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author John Tsiombikas <nuclear@member.fsf.org>
date Sat, 01 Feb 2014 19:58:19 +0200
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nuclear@0 1 /*
nuclear@0 2 ---------------------------------------------------------------------------
nuclear@0 3 Open Asset Import Library (assimp)
nuclear@0 4 ---------------------------------------------------------------------------
nuclear@0 5
nuclear@0 6 Copyright (c) 2006-2012, assimp team
nuclear@0 7
nuclear@0 8 All rights reserved.
nuclear@0 9
nuclear@0 10 Redistribution and use of this software in source and binary forms,
nuclear@0 11 with or without modification, are permitted provided that the following
nuclear@0 12 conditions are met:
nuclear@0 13
nuclear@0 14 * Redistributions of source code must retain the above
nuclear@0 15 copyright notice, this list of conditions and the
nuclear@0 16 following disclaimer.
nuclear@0 17
nuclear@0 18 * Redistributions in binary form must reproduce the above
nuclear@0 19 copyright notice, this list of conditions and the
nuclear@0 20 following disclaimer in the documentation and/or other
nuclear@0 21 materials provided with the distribution.
nuclear@0 22
nuclear@0 23 * Neither the name of the assimp team, nor the names of its
nuclear@0 24 contributors may be used to endorse or promote products
nuclear@0 25 derived from this software without specific prior
nuclear@0 26 written permission of the assimp team.
nuclear@0 27
nuclear@0 28 THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
nuclear@0 29 "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
nuclear@0 30 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
nuclear@0 31 A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
nuclear@0 32 OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
nuclear@0 33 SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
nuclear@0 34 LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
nuclear@0 35 DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
nuclear@0 36 THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
nuclear@0 37 (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
nuclear@0 38 OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
nuclear@0 39 ---------------------------------------------------------------------------
nuclear@0 40 */
nuclear@0 41
nuclear@0 42 /** @file aiMatrix3x3.inl
nuclear@0 43 * @brief Inline implementation of the 3x3 matrix operators
nuclear@0 44 */
nuclear@0 45 #ifndef AI_MATRIX3x3_INL_INC
nuclear@0 46 #define AI_MATRIX3x3_INL_INC
nuclear@0 47
nuclear@0 48 #ifdef __cplusplus
nuclear@0 49 #include "matrix3x3.h"
nuclear@0 50
nuclear@0 51 #include "matrix4x4.h"
nuclear@0 52 #include <algorithm>
nuclear@0 53 #include <limits>
nuclear@0 54
nuclear@0 55 // ------------------------------------------------------------------------------------------------
nuclear@0 56 // Construction from a 4x4 matrix. The remaining parts of the matrix are ignored.
nuclear@0 57 template <typename TReal>
nuclear@0 58 inline aiMatrix3x3t<TReal>::aiMatrix3x3t( const aiMatrix4x4t<TReal>& pMatrix)
nuclear@0 59 {
nuclear@0 60 a1 = pMatrix.a1; a2 = pMatrix.a2; a3 = pMatrix.a3;
nuclear@0 61 b1 = pMatrix.b1; b2 = pMatrix.b2; b3 = pMatrix.b3;
nuclear@0 62 c1 = pMatrix.c1; c2 = pMatrix.c2; c3 = pMatrix.c3;
nuclear@0 63 }
nuclear@0 64
nuclear@0 65 // ------------------------------------------------------------------------------------------------
nuclear@0 66 template <typename TReal>
nuclear@0 67 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::operator *= (const aiMatrix3x3t<TReal>& m)
nuclear@0 68 {
nuclear@0 69 *this = aiMatrix3x3t<TReal>(m.a1 * a1 + m.b1 * a2 + m.c1 * a3,
nuclear@0 70 m.a2 * a1 + m.b2 * a2 + m.c2 * a3,
nuclear@0 71 m.a3 * a1 + m.b3 * a2 + m.c3 * a3,
nuclear@0 72 m.a1 * b1 + m.b1 * b2 + m.c1 * b3,
nuclear@0 73 m.a2 * b1 + m.b2 * b2 + m.c2 * b3,
nuclear@0 74 m.a3 * b1 + m.b3 * b2 + m.c3 * b3,
nuclear@0 75 m.a1 * c1 + m.b1 * c2 + m.c1 * c3,
nuclear@0 76 m.a2 * c1 + m.b2 * c2 + m.c2 * c3,
nuclear@0 77 m.a3 * c1 + m.b3 * c2 + m.c3 * c3);
nuclear@0 78 return *this;
nuclear@0 79 }
nuclear@0 80
nuclear@0 81 // ------------------------------------------------------------------------------------------------
nuclear@0 82 template <typename TReal>
nuclear@0 83 template <typename TOther>
nuclear@0 84 aiMatrix3x3t<TReal>::operator aiMatrix3x3t<TOther> () const
nuclear@0 85 {
nuclear@0 86 return aiMatrix3x3t<TOther>(static_cast<TOther>(a1),static_cast<TOther>(a2),static_cast<TOther>(a3),
nuclear@0 87 static_cast<TOther>(b1),static_cast<TOther>(b2),static_cast<TOther>(b3),
nuclear@0 88 static_cast<TOther>(c1),static_cast<TOther>(c2),static_cast<TOther>(c3));
nuclear@0 89 }
nuclear@0 90
nuclear@0 91 // ------------------------------------------------------------------------------------------------
nuclear@0 92 template <typename TReal>
nuclear@0 93 inline aiMatrix3x3t<TReal> aiMatrix3x3t<TReal>::operator* (const aiMatrix3x3t<TReal>& m) const
nuclear@0 94 {
nuclear@0 95 aiMatrix3x3t<TReal> temp( *this);
nuclear@0 96 temp *= m;
nuclear@0 97 return temp;
nuclear@0 98 }
nuclear@0 99
nuclear@0 100 // ------------------------------------------------------------------------------------------------
nuclear@0 101 template <typename TReal>
nuclear@0 102 inline TReal* aiMatrix3x3t<TReal>::operator[] (unsigned int p_iIndex)
nuclear@0 103 {
nuclear@0 104 return &this->a1 + p_iIndex * 3;
nuclear@0 105 }
nuclear@0 106
nuclear@0 107 // ------------------------------------------------------------------------------------------------
nuclear@0 108 template <typename TReal>
nuclear@0 109 inline const TReal* aiMatrix3x3t<TReal>::operator[] (unsigned int p_iIndex) const
nuclear@0 110 {
nuclear@0 111 return &this->a1 + p_iIndex * 3;
nuclear@0 112 }
nuclear@0 113
nuclear@0 114 // ------------------------------------------------------------------------------------------------
nuclear@0 115 template <typename TReal>
nuclear@0 116 inline bool aiMatrix3x3t<TReal>::operator== (const aiMatrix4x4t<TReal> m) const
nuclear@0 117 {
nuclear@0 118 return a1 == m.a1 && a2 == m.a2 && a3 == m.a3 &&
nuclear@0 119 b1 == m.b1 && b2 == m.b2 && b3 == m.b3 &&
nuclear@0 120 c1 == m.c1 && c2 == m.c2 && c3 == m.c3;
nuclear@0 121 }
nuclear@0 122
nuclear@0 123 // ------------------------------------------------------------------------------------------------
nuclear@0 124 template <typename TReal>
nuclear@0 125 inline bool aiMatrix3x3t<TReal>::operator!= (const aiMatrix4x4t<TReal> m) const
nuclear@0 126 {
nuclear@0 127 return !(*this == m);
nuclear@0 128 }
nuclear@0 129
nuclear@0 130 // ------------------------------------------------------------------------------------------------
nuclear@0 131 template <typename TReal>
nuclear@0 132 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Transpose()
nuclear@0 133 {
nuclear@0 134 // (TReal&) don't remove, GCC complains cause of packed fields
nuclear@0 135 std::swap( (TReal&)a2, (TReal&)b1);
nuclear@0 136 std::swap( (TReal&)a3, (TReal&)c1);
nuclear@0 137 std::swap( (TReal&)b3, (TReal&)c2);
nuclear@0 138 return *this;
nuclear@0 139 }
nuclear@0 140
nuclear@0 141 // ----------------------------------------------------------------------------------------
nuclear@0 142 template <typename TReal>
nuclear@0 143 inline TReal aiMatrix3x3t<TReal>::Determinant() const
nuclear@0 144 {
nuclear@0 145 return a1*b2*c3 - a1*b3*c2 + a2*b3*c1 - a2*b1*c3 + a3*b1*c2 - a3*b2*c1;
nuclear@0 146 }
nuclear@0 147
nuclear@0 148 // ----------------------------------------------------------------------------------------
nuclear@0 149 template <typename TReal>
nuclear@0 150 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Inverse()
nuclear@0 151 {
nuclear@0 152 // Compute the reciprocal determinant
nuclear@0 153 TReal det = Determinant();
nuclear@0 154 if(det == static_cast<TReal>(0.0))
nuclear@0 155 {
nuclear@0 156 // Matrix not invertible. Setting all elements to nan is not really
nuclear@0 157 // correct in a mathematical sense; but at least qnans are easy to
nuclear@0 158 // spot. XXX we might throw an exception instead, which would
nuclear@0 159 // be even much better to spot :/.
nuclear@0 160 const TReal nan = std::numeric_limits<TReal>::quiet_NaN();
nuclear@0 161 *this = aiMatrix3x3t<TReal>( nan,nan,nan,nan,nan,nan,nan,nan,nan);
nuclear@0 162
nuclear@0 163 return *this;
nuclear@0 164 }
nuclear@0 165
nuclear@0 166 TReal invdet = static_cast<TReal>(1.0) / det;
nuclear@0 167
nuclear@0 168 aiMatrix3x3t<TReal> res;
nuclear@0 169 res.a1 = invdet * (b2 * c3 - b3 * c2);
nuclear@0 170 res.a2 = -invdet * (a2 * c3 - a3 * c2);
nuclear@0 171 res.a3 = invdet * (a2 * b3 - a3 * b2);
nuclear@0 172 res.b1 = -invdet * (b1 * c3 - b3 * c1);
nuclear@0 173 res.b2 = invdet * (a1 * c3 - a3 * c1);
nuclear@0 174 res.b3 = -invdet * (a1 * b3 - a3 * b1);
nuclear@0 175 res.c1 = invdet * (b1 * c2 - b2 * c1);
nuclear@0 176 res.c2 = -invdet * (a1 * c2 - a2 * c1);
nuclear@0 177 res.c3 = invdet * (a1 * b2 - a2 * b1);
nuclear@0 178 *this = res;
nuclear@0 179
nuclear@0 180 return *this;
nuclear@0 181 }
nuclear@0 182
nuclear@0 183 // ------------------------------------------------------------------------------------------------
nuclear@0 184 template <typename TReal>
nuclear@0 185 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::RotationZ(TReal a, aiMatrix3x3t<TReal>& out)
nuclear@0 186 {
nuclear@0 187 out.a1 = out.b2 = ::cos(a);
nuclear@0 188 out.b1 = ::sin(a);
nuclear@0 189 out.a2 = - out.b1;
nuclear@0 190
nuclear@0 191 out.a3 = out.b3 = out.c1 = out.c2 = 0.f;
nuclear@0 192 out.c3 = 1.f;
nuclear@0 193
nuclear@0 194 return out;
nuclear@0 195 }
nuclear@0 196
nuclear@0 197 // ------------------------------------------------------------------------------------------------
nuclear@0 198 // Returns a rotation matrix for a rotation around an arbitrary axis.
nuclear@0 199 template <typename TReal>
nuclear@0 200 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Rotation( TReal a, const aiVector3t<TReal>& axis, aiMatrix3x3t<TReal>& out)
nuclear@0 201 {
nuclear@0 202 TReal c = cos( a), s = sin( a), t = 1 - c;
nuclear@0 203 TReal x = axis.x, y = axis.y, z = axis.z;
nuclear@0 204
nuclear@0 205 // Many thanks to MathWorld and Wikipedia
nuclear@0 206 out.a1 = t*x*x + c; out.a2 = t*x*y - s*z; out.a3 = t*x*z + s*y;
nuclear@0 207 out.b1 = t*x*y + s*z; out.b2 = t*y*y + c; out.b3 = t*y*z - s*x;
nuclear@0 208 out.c1 = t*x*z - s*y; out.c2 = t*y*z + s*x; out.c3 = t*z*z + c;
nuclear@0 209
nuclear@0 210 return out;
nuclear@0 211 }
nuclear@0 212
nuclear@0 213 // ------------------------------------------------------------------------------------------------
nuclear@0 214 template <typename TReal>
nuclear@0 215 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::Translation( const aiVector2t<TReal>& v, aiMatrix3x3t<TReal>& out)
nuclear@0 216 {
nuclear@0 217 out = aiMatrix3x3t<TReal>();
nuclear@0 218 out.a3 = v.x;
nuclear@0 219 out.b3 = v.y;
nuclear@0 220 return out;
nuclear@0 221 }
nuclear@0 222
nuclear@0 223 // ----------------------------------------------------------------------------------------
nuclear@0 224 /** A function for creating a rotation matrix that rotates a vector called
nuclear@0 225 * "from" into another vector called "to".
nuclear@0 226 * Input : from[3], to[3] which both must be *normalized* non-zero vectors
nuclear@0 227 * Output: mtx[3][3] -- a 3x3 matrix in colum-major form
nuclear@0 228 * Authors: Tomas Möller, John Hughes
nuclear@0 229 * "Efficiently Building a Matrix to Rotate One Vector to Another"
nuclear@0 230 * Journal of Graphics Tools, 4(4):1-4, 1999
nuclear@0 231 */
nuclear@0 232 // ----------------------------------------------------------------------------------------
nuclear@0 233 template <typename TReal>
nuclear@0 234 inline aiMatrix3x3t<TReal>& aiMatrix3x3t<TReal>::FromToMatrix(const aiVector3t<TReal>& from,
nuclear@0 235 const aiVector3t<TReal>& to, aiMatrix3x3t<TReal>& mtx)
nuclear@0 236 {
nuclear@0 237 const TReal e = from * to;
nuclear@0 238 const TReal f = (e < 0)? -e:e;
nuclear@0 239
nuclear@0 240 if (f > static_cast<TReal>(1.0) - static_cast<TReal>(0.00001)) /* "from" and "to"-vector almost parallel */
nuclear@0 241 {
nuclear@0 242 aiVector3D u,v; /* temporary storage vectors */
nuclear@0 243 aiVector3D x; /* vector most nearly orthogonal to "from" */
nuclear@0 244
nuclear@0 245 x.x = (from.x > 0.0)? from.x : -from.x;
nuclear@0 246 x.y = (from.y > 0.0)? from.y : -from.y;
nuclear@0 247 x.z = (from.z > 0.0)? from.z : -from.z;
nuclear@0 248
nuclear@0 249 if (x.x < x.y)
nuclear@0 250 {
nuclear@0 251 if (x.x < x.z)
nuclear@0 252 {
nuclear@0 253 x.x = static_cast<TReal>(1.0); x.y = x.z = static_cast<TReal>(0.0);
nuclear@0 254 }
nuclear@0 255 else
nuclear@0 256 {
nuclear@0 257 x.z = static_cast<TReal>(1.0); x.y = x.z = static_cast<TReal>(0.0);
nuclear@0 258 }
nuclear@0 259 }
nuclear@0 260 else
nuclear@0 261 {
nuclear@0 262 if (x.y < x.z)
nuclear@0 263 {
nuclear@0 264 x.y = static_cast<TReal>(1.0); x.x = x.z = static_cast<TReal>(0.0);
nuclear@0 265 }
nuclear@0 266 else
nuclear@0 267 {
nuclear@0 268 x.z = static_cast<TReal>(1.0); x.x = x.y = static_cast<TReal>(0.0);
nuclear@0 269 }
nuclear@0 270 }
nuclear@0 271
nuclear@0 272 u.x = x.x - from.x; u.y = x.y - from.y; u.z = x.z - from.z;
nuclear@0 273 v.x = x.x - to.x; v.y = x.y - to.y; v.z = x.z - to.z;
nuclear@0 274
nuclear@0 275 const TReal c1 = static_cast<TReal>(2.0) / (u * u);
nuclear@0 276 const TReal c2 = static_cast<TReal>(2.0) / (v * v);
nuclear@0 277 const TReal c3 = c1 * c2 * (u * v);
nuclear@0 278
nuclear@0 279 for (unsigned int i = 0; i < 3; i++)
nuclear@0 280 {
nuclear@0 281 for (unsigned int j = 0; j < 3; j++)
nuclear@0 282 {
nuclear@0 283 mtx[i][j] = - c1 * u[i] * u[j] - c2 * v[i] * v[j]
nuclear@0 284 + c3 * v[i] * u[j];
nuclear@0 285 }
nuclear@0 286 mtx[i][i] += static_cast<TReal>(1.0);
nuclear@0 287 }
nuclear@0 288 }
nuclear@0 289 else /* the most common case, unless "from"="to", or "from"=-"to" */
nuclear@0 290 {
nuclear@0 291 const aiVector3D v = from ^ to;
nuclear@0 292 /* ... use this hand optimized version (9 mults less) */
nuclear@0 293 const TReal h = static_cast<TReal>(1.0)/(static_cast<TReal>(1.0) + e); /* optimization by Gottfried Chen */
nuclear@0 294 const TReal hvx = h * v.x;
nuclear@0 295 const TReal hvz = h * v.z;
nuclear@0 296 const TReal hvxy = hvx * v.y;
nuclear@0 297 const TReal hvxz = hvx * v.z;
nuclear@0 298 const TReal hvyz = hvz * v.y;
nuclear@0 299 mtx[0][0] = e + hvx * v.x;
nuclear@0 300 mtx[0][1] = hvxy - v.z;
nuclear@0 301 mtx[0][2] = hvxz + v.y;
nuclear@0 302
nuclear@0 303 mtx[1][0] = hvxy + v.z;
nuclear@0 304 mtx[1][1] = e + h * v.y * v.y;
nuclear@0 305 mtx[1][2] = hvyz - v.x;
nuclear@0 306
nuclear@0 307 mtx[2][0] = hvxz - v.y;
nuclear@0 308 mtx[2][1] = hvyz + v.x;
nuclear@0 309 mtx[2][2] = e + hvz * v.z;
nuclear@0 310 }
nuclear@0 311 return mtx;
nuclear@0 312 }
nuclear@0 313
nuclear@0 314
nuclear@0 315 #endif // __cplusplus
nuclear@0 316 #endif // AI_MATRIX3x3_INL_INC