0:89cf0851969b 407 {
AlanHuchin 0:89cf0851969b 408 elem[0][0] = v0[0];
AlanHuchin 0:89cf0851969b 409 elem[1][0] = v0[1];
AlanHuchin 0:89cf0851969b 410 elem[2][0] = v0[2];
AlanHuchin 0:89cf0851969b 411 elem[0][1] = v1[0];
AlanHuchin 0:89cf0851969b 412 elem[1][1] = v1[1];
AlanHuchin 0:89cf0851969b 413 elem[2][1] = v1[2];
AlanHuchin 0:89cf0851969b 414 elem[0][2] = v2[0];
AlanHuchin 0:89cf0851969b 415 elem[1][2] = v2[1];
AlanHuchin 0:89cf0851969b 416 elem[2][2] = v2[2];
AlanHuchin 0:89cf0851969b 417 }
AlanHuchin 0:89cf0851969b 418
AlanHuchin 0:89cf0851969b 419 explicit mat3(const mat4<T>& m);
AlanHuchin 0:89cf0851969b 420
AlanHuchin 0:89cf0851969b 421 MATRIX_CONSTRUCTOR_FROM_LOWER(mat3, mat2, 3, 2)
AlanHuchin 0:89cf0851969b 422 MATRIX_COMMON(mat3, 3)
AlanHuchin 0:89cf0851969b 423 };
AlanHuchin 0:89cf0851969b 424
AlanHuchin 0:89cf0851969b 425 template <typename T>
AlanHuchin 0:89cf0851969b 426 struct mat4 {
AlanHuchin 0:89cf0851969b 427 T elem[4][4];
AlanHuchin 0:89cf0851969b 428
AlanHuchin 0:89cf0851969b 429 mat4() {}
AlanHuchin 0:89cf0851969b 430
AlanHuchin 0:89cf0851969b 431 explicit mat4(
AlanHuchin 0:89cf0851969b 432 const T m00, const T m01, const T m02, const T m03,
AlanHuchin 0:89cf0851969b 433 const T m10, const T m11, const T m12, const T m13,
AlanHuchin 0:89cf0851969b 434 const T m20, const T m21, const T m22, const T m23,
AlanHuchin 0:89cf0851969b 435 const T m30, const T m31, const T m32, const T m33)
AlanHuchin 0:89cf0851969b 436 {
AlanHuchin 0:89cf0851969b 437 elem[0][0] = m00; elem[0][1] = m01; elem[0][2] = m02; elem[0][3] = m03;
AlanHuchin 0:89cf0851969b 438 elem[1][0] = m10; elem[1][1] = m11; elem[1][2] = m12; elem[1][3] = m13;
AlanHuchin 0:89cf0851969b 439 elem[2][0] = m20; elem[2][1] = m21; elem[2][2] = m22; elem[2][3] = m23;
AlanHuchin 0:89cf0851969b 440 elem[3][0] = m30; elem[3][1] = m31; elem[3][2] = m32; elem[3][3] = m33;
AlanHuchin 0:89cf0851969b 441 }
AlanHuchin 0:89cf0851969b 442
AlanHuchin 0:89cf0851969b 443 explicit mat4(const vec4<T>& v0, const vec4<T>& v1, const vec4<T>& v2, const vec4<T>& v3)
AlanHuchin 0:89cf0851969b 444 {
AlanHuchin 0:89cf0851969b 445 elem[0][0] = v0[0];
AlanHuchin 0:89cf0851969b 446 elem[1][0] = v0[1];
AlanHuchin 0:89cf0851969b 447 elem[2][0] = v0[2];
AlanHuchin 0:89cf0851969b 448 elem[3][0] = v0[3];
AlanHuchin 0:89cf0851969b 449 elem[0][1] = v1[0];
AlanHuchin 0:89cf0851969b 450 elem[1][1] = v1[1];
AlanHuchin 0:89cf0851969b 451 elem[2][1] = v1[2];
AlanHuchin 0:89cf0851969b 452 elem[3][1] = v1[3];
AlanHuchin 0:89cf0851969b 453 elem[0][2] = v2[0];
AlanHuchin 0:89cf0851969b 454 elem[1][2] = v2[1];
AlanHuchin 0:89cf0851969b 455 elem[2][2] = v2[2];
AlanHuchin 0:89cf0851969b 456 elem[3][2] = v2[3];
AlanHuchin 0:89cf0851969b 457 elem[0][3] = v3[0];
AlanHuchin 0:89cf0851969b 458 elem[1][3] = v3[1];
AlanHuchin 0:89cf0851969b 459 elem[2][3] = v3[2];
AlanHuchin 0:89cf0851969b 460 elem[3][3] = v3[3];
AlanHuchin 0:89cf0851969b 461 }
AlanHuchin 0:89cf0851969b 462
AlanHuchin 0:89cf0851969b 463 MATRIX_CONSTRUCTOR_FROM_LOWER(mat4, mat3, 4, 3)
AlanHuchin 0:89cf0851969b 464 MATRIX_COMMON(mat4, 4)
AlanHuchin 0:89cf0851969b 465 };
AlanHuchin 0:89cf0851969b 466
AlanHuchin 0:89cf0851969b 467 #define MATRIX_CONSTRUCTOR_FROM_HIGHER(CLASS1, CLASS2, SIZE) \
AlanHuchin 0:89cf0851969b 468 template <typename T> \
AlanHuchin 0:89cf0851969b 469 inline CLASS1<T>::CLASS1(const CLASS2<T>& m) \
AlanHuchin 0:89cf0851969b 470 { \
AlanHuchin 0:89cf0851969b 471 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 472 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 473 elem[r][c] = m.elem[r][c]; \
AlanHuchin 0:89cf0851969b 474 }
AlanHuchin 0:89cf0851969b 475
AlanHuchin 0:89cf0851969b 476 MATRIX_CONSTRUCTOR_FROM_HIGHER(mat2, mat3, 2)
AlanHuchin 0:89cf0851969b 477 MATRIX_CONSTRUCTOR_FROM_HIGHER(mat3, mat4, 3)
AlanHuchin 0:89cf0851969b 478
AlanHuchin 0:89cf0851969b 479 #define MAT_FUNC_TEMPLATE(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 480 template <typename T> \
AlanHuchin 0:89cf0851969b 481 inline CLASS transpose(const CLASS & m) \
AlanHuchin 0:89cf0851969b 482 { \
AlanHuchin 0:89cf0851969b 483 CLASS result; \
AlanHuchin 0:89cf0851969b 484 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 485 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 486 result.elem[r][c] = m.elem[c][r]; \
AlanHuchin 0:89cf0851969b 487 return result; \
AlanHuchin 0:89cf0851969b 488 } \
AlanHuchin 0:89cf0851969b 489 template <typename T> \
AlanHuchin 0:89cf0851969b 490 inline CLASS identity ## SIZE() \
AlanHuchin 0:89cf0851969b 491 { \
AlanHuchin 0:89cf0851969b 492 CLASS result; \
AlanHuchin 0:89cf0851969b 493 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 494 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 495 result.elem[r][c] = r == c ? T(1) : T(0); \
AlanHuchin 0:89cf0851969b 496 return result; \
AlanHuchin 0:89cf0851969b 497 } \
AlanHuchin 0:89cf0851969b 498 template <typename T> \
AlanHuchin 0:89cf0851969b 499 inline T trace(const CLASS & m) \
AlanHuchin 0:89cf0851969b 500 { \
AlanHuchin 0:89cf0851969b 501 T result = T(0); \
AlanHuchin 0:89cf0851969b 502 for (int i = 0; i < SIZE; ++i) \
AlanHuchin 0:89cf0851969b 503 result += m.elem[i][i]; \
AlanHuchin 0:89cf0851969b 504 return result; \
AlanHuchin 0:89cf0851969b 505 }
AlanHuchin 0:89cf0851969b 506
AlanHuchin 0:89cf0851969b 507 MAT_FUNC_TEMPLATE(mat2<T>, 2)
AlanHuchin 0:89cf0851969b 508 MAT_FUNC_TEMPLATE(mat3<T>, 3)
AlanHuchin 0:89cf0851969b 509 MAT_FUNC_TEMPLATE(mat4<T>, 4)
AlanHuchin 0:89cf0851969b 510
AlanHuchin 0:89cf0851969b 511 #define MAT_FUNC_MINOR_TEMPLATE(CLASS1, CLASS2, SIZE) \
AlanHuchin 0:89cf0851969b 512 template <typename T> \
AlanHuchin 0:89cf0851969b 513 inline CLASS2 minor(const CLASS1 & m, int _r = SIZE, int _c = SIZE) { \
AlanHuchin 0:89cf0851969b 514 CLASS2 result; \
AlanHuchin 0:89cf0851969b 515 for (int r = 0; r < SIZE - 1; ++r) \
AlanHuchin 0:89cf0851969b 516 for (int c = 0; c < SIZE - 1; ++c) { \
AlanHuchin 0:89cf0851969b 517 int rs = r >= _r ? 1 : 0; \
AlanHuchin 0:89cf0851969b 518 int cs = c >= _c ? 1 : 0; \
AlanHuchin 0:89cf0851969b 519 result.elem[r][c] = m.elem[r + rs][c + cs]; \
AlanHuchin 0:89cf0851969b 520 } \
AlanHuchin 0:89cf0851969b 521 return result; \
AlanHuchin 0:89cf0851969b 522 }
AlanHuchin 0:89cf0851969b 523
AlanHuchin 0:89cf0851969b 524 MAT_FUNC_MINOR_TEMPLATE(mat3<T>, mat2<T>, 3)
AlanHuchin 0:89cf0851969b 525 MAT_FUNC_MINOR_TEMPLATE(mat4<T>, mat3<T>, 4)
AlanHuchin 0:89cf0851969b 526
AlanHuchin 0:89cf0851969b 527 template <typename T>
AlanHuchin 0:89cf0851969b 528 inline T det(const mat2<T>& m)
AlanHuchin 0:89cf0851969b 529 {
AlanHuchin 0:89cf0851969b 530 return dot(
AlanHuchin 0:89cf0851969b 531 vec2<T>(m.elem[0][0], -m.elem[0][1]),
AlanHuchin 0:89cf0851969b 532 vec2<T>(m.elem[1][1], m.elem[1][0]));
AlanHuchin 0:89cf0851969b 533 }
AlanHuchin 0:89cf0851969b 534
AlanHuchin 0:89cf0851969b 535 template <typename T>
AlanHuchin 0:89cf0851969b 536 inline T det(const mat3<T>& m)
AlanHuchin 0:89cf0851969b 537 {
AlanHuchin 0:89cf0851969b 538 return dot(cross(MATRIX_COL3(m, 0), MATRIX_COL3(m, 1)), MATRIX_COL3(m, 2));
AlanHuchin 0:89cf0851969b 539 }
AlanHuchin 0:89cf0851969b 540
AlanHuchin 0:89cf0851969b 541 template <typename T>
AlanHuchin 0:89cf0851969b 542 inline T det(const mat4<T>& m)
AlanHuchin 0:89cf0851969b 543 {
AlanHuchin 0:89cf0851969b 544 vec4<T> b;
AlanHuchin 0:89cf0851969b 545 for (int i = 0; i < 4; ++i)
AlanHuchin 0:89cf0851969b 546 b[i] = (i & 1 ? -1 : 1) * det(minor(m, 0, i));
AlanHuchin 0:89cf0851969b 547 return dot(MATRIX_ROW4(m, 0), b);
AlanHuchin 0:89cf0851969b 548 }
AlanHuchin 0:89cf0851969b 549
AlanHuchin 0:89cf0851969b 550 #define MAT_ADJOINT_TEMPLATE(CLASS, SIZE) \
AlanHuchin 0:89cf0851969b 551 template <typename T> \
AlanHuchin 0:89cf0851969b 552 inline CLASS adjoint(const CLASS & m) \
AlanHuchin 0:89cf0851969b 553 { \
AlanHuchin 0:89cf0851969b 554 CLASS result; \
AlanHuchin 0:89cf0851969b 555 for (int r = 0; r < SIZE; ++r) \
AlanHuchin 0:89cf0851969b 556 for (int c = 0; c < SIZE; ++c) \
AlanHuchin 0:89cf0851969b 557 result.elem[r][c] = ((r + c) & 1 ? -1 : 1) * det(minor(m, c, r)); \
AlanHuchin 0:89cf0851969b 558 return result; \
AlanHuchin 0:89cf0851969b 559 }
AlanHuchin 0:89cf0851969b 560
AlanHuchin 0:89cf0851969b 561 MAT_ADJOINT_TEMPLATE(mat3<T>, 3)
AlanHuchin 0:89cf0851969b 562 MAT_ADJOINT_TEMPLATE(mat4<T>, 4)
AlanHuchin 0:89cf0851969b 563
AlanHuchin 0:89cf0851969b 564 template <typename T>
AlanHuchin 0:89cf0851969b 565 inline mat2<T> adjoint(const mat2<T> & m)
AlanHuchin 0:89cf0851969b 566 {
AlanHuchin 0:89cf0851969b 567 return mat2<T>(
AlanHuchin 0:89cf0851969b 568 m.elem[1][1], -m.elem[0][1],
AlanHuchin 0:89cf0851969b 569 -m.elem[1][0], m.elem[0][0]
AlanHuchin 0:89cf0851969b 570 );
AlanHuchin 0:89cf0851969b 571 }
AlanHuchin 0:89cf0851969b 572
AlanHuchin 0:89cf0851969b 573 #define MAT_INVERSE_TEMPLATE(CLASS) \
AlanHuchin 0:89cf0851969b 574 template <typename T> \
AlanHuchin 0:89cf0851969b 575 inline CLASS inverse(const CLASS & m) \
AlanHuchin 0:89cf0851969b 576 { \
AlanHuchin 0:89cf0851969b 577 return adjoint(m) * inv(det(m)); \
AlanHuchin 0:89cf0851969b 578 }
AlanHuchin 0:89cf0851969b 579
AlanHuchin 0:89cf0851969b 580 MAT_INVERSE_TEMPLATE(mat2<T>)
AlanHuchin 0:89cf0851969b 581 MAT_INVERSE_TEMPLATE(mat3<T>)
AlanHuchin 0:89cf0851969b 582 MAT_INVERSE_TEMPLATE(mat4<T>)
AlanHuchin 0:89cf0851969b 583
AlanHuchin 0:89cf0851969b 584 #define MAT_VEC_FUNCS_TEMPLATE(MATCLASS, VECCLASS, SIZE) \
AlanHuchin 0:89cf0851969b 585 template <typename T> \
AlanHuchin 0:89cf0851969b 586 inline VECCLASS operator * (const MATCLASS & m, const VECCLASS & v) \
AlanHuchin 0:89cf0851969b 587 { \
AlanHuchin 0:89cf0851969b 588 VECCLASS result; \
AlanHuchin 0:89cf0851969b 589 for (int i = 0; i < SIZE; ++i) {\
AlanHuchin 0:89cf0851969b 590 result[i] = dot(MATRIX_ROW ## SIZE(m, i), v); \
AlanHuchin 0:89cf0851969b 591 } \
AlanHuchin 0:89cf0851969b 592 return result; \
AlanHuchin 0:89cf0851969b 593 } \
AlanHuchin 0:89cf0851969b 594 template <typename T> \
AlanHuchin 0:89cf0851969b 595 inline VECCLASS operator * (const VECCLASS & v, const MATCLASS & m) \
AlanHuchin 0:89cf0851969b 596 { \
AlanHuchin 0:89cf0851969b 597 VECCLASS result; \
AlanHuchin 0:89cf0851969b 598 for (int i = 0; i < SIZE; ++i) \
AlanHuchin 0:89cf0851969b 599 result[i] = dot(v, MATRIX_COL ## SIZE(m, i)); \
AlanHuchin 0:89cf0851969b 600 return result; \
AlanHuchin 0:89cf0851969b 601 }
AlanHuchin 0:89cf0851969b 602
AlanHuchin 0:89cf0851969b 603 MAT_VEC_FUNCS_TEMPLATE(mat2<T>, vec2<T>, 2)
AlanHuchin 0:89cf0851969b 604 MAT_VEC_FUNCS_TEMPLATE(mat3<T>, vec3<T>, 3)
AlanHuchin 0:89cf0851969b 605 MAT_VEC_FUNCS_TEMPLATE(mat4<T>, vec4<T>, 4)
AlanHuchin 0:89cf0851969b 606
AlanHuchin 0:89cf0851969b 607 // Returns the inverse of a 4x4 matrix. It is assumed that the matrix passed
AlanHuchin 0:89cf0851969b 608 // as argument describes a rigid-body transformation.
AlanHuchin 0:89cf0851969b 609 template <typename T>
AlanHuchin 0:89cf0851969b 610 inline mat4<T> fast_inverse(const mat4<T>& m)
AlanHuchin 0:89cf0851969b 611 {
AlanHuchin 0:89cf0851969b 612 const vec3<T> t = MATRIX_COL3(m, 3);
AlanHuchin 0:89cf0851969b 613 const T tx = -dot(MATRIX_COL3(m, 0), t);
AlanHuchin 0:89cf0851969b 614 const T ty = -dot(MATRIX_COL3(m, 1), t);
AlanHuchin 0:89cf0851969b 615 const T tz = -dot(MATRIX_COL3(m, 2), t);
AlanHuchin 0:89cf0851969b 616
AlanHuchin 0:89cf0851969b 617 return mat4<T>(
AlanHuchin 0:89cf0851969b 618 m.elem[0][0], m.elem[1][0], m.elem[2][0], tx,
AlanHuchin 0:89cf0851969b 619 m.elem[0][1], m.elem[1][1], m.elem[2][1], ty,
AlanHuchin 0:89cf0851969b 620 m.elem[0][2], m.elem[1][2], m.elem[2][2], tz,
AlanHuchin 0:89cf0851969b 621 T(0), T(0), T(0), T(1)
AlanHuchin 0:89cf0851969b 622 );
AlanHuchin 0:89cf0851969b 623 }
AlanHuchin 0:89cf0851969b 624
AlanHuchin 0:89cf0851969b 625 // Transformations for points and vectors. Potentially faster than a full
AlanHuchin 0:89cf0851969b 626 // matrix * vector multiplication
AlanHuchin 0:89cf0851969b 627
AlanHuchin 0:89cf0851969b 628 #define MAT_TRANFORMS_TEMPLATE(MATCLASS, VECCLASS, VECSIZE) \
AlanHuchin 0:89cf0851969b 629 /* computes vec3<T>(m * vec4<T>(v, 0.0)) */ \
AlanHuchin 0:89cf0851969b 630 template <typename T> \
AlanHuchin 0:89cf0851969b 631 inline VECCLASS transform_vector(const MATCLASS & m, const VECCLASS & v) \
AlanHuchin 0:89cf0851969b 632 { \
AlanHuchin 0:89cf0851969b 633 VECCLASS result; \
AlanHuchin 0:89cf0851969b 634 for (int i = 0; i < VECSIZE; ++i) \
AlanHuchin 0:89cf0851969b 635 result[i] = dot(MATRIX_ROW ## VECSIZE(m, i), v); \
AlanHuchin 0:89cf0851969b 636 return result;\
AlanHuchin 0:89cf0851969b 637 } \
AlanHuchin 0:89cf0851969b 638 /* computes vec3(m * vec4(v, 1.0)) */ \
AlanHuchin 0:89cf0851969b 639 template <typename T> \
AlanHuchin 0:89cf0851969b 640 inline VECCLASS transform_point(const MATCLASS & m, const VECCLASS & v) \
AlanHuchin 0:89cf0851969b 641 { \
AlanHuchin 0:89cf0851969b 642 /*return transform_vector(m, v) + MATRIX_ROW ## VECSIZE(m, VECSIZE); */\
AlanHuchin 0:89cf0851969b 643 VECCLASS result; \
AlanHuchin 0:89cf0851969b 644 for (int i = 0; i < VECSIZE; ++i) \
AlanHuchin 0:89cf0851969b 645 result[i] = dot(MATRIX_ROW ## VECSIZE(m, i), v) + m.elem[i][VECSIZE]; \
AlanHuchin 0:89cf0851969b 646 return result; \
AlanHuchin 0:89cf0851969b 647 } \
AlanHuchin 0:89cf0851969b 648 /* computes VECCLASS(transpose(m) * vec4<T>(v, 0.0)) */ \
AlanHuchin 0:89cf0851969b 649 template <typename T> \
AlanHuchin 0:89cf0851969b 650 inline VECCLASS transform_vector_transpose(const MATCLASS & m, const VECCLASS& v) \
AlanHuchin 0:89cf0851969b 651 { \
AlanHuchin 0:89cf0851969b 652 VECCLASS result; \
AlanHuchin 0:89cf0851969b 653 for (int i = 0; i < VECSIZE; ++i) \
AlanHuchin 0:89cf0851969b 654 result[i] = dot(MATRIX_COL ## VECSIZE(m, i), v); \
AlanHuchin 0:89cf0851969b 655 return result; \
AlanHuchin 0:89cf0851969b 656 } \
AlanHuchin 0:89cf0851969b 657 /* computes VECCLASS(transpose(m) * vec4<T>(v, 1.0)) */ \
AlanHuchin 0:89cf0851969b 658 template <typename T> \
AlanHuchin 0:89cf0851969b 659 inline VECCLASS transform_point_transpose(const MATCLASS & m, const VECCLASS& v) \
AlanHuchin 0:89cf0851969b 660 { \
AlanHuchin 0:89cf0851969b 661 /*return transform_vector_transpose(m, v) + MATRIX_COL ## VECSIZE(m, VECSIZE); */\
AlanHuchin 0:89cf0851969b 662 VECCLASS result; \
AlanHuchin 0:89cf0851969b 663 for (int i = 0; i < VECSIZE; ++i) \
AlanHuchin 0:89cf0851969b 664 result[i] = dot(MATRIX_COL ## VECSIZE(m, i), v) + m.elem[VECSIZE][i]; \
AlanHuchin 0:89cf0851969b 665 return result; \
AlanHuchin 0:89cf0851969b 666 }
AlanHuchin 0:89cf0851969b 667
AlanHuchin 0:89cf0851969b 668 MAT_TRANFORMS_TEMPLATE(mat4<T>, vec3<T>, 3)
AlanHuchin 0:89cf0851969b 669 MAT_TRANFORMS_TEMPLATE(mat3<T>, vec2<T>, 2)
AlanHuchin 0:89cf0851969b 670
AlanHuchin 0:89cf0851969b 671 #define MAT_OUTERPRODUCT_TEMPLATE(MATCLASS, VECCLASS, MATSIZE) \
AlanHuchin 0:89cf0851969b 672 template <typename T> \
AlanHuchin 0:89cf0851969b 673 inline MATCLASS outer_product(const VECCLASS & v1, const VECCLASS & v2) \
AlanHuchin 0:89cf0851969b 674 { \
AlanHuchin 0:89cf0851969b 675 MATCLASS r; \
AlanHuchin 0:89cf0851969b 676 for ( int j = 0; j < MATSIZE; ++j ) \
AlanHuchin 0:89cf0851969b 677 for ( int k = 0; k < MATSIZE; ++k ) \
AlanHuchin 0:89cf0851969b 678 r.elem[j][k] = v1[j] * v2[k]; \
AlanHuchin 0:89cf0851969b 679 return r; \
AlanHuchin 0:89cf0851969b 680 }
AlanHuchin 0:89cf0851969b 681
AlanHuchin 0:89cf0851969b 682 MAT_OUTERPRODUCT_TEMPLATE(mat4<T>, vec4<T>, 4)
AlanHuchin 0:89cf0851969b 683 MAT_OUTERPRODUCT_TEMPLATE(mat3<T>, vec3<T>, 3)
AlanHuchin 0:89cf0851969b 684 MAT_OUTERPRODUCT_TEMPLATE(mat2<T>, vec2<T>, 2)
AlanHuchin 0:89cf0851969b 685
AlanHuchin 0:89cf0851969b 686 template <typename T>
AlanHuchin 0:89cf0851969b 687 inline mat4<T> translation_matrix(const T x, const T y, const T z)
AlanHuchin 0:89cf0851969b 688 {
AlanHuchin 0:89cf0851969b 689 mat4<T> r(T(1));
AlanHuchin 0:89cf0851969b 690 r.elem[0][3] = x;
AlanHuchin 0:89cf0851969b 691 r.elem[1][3] = y;
AlanHuchin 0:89cf0851969b 692 r.elem[2][3] = z;
AlanHuchin 0:89cf0851969b 693 return r;
AlanHuchin 0:89cf0851969b 694 }
AlanHuchin 0:89cf0851969b 695
AlanHuchin 0:89cf0851969b 696 template <typename T>
AlanHuchin 0:89cf0851969b 697 inline mat4<T> translation_matrix(const vec3<T>& v)
AlanHuchin 0:89cf0851969b 698 {
AlanHuchin 0:89cf0851969b 699 return translation_matrix(v.x, v.y, v.z);
AlanHuchin 0:89cf0851969b 700 }
AlanHuchin 0:89cf0851969b 701
AlanHuchin 0:89cf0851969b 702 template <typename T>
AlanHuchin 0:89cf0851969b 703 inline mat4<T> scaling_matrix(const T x, const T y, const T z)
AlanHuchin 0:89cf0851969b 704 {
AlanHuchin 0:89cf0851969b 705 mat4<T> r(T(0));
AlanHuchin 0:89cf0851969b 706 r.elem[0][0] = x;
AlanHuchin 0:89cf0851969b 707 r.elem[1][1] = y;
AlanHuchin 0:89cf0851969b 708 r.elem[2][2] = z;
AlanHuchin 0:89cf0851969b 709 r.elem[3][3] = T(1);
AlanHuchin 0:89cf0851969b 710 return r;
AlanHuchin 0:89cf0851969b 711 }
AlanHuchin 0:89cf0851969b 712
AlanHuchin 0:89cf0851969b 713 template <typename T>
AlanHuchin 0:89cf0851969b 714 inline mat4<T> scaling_matrix(const vec3<T>& v)
AlanHuchin 0:89cf0851969b 715 {
AlanHuchin 0:89cf0851969b 716 return scaling_matrix(v.x, v.y, v.z);
AlanHuchin 0:89cf0851969b 717 }
AlanHuchin 0:89cf0851969b 718
AlanHuchin 0:89cf0851969b 719 template <typename T>
AlanHuchin 0:89cf0851969b 720 inline mat4<T> rotation_matrix(const T angle, const vec3<T>& v)
AlanHuchin 0:89cf0851969b 721 {
AlanHuchin 0:89cf0851969b 722 const T a = angle * T(M_PI/180) ;
AlanHuchin 0:89cf0851969b 723 const vec3<T> u = normalize(v);
AlanHuchin 0:89cf0851969b 724
AlanHuchin 0:89cf0851969b 725 const mat3<T> S(
AlanHuchin 0:89cf0851969b 726 T(0), -u[2], u[1],
AlanHuchin 0:89cf0851969b 727 u[2], T(0), -u[0],
AlanHuchin 0:89cf0851969b 728 -u[1], u[0], T(0)
AlanHuchin 0:89cf0851969b 729 );
AlanHuchin 0:89cf0851969b 730
AlanHuchin 0:89cf0851969b 731 const mat3<T> uut = outer_product(u, u);
AlanHuchin 0:89cf0851969b 732 const mat3<T> R = uut + T(cos(a)) * (identity3<T>() - uut) + T(sin(a)) * S;
AlanHuchin 0:89cf0851969b 733
AlanHuchin 0:89cf0851969b 734 return mat4<T>(R);
AlanHuchin 0:89cf0851969b 735 }
AlanHuchin 0:89cf0851969b 736
AlanHuchin 0:89cf0851969b 737
AlanHuchin 0:89cf0851969b 738 template <typename T>
AlanHuchin 0:89cf0851969b 739 inline mat4<T> rotation_matrix(const T angle, const T x, const T y, const T z)
AlanHuchin 0:89cf0851969b 740 {
AlanHuchin 0:89cf0851969b 741 return rotation_matrix(angle, vec3<T>(x, y, z));
AlanHuchin 0:89cf0851969b 742 }
AlanHuchin 0:89cf0851969b 743
AlanHuchin 0:89cf0851969b 744 // Constructs a shear-matrix that shears component i by factor with
AlanHuchin 0:89cf0851969b 745 // Respect to component j.
AlanHuchin 0:89cf0851969b 746 template <typename T>
AlanHuchin 0:89cf0851969b 747 inline mat4<T> shear_matrix(const int i, const int j, const T factor)
AlanHuchin 0:89cf0851969b 748 {
AlanHuchin 0:89cf0851969b 749 mat4<T> m = identity4<T>();
AlanHuchin 0:89cf0851969b 750 m.elem[i][j] = factor;
AlanHuchin 0:89cf0851969b 751 return m;
AlanHuchin 0:89cf0851969b 752 }
AlanHuchin 0:89cf0851969b 753
AlanHuchin 0:89cf0851969b 754 template <typename T>
AlanHuchin 0:89cf0851969b 755 inline mat4<T> euler(const T head, const T pitch, const T roll)
AlanHuchin 0:89cf0851969b 756 {
AlanHuchin 0:89cf0851969b 757 return rotation_matrix(roll, T(0), T(0), T(1)) *
AlanHuchin 0:89cf0851969b 758 rotation_matrix(pitch, T(1), T(0), T(0)) *
AlanHuchin 0:89cf0851969b 759 rotation_matrix(head, T(0), T(1), T(0));
AlanHuchin 0:89cf0851969b 760 }
AlanHuchin 0:89cf0851969b 761
AlanHuchin 0:89cf0851969b 762 template <typename T>
AlanHuchin 0:89cf0851969b 763 inline mat4<T> frustum_matrix(const T l, const T r, const T b, const T t, const T n, const T f)
AlanHuchin 0:89cf0851969b 764 {
AlanHuchin 0:89cf0851969b 765 return mat4<T>(
AlanHuchin 0:89cf0851969b 766 (2 * n)/(r - l), T(0), (r + l)/(r - l), T(0),
AlanHuchin 0:89cf0851969b 767 T(0), (2 * n)/(t - b), (t + b)/(t - b), T(0),
AlanHuchin 0:89cf0851969b 768 T(0), T(0), -(f + n)/(f - n), -(2 * f * n)/(f - n),
AlanHuchin 0:89cf0851969b 769 T(0), T(0), -T(1), T(0)
AlanHuchin 0:89cf0851969b 770 );
AlanHuchin 0:89cf0851969b 771 }
AlanHuchin 0:89cf0851969b 772
AlanHuchin 0:89cf0851969b 773 template <typename T>
AlanHuchin 0:89cf0851969b 774 inline mat4<T> perspective_matrix(const T fovy, const T aspect, const T zNear, const T zFar)
AlanHuchin 0:89cf0851969b 775 {
AlanHuchin 0:89cf0851969b 776 const T dz = zFar - zNear;
AlanHuchin 0:89cf0851969b 777 const T rad = fovy / T(2) * T(M_PI/180);
AlanHuchin 0:89cf0851969b 778 const T s = sin(rad);
AlanHuchin 0:89cf0851969b 779
AlanHuchin 0:89cf0851969b 780 if ( ( dz == T(0) ) || ( s == T(0) ) || ( aspect == T(0) ) ) {
AlanHuchin 0:89cf0851969b 781 return identity4<T>();
AlanHuchin 0:89cf0851969b 782 }
AlanHuchin 0:89cf0851969b 783
AlanHuchin 0:89cf0851969b 784 const T cot = cos(rad) / s;
AlanHuchin 0:89cf0851969b 785
AlanHuchin 0:89cf0851969b 786 mat4<T> m = identity4<T>();
AlanHuchin 0:89cf0851969b 787 m[0] = cot / aspect;
AlanHuchin 0:89cf0851969b 788 m[5] = cot;
AlanHuchin 0:89cf0851969b 789 m[10] = -(zFar + zNear) / dz;
AlanHuchin 0:89cf0851969b 790 m[14] = T(-1);
AlanHuchin 0:89cf0851969b 791 m[11] = -2 * zNear * zFar / dz;
AlanHuchin 0:89cf0851969b 792 m[15] = T(0);
AlanHuchin 0:89cf0851969b 793
AlanHuchin 0:89cf0851969b 794 return m;
AlanHuchin 0:89cf0851969b 795 }
AlanHuchin 0:89cf0851969b 796
AlanHuchin 0:89cf0851969b 797 template <typename T>
AlanHuchin 0:89cf0851969b 798 inline mat4<T> ortho_matrix(const T l, const T r, const T b, const T t, const T n, const T f)
AlanHuchin 0:89cf0851969b 799 {
AlanHuchin 0:89cf0851969b 800 return mat4<T>(
AlanHuchin 0:89cf0851969b 801 T(2)/(r - l), T(0), T(0), -(r + l)/(r - l),
AlanHuchin 0:89cf0851969b 802 T(0), T(2)/(t - b), T(0), -(t + b)/(t - b),
AlanHuchin 0:89cf0851969b 803 T(0), T(0), -T(2)/(f - n), -(f + n)/(f - n),
AlanHuchin 0:89cf0851969b 804 T(0), T(0), T(0), T(1)
AlanHuchin 0:89cf0851969b 805 );
AlanHuchin 0:89cf0851969b 806 }
AlanHuchin 0:89cf0851969b 807
AlanHuchin 0:89cf0851969b 808 template <typename T>
AlanHuchin 0:89cf0851969b 809 inline mat4<T> lookat_matrix(const vec3<T>& eye, const vec3<T>& center, const vec3<T>& up) {
AlanHuchin 0:89cf0851969b 810 const vec3<T> forward = normalize(center - eye);
AlanHuchin 0:89cf0851969b 811 const vec3<T> side = normalize(cross(forward, up));
AlanHuchin 0:89cf0851969b 812
AlanHuchin 0:89cf0851969b 813 const vec3<T> up2 = cross(side, forward);
AlanHuchin 0:89cf0851969b 814
AlanHuchin 0:89cf0851969b 815 mat4<T> m = identity4<T>();
AlanHuchin 0:89cf0851969b 816
AlanHuchin 0:89cf0851969b 817 m.elem[0][0] = side[0];
AlanHuchin 0:89cf0851969b 818 m.elem[0][1] = side[1];
AlanHuchin 0:89cf0851969b 819 m.elem[0][2] = side[2];
AlanHuchin 0:89cf0851969b 820
AlanHuchin 0:89cf0851969b 821 m.elem[1][0] = up2[0];
AlanHuchin 0:89cf0851969b 822 m.elem[1][1] = up2[1];
AlanHuchin 0:89cf0851969b 823 m.elem[1][2] = up2[2];
AlanHuchin 0:89cf0851969b 824
AlanHuchin 0:89cf0851969b 825 m.elem[2][0] = -forward[0];
AlanHuchin 0:89cf0851969b 826 m.elem[2][1] = -forward[1];
AlanHuchin 0:89cf0851969b 827 m.elem[2][2] = -forward[2];
AlanHuchin 0:89cf0851969b 828
AlanHuchin 0:89cf0851969b 829 return m * translation_matrix(-eye);
AlanHuchin 0:89cf0851969b 830 }
AlanHuchin 0:89cf0851969b 831
AlanHuchin 0:89cf0851969b 832 template <typename T>
AlanHuchin 0:89cf0851969b 833 inline mat4<T> picking_matrix(const T x, const T y, const T dx, const T dy, int viewport[4]) {
AlanHuchin 0:89cf0851969b 834 if (dx <= 0 || dy <= 0) {
AlanHuchin 0:89cf0851969b 835 return identity4<T>();
AlanHuchin 0:89cf0851969b 836 }
AlanHuchin 0:89cf0851969b 837
AlanHuchin 0:89cf0851969b 838 mat4<T> r = translation_matrix((viewport[2] - 2 * (x - viewport[0])) / dx,
AlanHuchin 0:89cf0851969b 839 (viewport[3] - 2 * (y - viewport[1])) / dy, 0);
AlanHuchin 0:89cf0851969b 840 r *= scaling_matrix(viewport[2] / dx, viewport[2] / dy, 1);
AlanHuchin 0:89cf0851969b 841 return r;
AlanHuchin 0:89cf0851969b 842 }
AlanHuchin 0:89cf0851969b 843
AlanHuchin 0:89cf0851969b 844 // Constructs a shadow matrix. q is the light source and p is the plane.
AlanHuchin 0:89cf0851969b 845 template <typename T> inline mat4<T> shadow_matrix(const vec4<T>& q, const vec4<T>& p) {
AlanHuchin 0:89cf0851969b 846 mat4<T> m;
AlanHuchin 0:89cf0851969b 847
AlanHuchin 0:89cf0851969b 848 m.elem[0][0] = p.y * q[1] + p.z * q[2] + p.w * q[3];
AlanHuchin 0:89cf0851969b 849 m.elem[0][1] = -p.y * q[0];
AlanHuchin 0:89cf0851969b 850 m.elem[0][2] = -p.z * q[0];
AlanHuchin 0:89cf0851969b 851 m.elem[0][3] = -p.w * q[0];
AlanHuchin 0:89cf0851969b 852
AlanHuchin 0:89cf0851969b 853 m.elem[1][0] = -p.x * q[1];
AlanHuchin 0:89cf0851969b 854 m.elem[1][1] = p.x * q[0] + p.z * q[2] + p.w * q[3];
AlanHuchin 0:89cf0851969b 855 m.elem[1][2] = -p.z * q[1];
AlanHuchin 0:89cf0851969b 856 m.elem[1][3] = -p.w * q[1];
AlanHuchin 0:89cf0851969b 857
AlanHuchin 0:89cf0851969b 858
AlanHuchin 0:89cf0851969b 859 m.elem[2][0] = -p.x * q[2];
AlanHuchin 0:89cf0851969b 860 m.elem[2][1] = -p.y * q[2];
AlanHuchin 0:89cf0851969b 861 m.elem[2][2] = p.x * q[0] + p.y * q[1] + p.w * q[3];
AlanHuchin 0:89cf0851969b 862 m.elem[2][3] = -p.w * q[2];
AlanHuchin 0:89cf0851969b 863
AlanHuchin 0:89cf0851969b 864 m.elem[3][1] = -p.x * q[3];
AlanHuchin 0:89cf0851969b 865 m.elem[3][2] = -p.y * q[3];
AlanHuchin 0:89cf0851969b 866 m.elem[3][3] = -p.z * q[3];
AlanHuchin 0:89cf0851969b 867 m.elem[3][0] = p.x * q[0] + p.y * q[1] + p.z * q[2];
AlanHuchin 0:89cf0851969b 868
AlanHuchin 0:89cf0851969b 869 return m;
AlanHuchin 0:89cf0851969b 870 }
AlanHuchin 0:89cf0851969b 871
AlanHuchin 0:89cf0851969b 872 // Quaternion class
AlanHuchin 0:89cf0851969b 873 template <typename T>
AlanHuchin 0:89cf0851969b 874 struct quat {
AlanHuchin 0:89cf0851969b 875 vec3<T> v;
AlanHuchin 0:89cf0851969b 876 T w;
AlanHuchin 0:89cf0851969b 877
AlanHuchin 0:89cf0851969b 878 quat() {}
AlanHuchin 0:89cf0851969b 879 quat(const vec3<T>& iv, const T iw) : v(iv), w(iw) {}
AlanHuchin 0:89cf0851969b 880 quat(const T vx, const T vy, const T vz, const T iw) : v(vx, vy, vz), w(iw) {}
AlanHuchin 0:89cf0851969b 881 quat(const vec4<T>& i) : v(i.x, i.y, i.z), w(i.w) {}
AlanHuchin 0:89cf0851969b 882
AlanHuchin 0:89cf0851969b 883 operator const T* () const { return &(v[0]); }
AlanHuchin 0:89cf0851969b 884 operator T* () { return &(v[0]); }
AlanHuchin 0:89cf0851969b 885
AlanHuchin 0:89cf0851969b 886 quat& operator += (const quat& q) { v += q.v; w += q.w; return *this; }
AlanHuchin 0:89cf0851969b 887 quat& operator -= (const quat& q) { v -= q.v; w -= q.w; return *this; }
AlanHuchin 0:89cf0851969b 888
AlanHuchin 0:89cf0851969b 889 quat& operator *= (const T& s) { v *= s; w *= s; return *this; }
AlanHuchin 0:89cf0851969b 890 quat& operator /= (const T& s) { v /= s; w /= s; return *this; }
AlanHuchin 0:89cf0851969b 891
AlanHuchin 0:89cf0851969b 892 quat& operator *= (const quat& r)
AlanHuchin 0:89cf0851969b 893 {
AlanHuchin 0:89cf0851969b 894 //q1 x q2 = [s1,v1] x [s2,v2] = [(s1*s2 - v1*v2),(s1*v2 + s2*v1 + v1xv2)].
AlanHuchin 0:89cf0851969b 895 quat q;
AlanHuchin 0:89cf0851969b 896 q.v = cross(v, r.v) + r.w * v + w * r.v;
AlanHuchin 0:89cf0851969b 897 q.w = w * r.w - dot(v, r.v);
AlanHuchin 0:89cf0851969b 898 return *this = q;
AlanHuchin 0:89cf0851969b 899 }
AlanHuchin 0:89cf0851969b 900
AlanHuchin 0:89cf0851969b 901 quat& operator /= (const quat& q) { return (*this) *= inverse(q); }
AlanHuchin 0:89cf0851969b 902 };
AlanHuchin 0:89cf0851969b 903
AlanHuchin 0:89cf0851969b 904 // Quaternion functions
AlanHuchin 0:89cf0851969b 905
AlanHuchin 0:89cf0851969b 906 template <typename T>
AlanHuchin 0:89cf0851969b 907 inline quat<T> identityq()
AlanHuchin 0:89cf0851969b 908 {
AlanHuchin 0:89cf0851969b 909 return quat<T>(T(0), T(0), T(0), T(1));
AlanHuchin 0:89cf0851969b 910 }
AlanHuchin 0:89cf0851969b 911
AlanHuchin 0:89cf0851969b 912 template <typename T>
AlanHuchin 0:89cf0851969b 913 inline quat<T> conjugate(const quat<T>& q)
AlanHuchin 0:89cf0851969b 914 {
AlanHuchin 0:89cf0851969b 915 return quat<T>(-q.v, q.w);
AlanHuchin 0:89cf0851969b 916 }
AlanHuchin 0:89cf0851969b 917
AlanHuchin 0:89cf0851969b 918 template <typename T>
AlanHuchin 0:89cf0851969b 919 inline quat<T> inverse(const quat<T>& q)
AlanHuchin 0:89cf0851969b 920 {
AlanHuchin 0:89cf0851969b 921 const T l = dot(q, q);
AlanHuchin 0:89cf0851969b 922 if ( l > T(0) ) return conjugate(q) * inv(l);
AlanHuchin 0:89cf0851969b 923 else return identityq<T>();
AlanHuchin 0:89cf0851969b 924 }
AlanHuchin 0:89cf0851969b 925
AlanHuchin 0:89cf0851969b 926 // quaternion utility functions
AlanHuchin 0:89cf0851969b 927
AlanHuchin 0:89cf0851969b 928 // the input quaternion is assumed to be normalized
AlanHuchin 0:89cf0851969b 929 template <typename T>
AlanHuchin 0:89cf0851969b 930 inline mat3<T> quat_to_mat3(const quat<T>& q)
AlanHuchin 0:89cf0851969b 931 {
AlanHuchin 0:89cf0851969b 932 // const quat<T> q = normalize(qq);
AlanHuchin 0:89cf0851969b 933
AlanHuchin 0:89cf0851969b 934 const T xx = q[0] * q[0];
AlanHuchin 0:89cf0851969b 935 const T xy = q[0] * q[1];
AlanHuchin 0:89cf0851969b 936 const T xz = q[0] * q[2];
AlanHuchin 0:89cf0851969b 937 const T xw = q[0] * q[3];
AlanHuchin 0:89cf0851969b 938
AlanHuchin 0:89cf0851969b 939 const T yy = q[1] * q[1];
AlanHuchin 0:89cf0851969b 940 const T yz = q[1] * q[2];
AlanHuchin 0:89cf0851969b 941 const T yw = q[1] * q[3];
AlanHuchin 0:89cf0851969b 942
AlanHuchin 0:89cf0851969b 943 const T zz = q[2] * q[2];
AlanHuchin 0:89cf0851969b 944 const T zw = q[2] * q[3];
AlanHuchin 0:89cf0851969b 945
AlanHuchin 0:89cf0851969b 946 return mat3<T>(
AlanHuchin 0:89cf0851969b 947 1 - 2*(yy + zz), 2*(xy - zw), 2*(xz + yw),
AlanHuchin 0:89cf0851969b 948 2*(xy + zw), 1 - 2*(xx + zz), 2*(yz - xw),
AlanHuchin 0:89cf0851969b 949 2*(xz - yw), 2*(yz + xw), 1 - 2*(xx + yy)
AlanHuchin 0:89cf0851969b 950 );
AlanHuchin 0:89cf0851969b 951 }
AlanHuchin 0:89cf0851969b 952
AlanHuchin 0:89cf0851969b 953 // the input quat<T>ernion is assumed to be normalized
AlanHuchin 0:89cf0851969b 954 template <typename T>
AlanHuchin 0:89cf0851969b 955 inline mat4<T> quat_to_mat4(const quat<T>& q)
AlanHuchin 0:89cf0851969b 956 {
AlanHuchin 0:89cf0851969b 957 // const quat<T> q = normalize(qq);
AlanHuchin 0:89cf0851969b 958
AlanHuchin 0:89cf0851969b 959 return mat4<T>(quat_to_mat3(q));
AlanHuchin 0:89cf0851969b 960 }
AlanHuchin 0:89cf0851969b 961
AlanHuchin 0:89cf0851969b 962 template <typename T>
AlanHuchin 0:89cf0851969b 963 inline quat<T> mat_to_quat(const mat4<T>& m)
AlanHuchin 0:89cf0851969b 964 {
AlanHuchin 0:89cf0851969b 965 const T t = m.elem[0][0] + m.elem[1][1] + m.elem[2][2] + T(1);
AlanHuchin 0:89cf0851969b 966 quat<T> q;
AlanHuchin 0:89cf0851969b 967
AlanHuchin 0:89cf0851969b 968 if ( t > 0 ) {
AlanHuchin 0:89cf0851969b 969 const T s = T(0.5) / sqrt(t);
AlanHuchin 0:89cf0851969b 970 q[3] = T(0.25) * inv(s);
AlanHuchin 0:89cf0851969b 971 q[0] = (m.elem[2][1] - m.elem[1][2]) * s;
AlanHuchin 0:89cf0851969b 972 q[1] = (m.elem[0][2] - m.elem[2][0]) * s;
AlanHuchin 0:89cf0851969b 973 q[2] = (m.elem[1][0] - m.elem[0][1]) * s;
AlanHuchin 0:89cf0851969b 974 } else {
AlanHuchin 0:89cf0851969b 975 if ( m.elem[0][0] > m.elem[1][1] && m.elem[0][0] > m.elem[2][2] ) {
AlanHuchin 0:89cf0851969b 976 const T s = T(2) * sqrt( T(1) + m.elem[0][0] - m.elem[1][1] - m.elem[2][2]);
AlanHuchin 0:89cf0851969b 977 const T invs = inv(s);
AlanHuchin 0:89cf0851969b 978 q[0] = T(0.25) * s;
AlanHuchin 0:89cf0851969b 979 q[1] = (m.elem[0][1] + m.elem[1][0] ) * invs;
AlanHuchin 0:89cf0851969b 980 q[2] = (m.elem[0][2] + m.elem[2][0] ) * invs;
AlanHuchin 0:89cf0851969b 981 q[3] = (m.elem[1][2] - m.elem[2][1] ) * invs;
AlanHuchin 0:89cf0851969b 982 } else if (m.elem[1][1] > m.elem[2][2]) {
AlanHuchin 0:89cf0851969b 983 const T s = T(2) * sqrt( T(1) + m.elem[1][1] - m.elem[0][0] - m.elem[2][2]);
AlanHuchin 0:89cf0851969b 984 const T invs = inv(s);
AlanHuchin 0:89cf0851969b 985 q[0] = (m.elem[0][1] + m.elem[1][0] ) * invs;
AlanHuchin 0:89cf0851969b 986 q[1] = T(0.25) * s;
AlanHuchin 0:89cf0851969b 987 q[2] = (m.elem[1][2] + m.elem[2][1] ) * invs;
AlanHuchin 0:89cf0851969b 988 q[3] = (m.elem[0][2] - m.elem[2][0] ) * invs;
AlanHuchin 0:89cf0851969b 989 } else {
AlanHuchin 0:89cf0851969b 990 const T s = T(2) * sqrt( T(1) + m.elem[2][2] - m.elem[0][0] - m.elem[1][1] );
AlanHuchin 0:89cf0851969b 991 const T invs = inv(s);
AlanHuchin 0:89cf0851969b 992 q[0] = (m.elem[0][2] + m.elem[2][0] ) * invs;
AlanHuchin 0:89cf0851969b 993 q[1] = (m.elem[1][2] + m.elem[2][1] ) * invs;
AlanHuchin 0:89cf0851969b 994 q[2] = T(0.25) * s;
AlanHuchin 0:89cf0851969b 995 q[3] = (m.elem[0][1] - m.elem[1][0] ) * invs;
AlanHuchin 0:89cf0851969b 996 }
AlanHuchin 0:89cf0851969b 997 }
AlanHuchin 0:89cf0851969b 998
AlanHuchin 0:89cf0851969b 999 return q;
AlanHuchin 0:89cf0851969b 1000 }
AlanHuchin 0:89cf0851969b 1001
AlanHuchin 0:89cf0851969b 1002 template <typename T>
AlanHuchin 0:89cf0851969b 1003 inline quat<T> mat_to_quat(const mat3<T>& m)
AlanHuchin 0:89cf0851969b 1004 {
AlanHuchin 0:89cf0851969b 1005 return mat_to_quat(mat4<T>(m));
AlanHuchin 0:89cf0851969b 1006 }
AlanHuchin 0:89cf0851969b 1007
AlanHuchin 0:89cf0851969b 1008 // the angle is in radians
AlanHuchin 0:89cf0851969b 1009 template <typename T>
AlanHuchin 0:89cf0851969b 1010 inline quat<T> quat_from_axis_angle(const vec3<T>& axis, const T a)
AlanHuchin 0:89cf0851969b 1011 {
AlanHuchin 0:89cf0851969b 1012 quat<T> r;
AlanHuchin 0:89cf0851969b 1013 const T inv2 = inv(T(2));
AlanHuchin 0:89cf0851969b 1014 r.v = sin(a * inv2) * normalize(axis);
AlanHuchin 0:89cf0851969b 1015 r.w = cos(a * inv2);
AlanHuchin 0:89cf0851969b 1016
AlanHuchin 0:89cf0851969b 1017 return r;
AlanHuchin 0:89cf0851969b 1018 }
AlanHuchin 0:89cf0851969b 1019
AlanHuchin 0:89cf0851969b 1020 // the angle is in radians
AlanHuchin 0:89cf0851969b 1021 template <typename T>
AlanHuchin 0:89cf0851969b 1022 inline quat<T> quat_from_axis_angle(const T x, const T y, const T z, const T angle)
AlanHuchin 0:89cf0851969b 1023 {
AlanHuchin 0:89cf0851969b 1024 return quat_from_axis_angle<T>(vec3<T>(x, y, z), angle);
AlanHuchin 0:89cf0851969b 1025 }
AlanHuchin 0:89cf0851969b 1026
AlanHuchin 0:89cf0851969b 1027 // the angle is stored in radians
AlanHuchin 0:89cf0851969b 1028 template <typename T>
AlanHuchin 0:89cf0851969b 1029 inline void quat_to_axis_angle(const quat<T>& qq, vec3<T>* axis, T *angle)
AlanHuchin 0:89cf0851969b 1030 {
AlanHuchin 0:89cf0851969b 1031 quat<T> q = normalize(qq);
AlanHuchin 0:89cf0851969b 1032
AlanHuchin 0:89cf0851969b 1033 *angle = 2 * acos(q.w);
AlanHuchin 0:89cf0851969b 1034
AlanHuchin 0:89cf0851969b 1035 const T s = sin((*angle) * inv(T(2)));
AlanHuchin 0:89cf0851969b 1036 if ( s != T(0) )
AlanHuchin 0:89cf0851969b 1037 *axis = q.v * inv(s);
AlanHuchin 0:89cf0851969b 1038 else
AlanHuchin 0:89cf0851969b 1039 * axis = vec3<T>(T(0), T(0), T(0));
AlanHuchin 0:89cf0851969b 1040 }
AlanHuchin 0:89cf0851969b 1041
AlanHuchin 0:89cf0851969b 1042 // Spherical linear interpolation
AlanHuchin 0:89cf0851969b 1043 template <typename T>
AlanHuchin 0:89cf0851969b 1044 inline quat<T> slerp(const quat<T>& qq1, const quat<T>& qq2, const T t)
AlanHuchin 0:89cf0851969b 1045 {
AlanHuchin 0:89cf0851969b 1046 // slerp(q1,q2) = sin((1-t)*a)/sin(a) * q1 + sin(t*a)/sin(a) * q2
AlanHuchin 0:89cf0851969b 1047 const quat<T> q1 = normalize(qq1);
AlanHuchin 0:89cf0851969b 1048 const quat<T> q2 = normalize(qq2);
AlanHuchin 0:89cf0851969b 1049
AlanHuchin 0:89cf0851969b 1050 const T a = acos(dot(q1, q2));
AlanHuchin 0:89cf0851969b 1051 const T s = sin(a);
AlanHuchin 0:89cf0851969b 1052
AlanHuchin 0:89cf0851969b 1053 #define EPS T(1e-5)
AlanHuchin 0:89cf0851969b 1054
AlanHuchin 0:89cf0851969b 1055 if ( !(-EPS <= s && s <= EPS) ) {
AlanHuchin 0:89cf0851969b 1056 return sin((T(1)-t)*a)/s * q1 + sin(t*a)/s * q2;
AlanHuchin 0:89cf0851969b 1057 } else {
AlanHuchin 0:89cf0851969b 1058 // if the angle is to small use a linear interpolation
AlanHuchin 0:89cf0851969b 1059 return lerp(q1, q2, t);
AlanHuchin 0:89cf0851969b 1060 }
AlanHuchin 0:89cf0851969b 1061
AlanHuchin 0:89cf0851969b 1062 #undef EPS
AlanHuchin 0:89cf0851969b 1063 }
AlanHuchin 0:89cf0851969b 1064
AlanHuchin 0:89cf0851969b 1065 // Sperical quadtratic interpolation using a smooth cubic spline
AlanHuchin 0:89cf0851969b 1066 // The parameters a and b are the control points.
AlanHuchin 0:89cf0851969b 1067 template <typename T>
AlanHuchin 0:89cf0851969b 1068 inline quat<T> squad(
AlanHuchin 0:89cf0851969b 1069 const quat<T>& q0,
AlanHuchin 0:89cf0851969b 1070 const quat<T>& a,
AlanHuchin 0:89cf0851969b 1071 const quat<T>& b,
AlanHuchin 0:89cf0851969b 1072 const quat<T>& q1,
AlanHuchin 0:89cf0851969b 1073 const T t)
AlanHuchin 0:89cf0851969b 1074 {
AlanHuchin 0:89cf0851969b 1075 return slerp(slerp(q0, q1, t),slerp(a, b, t), 2 * t * (1 - t));
AlanHuchin 0:89cf0851969b 1076 }
AlanHuchin 0:89cf0851969b 1077
AlanHuchin 0:89cf0851969b 1078 #undef MOP_M_CLASS_TEMPLATE
AlanHuchin 0:89cf0851969b 1079 #undef MOP_M_TYPE_TEMPLATE
AlanHuchin 0:89cf0851969b 1080 #undef MOP_COMP_TEMPLATE
AlanHuchin 0:89cf0851969b 1081 #undef MOP_G_UMINUS_TEMPLATE
AlanHuchin 0:89cf0851969b 1082 #undef COMMON_OPERATORS
AlanHuchin 0:89cf0851969b 1083 #undef VECTOR_COMMON
AlanHuchin 0:89cf0851969b 1084 #undef FOP_G_SOURCE_TEMPLATE
AlanHuchin 0:89cf0851969b 1085 #undef FOP_G_CLASS_TEMPLATE
AlanHuchin 0:89cf0851969b 1086 #undef FOP_G_TYPE_TEMPLATE
AlanHuchin 0:89cf0851969b 1087 #undef VEC_QUAT_FUNC_TEMPLATE
AlanHuchin 0:89cf0851969b 1088 #undef VEC_FUNC_TEMPLATE
AlanHuchin 0:89cf0851969b 1089 #undef MATRIX_COL4
AlanHuchin 0:89cf0851969b 1090 #undef MATRIX_ROW4
AlanHuchin 0:89cf0851969b 1091 #undef MATRIX_COL3
AlanHuchin 0:89cf0851969b 1092 #undef MATRIX_ROW3
AlanHuchin 0:89cf0851969b 1093 #undef MATRIX_COL2
AlanHuchin 0:89cf0851969b 1094 #undef MATRIX_ROW2
AlanHuchin 0:89cf0851969b 1095 #undef MOP_M_MATRIX_MULTIPLY
AlanHuchin 0:89cf0851969b 1096 #undef MATRIX_CONSTRUCTOR_FROM_T
AlanHuchin 0:89cf0851969b 1097 #undef MATRIX_CONSTRUCTOR_FROM_LOWER
AlanHuchin 0:89cf0851969b 1098 #undef MATRIX_COMMON
AlanHuchin 0:89cf0851969b 1099 #undef MATRIX_CONSTRUCTOR_FROM_HIGHER
AlanHuchin 0:89cf0851969b 1100 #undef MAT_FUNC_TEMPLATE
AlanHuchin 0:89cf0851969b 1101 #undef MAT_FUNC_MINOR_TEMPLATE
AlanHuchin 0:89cf0851969b 1102 #undef MAT_ADJOINT_TEMPLATE
AlanHuchin 0:89cf0851969b 1103 #undef MAT_INVERSE_TEMPLATE
AlanHuchin 0:89cf0851969b 1104 #undef MAT_VEC_FUNCS_TEMPLATE
AlanHuchin 0:89cf0851969b 1105 #undef MAT_TRANFORMS_TEMPLATE
AlanHuchin 0:89cf0851969b 1106 #undef MAT_OUTERPRODUCT_TEMPLATE
AlanHuchin 0:89cf0851969b 1107 #undef FREE_MODIFYING_OPERATORS
AlanHuchin 0:89cf0851969b 1108 #undef FREE_OPERATORS
AlanHuchin 0:89cf0851969b 1109
AlanHuchin 0:89cf0851969b 1110 } // end namespace vmath
AlanHuchin 0:89cf0851969b 1111
AlanHuchin 0:89cf0851969b 1112 #endif
AlanHuchin 0:89cf0851969b 1113
AlanHuchin 0:89cf0851969b 1114
AlanHuchin 0:89cf0851969b 1115
AlanHuchin 0:89cf0851969b 1116