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gfx/thebes/gfx3DMatrix.cpp@b8a032363ba2 (annotated)

gfx/thebes/gfx3DMatrix.cpp

Thu, 22 Jan 2015 13:21:57 +0100

author
Michael Schloh von Bennewitz <michael@schloh.com>
date
Thu, 22 Jan 2015 13:21:57 +0100
branch
TOR_BUG_9701
changeset 15
b8a032363ba2
permissions
-rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

michael@0 1 /* -*- Mode: C++; tab-width: 20; indent-tabs-mode: nil; c-basic-offset: 4 -*-
michael@0 2 * This Source Code Form is subject to the terms of the Mozilla Public
michael@0 3 * License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0 4 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0 5
michael@0 6 #include "gfxMatrix.h"
michael@0 7 #include "gfx3DMatrix.h"
michael@0 8 #include "mozilla/gfx/Tools.h"
michael@0 9 #include <math.h>
michael@0 10 #include <algorithm>
michael@0 11
michael@0 12 using namespace std;
michael@0 13 using namespace mozilla;
michael@0 14 using namespace mozilla::gfx;
michael@0 15
michael@0 16 /* Force small values to zero. We do this to avoid having sin(360deg)
michael@0 17 * evaluate to a tiny but nonzero value.
michael@0 18 */
michael@0 19 static double FlushToZero(double aVal)
michael@0 20 {
michael@0 21 if (-FLT_EPSILON < aVal && aVal < FLT_EPSILON)
michael@0 22 return 0.0f;
michael@0 23 else
michael@0 24 return aVal;
michael@0 25 }
michael@0 26
michael@0 27 /* Computes tan(aTheta). For values of aTheta such that tan(aTheta) is
michael@0 28 * undefined or very large, SafeTangent returns a manageably large value
michael@0 29 * of the correct sign.
michael@0 30 */
michael@0 31 static double SafeTangent(double aTheta)
michael@0 32 {
michael@0 33 const double kEpsilon = 0.0001;
michael@0 34
michael@0 35 /* tan(theta) = sin(theta)/cos(theta); problems arise when
michael@0 36 * cos(theta) is too close to zero. Limit cos(theta) to the
michael@0 37 * range [-1, -epsilon] U [epsilon, 1].
michael@0 38 */
michael@0 39 double sinTheta = sin(aTheta);
michael@0 40 double cosTheta = cos(aTheta);
michael@0 41
michael@0 42 if (cosTheta >= 0 && cosTheta < kEpsilon)
michael@0 43 cosTheta = kEpsilon;
michael@0 44 else if (cosTheta < 0 && cosTheta >= -kEpsilon)
michael@0 45 cosTheta = -kEpsilon;
michael@0 46
michael@0 47 return FlushToZero(sinTheta / cosTheta);
michael@0 48 }
michael@0 49
michael@0 50 gfx3DMatrix::gfx3DMatrix(void)
michael@0 51 {
michael@0 52 _11 = _22 = _33 = _44 = 1.0f;
michael@0 53 _12 = _13 = _14 = 0.0f;
michael@0 54 _21 = _23 = _24 = 0.0f;
michael@0 55 _31 = _32 = _34 = 0.0f;
michael@0 56 _41 = _42 = _43 = 0.0f;
michael@0 57 }
michael@0 58
michael@0 59 gfx3DMatrix
michael@0 60 gfx3DMatrix::operator*(const gfx3DMatrix &aMatrix) const
michael@0 61 {
michael@0 62 if (Is2D() && aMatrix.Is2D()) {
michael@0 63 return Multiply2D(aMatrix);
michael@0 64 }
michael@0 65
michael@0 66 gfx3DMatrix matrix;
michael@0 67
michael@0 68 matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21 + _13 * aMatrix._31 + _14 * aMatrix._41;
michael@0 69 matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21 + _23 * aMatrix._31 + _24 * aMatrix._41;
michael@0 70 matrix._31 = _31 * aMatrix._11 + _32 * aMatrix._21 + _33 * aMatrix._31 + _34 * aMatrix._41;
michael@0 71 matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + _43 * aMatrix._31 + _44 * aMatrix._41;
michael@0 72 matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22 + _13 * aMatrix._32 + _14 * aMatrix._42;
michael@0 73 matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22 + _23 * aMatrix._32 + _24 * aMatrix._42;
michael@0 74 matrix._32 = _31 * aMatrix._12 + _32 * aMatrix._22 + _33 * aMatrix._32 + _34 * aMatrix._42;
michael@0 75 matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + _43 * aMatrix._32 + _44 * aMatrix._42;
michael@0 76 matrix._13 = _11 * aMatrix._13 + _12 * aMatrix._23 + _13 * aMatrix._33 + _14 * aMatrix._43;
michael@0 77 matrix._23 = _21 * aMatrix._13 + _22 * aMatrix._23 + _23 * aMatrix._33 + _24 * aMatrix._43;
michael@0 78 matrix._33 = _31 * aMatrix._13 + _32 * aMatrix._23 + _33 * aMatrix._33 + _34 * aMatrix._43;
michael@0 79 matrix._43 = _41 * aMatrix._13 + _42 * aMatrix._23 + _43 * aMatrix._33 + _44 * aMatrix._43;
michael@0 80 matrix._14 = _11 * aMatrix._14 + _12 * aMatrix._24 + _13 * aMatrix._34 + _14 * aMatrix._44;
michael@0 81 matrix._24 = _21 * aMatrix._14 + _22 * aMatrix._24 + _23 * aMatrix._34 + _24 * aMatrix._44;
michael@0 82 matrix._34 = _31 * aMatrix._14 + _32 * aMatrix._24 + _33 * aMatrix._34 + _34 * aMatrix._44;
michael@0 83 matrix._44 = _41 * aMatrix._14 + _42 * aMatrix._24 + _43 * aMatrix._34 + _44 * aMatrix._44;
michael@0 84
michael@0 85 return matrix;
michael@0 86 }
michael@0 87
michael@0 88 gfx3DMatrix&
michael@0 89 gfx3DMatrix::operator*=(const gfx3DMatrix &aMatrix)
michael@0 90 {
michael@0 91 return *this = *this * aMatrix;
michael@0 92 }
michael@0 93
michael@0 94 gfx3DMatrix
michael@0 95 gfx3DMatrix::Multiply2D(const gfx3DMatrix &aMatrix) const
michael@0 96 {
michael@0 97 gfx3DMatrix matrix;
michael@0 98
michael@0 99 matrix._11 = _11 * aMatrix._11 + _12 * aMatrix._21;
michael@0 100 matrix._21 = _21 * aMatrix._11 + _22 * aMatrix._21;
michael@0 101 matrix._41 = _41 * aMatrix._11 + _42 * aMatrix._21 + aMatrix._41;
michael@0 102 matrix._12 = _11 * aMatrix._12 + _12 * aMatrix._22;
michael@0 103 matrix._22 = _21 * aMatrix._12 + _22 * aMatrix._22;
michael@0 104 matrix._42 = _41 * aMatrix._12 + _42 * aMatrix._22 + aMatrix._42;
michael@0 105
michael@0 106 return matrix;
michael@0 107 }
michael@0 108
michael@0 109 bool
michael@0 110 gfx3DMatrix::operator==(const gfx3DMatrix& o) const
michael@0 111 {
michael@0 112 // XXX would be nice to memcmp here, but that breaks IEEE 754 semantics
michael@0 113 return _11 == o._11 && _12 == o._12 && _13 == o._13 && _14 == o._14 &&
michael@0 114 _21 == o._21 && _22 == o._22 && _23 == o._23 && _24 == o._24 &&
michael@0 115 _31 == o._31 && _32 == o._32 && _33 == o._33 && _34 == o._34 &&
michael@0 116 _41 == o._41 && _42 == o._42 && _43 == o._43 && _44 == o._44;
michael@0 117 }
michael@0 118
michael@0 119 bool
michael@0 120 gfx3DMatrix::operator!=(const gfx3DMatrix& o) const
michael@0 121 {
michael@0 122 return !((*this) == o);
michael@0 123 }
michael@0 124
michael@0 125 bool
michael@0 126 gfx3DMatrix::FuzzyEqual(const gfx3DMatrix& o) const
michael@0 127 {
michael@0 128 static const float error = 1e-4;
michael@0 129 return gfx::FuzzyEqual(_11, o._11, error) && gfx::FuzzyEqual(_12, o._12, error) &&
michael@0 130 gfx::FuzzyEqual(_13, o._13, error) && gfx::FuzzyEqual(_14, o._14, error) &&
michael@0 131 gfx::FuzzyEqual(_21, o._21, error) && gfx::FuzzyEqual(_22, o._22, error) &&
michael@0 132 gfx::FuzzyEqual(_23, o._23, error) && gfx::FuzzyEqual(_24, o._24, error) &&
michael@0 133 gfx::FuzzyEqual(_31, o._31, error) && gfx::FuzzyEqual(_32, o._32, error) &&
michael@0 134 gfx::FuzzyEqual(_33, o._33, error) && gfx::FuzzyEqual(_34, o._34, error) &&
michael@0 135 gfx::FuzzyEqual(_41, o._41, error) && gfx::FuzzyEqual(_42, o._42, error) &&
michael@0 136 gfx::FuzzyEqual(_43, o._43, error) && gfx::FuzzyEqual(_44, o._44, error);
michael@0 137 }
michael@0 138
michael@0 139 gfx3DMatrix&
michael@0 140 gfx3DMatrix::operator/=(const gfxFloat scalar)
michael@0 141 {
michael@0 142 _11 /= scalar;
michael@0 143 _12 /= scalar;
michael@0 144 _13 /= scalar;
michael@0 145 _14 /= scalar;
michael@0 146 _21 /= scalar;
michael@0 147 _22 /= scalar;
michael@0 148 _23 /= scalar;
michael@0 149 _24 /= scalar;
michael@0 150 _31 /= scalar;
michael@0 151 _32 /= scalar;
michael@0 152 _33 /= scalar;
michael@0 153 _34 /= scalar;
michael@0 154 _41 /= scalar;
michael@0 155 _42 /= scalar;
michael@0 156 _43 /= scalar;
michael@0 157 _44 /= scalar;
michael@0 158 return *this;
michael@0 159 }
michael@0 160
michael@0 161 gfx3DMatrix
michael@0 162 gfx3DMatrix::From2D(const gfxMatrix &aMatrix)
michael@0 163 {
michael@0 164 gfx3DMatrix matrix;
michael@0 165 matrix._11 = (float)aMatrix.xx;
michael@0 166 matrix._12 = (float)aMatrix.yx;
michael@0 167 matrix._21 = (float)aMatrix.xy;
michael@0 168 matrix._22 = (float)aMatrix.yy;
michael@0 169 matrix._41 = (float)aMatrix.x0;
michael@0 170 matrix._42 = (float)aMatrix.y0;
michael@0 171 return matrix;
michael@0 172 }
michael@0 173
michael@0 174 bool
michael@0 175 gfx3DMatrix::IsIdentity() const
michael@0 176 {
michael@0 177 return _11 == 1.0f && _12 == 0.0f && _13 == 0.0f && _14 == 0.0f &&
michael@0 178 _21 == 0.0f && _22 == 1.0f && _23 == 0.0f && _24 == 0.0f &&
michael@0 179 _31 == 0.0f && _32 == 0.0f && _33 == 1.0f && _34 == 0.0f &&
michael@0 180 _41 == 0.0f && _42 == 0.0f && _43 == 0.0f && _44 == 1.0f;
michael@0 181 }
michael@0 182
michael@0 183 void
michael@0 184 gfx3DMatrix::Translate(const gfxPoint3D& aPoint)
michael@0 185 {
michael@0 186 _41 += aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31;
michael@0 187 _42 += aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32;
michael@0 188 _43 += aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33;
michael@0 189 _44 += aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34;
michael@0 190 }
michael@0 191
michael@0 192 void
michael@0 193 gfx3DMatrix::TranslatePost(const gfxPoint3D& aPoint)
michael@0 194 {
michael@0 195 _11 += _14 * aPoint.x;
michael@0 196 _21 += _24 * aPoint.x;
michael@0 197 _31 += _34 * aPoint.x;
michael@0 198 _41 += _44 * aPoint.x;
michael@0 199 _12 += _14 * aPoint.y;
michael@0 200 _22 += _24 * aPoint.y;
michael@0 201 _32 += _34 * aPoint.y;
michael@0 202 _42 += _44 * aPoint.y;
michael@0 203 _13 += _14 * aPoint.z;
michael@0 204 _23 += _24 * aPoint.z;
michael@0 205 _33 += _34 * aPoint.z;
michael@0 206 _43 += _44 * aPoint.z;
michael@0 207 }
michael@0 208
michael@0 209 void
michael@0 210 gfx3DMatrix::ScalePost(float aX, float aY, float aZ)
michael@0 211 {
michael@0 212 _11 *= aX;
michael@0 213 _21 *= aX;
michael@0 214 _31 *= aX;
michael@0 215 _41 *= aX;
michael@0 216
michael@0 217 _12 *= aY;
michael@0 218 _22 *= aY;
michael@0 219 _32 *= aY;
michael@0 220 _42 *= aY;
michael@0 221
michael@0 222 _13 *= aZ;
michael@0 223 _23 *= aZ;
michael@0 224 _33 *= aZ;
michael@0 225 _43 *= aZ;
michael@0 226 }
michael@0 227
michael@0 228 void
michael@0 229 gfx3DMatrix::SkewXY(double aSkew)
michael@0 230 {
michael@0 231 (*this)[1] += (*this)[0] * aSkew;
michael@0 232 }
michael@0 233
michael@0 234 void
michael@0 235 gfx3DMatrix::SkewXZ(double aSkew)
michael@0 236 {
michael@0 237 (*this)[2] += (*this)[0] * aSkew;
michael@0 238 }
michael@0 239
michael@0 240 void
michael@0 241 gfx3DMatrix::SkewYZ(double aSkew)
michael@0 242 {
michael@0 243 (*this)[2] += (*this)[1] * aSkew;
michael@0 244 }
michael@0 245
michael@0 246 void
michael@0 247 gfx3DMatrix::Scale(float aX, float aY, float aZ)
michael@0 248 {
michael@0 249 (*this)[0] *= aX;
michael@0 250 (*this)[1] *= aY;
michael@0 251 (*this)[2] *= aZ;
michael@0 252 }
michael@0 253
michael@0 254 void
michael@0 255 gfx3DMatrix::Perspective(float aDepth)
michael@0 256 {
michael@0 257 NS_ASSERTION(aDepth > 0.0f, "Perspective must be positive!");
michael@0 258 _31 += -1.0/aDepth * _41;
michael@0 259 _32 += -1.0/aDepth * _42;
michael@0 260 _33 += -1.0/aDepth * _43;
michael@0 261 _34 += -1.0/aDepth * _44;
michael@0 262 }
michael@0 263
michael@0 264 void gfx3DMatrix::SkewXY(double aXSkew, double aYSkew)
michael@0 265 {
michael@0 266 float tanX = SafeTangent(aXSkew);
michael@0 267 float tanY = SafeTangent(aYSkew);
michael@0 268 float temp;
michael@0 269
michael@0 270 temp = _11;
michael@0 271 _11 += tanY * _21;
michael@0 272 _21 += tanX * temp;
michael@0 273
michael@0 274 temp = _12;
michael@0 275 _12 += tanY * _22;
michael@0 276 _22 += tanX * temp;
michael@0 277
michael@0 278 temp = _13;
michael@0 279 _13 += tanY * _23;
michael@0 280 _23 += tanX * temp;
michael@0 281
michael@0 282 temp = _14;
michael@0 283 _14 += tanY * _24;
michael@0 284 _24 += tanX * temp;
michael@0 285 }
michael@0 286
michael@0 287 void
michael@0 288 gfx3DMatrix::RotateX(double aTheta)
michael@0 289 {
michael@0 290 double cosTheta = FlushToZero(cos(aTheta));
michael@0 291 double sinTheta = FlushToZero(sin(aTheta));
michael@0 292
michael@0 293 float temp;
michael@0 294
michael@0 295 temp = _21;
michael@0 296 _21 = cosTheta * _21 + sinTheta * _31;
michael@0 297 _31 = -sinTheta * temp + cosTheta * _31;
michael@0 298
michael@0 299 temp = _22;
michael@0 300 _22 = cosTheta * _22 + sinTheta * _32;
michael@0 301 _32 = -sinTheta * temp + cosTheta * _32;
michael@0 302
michael@0 303 temp = _23;
michael@0 304 _23 = cosTheta * _23 + sinTheta * _33;
michael@0 305 _33 = -sinTheta * temp + cosTheta * _33;
michael@0 306
michael@0 307 temp = _24;
michael@0 308 _24 = cosTheta * _24 + sinTheta * _34;
michael@0 309 _34 = -sinTheta * temp + cosTheta * _34;
michael@0 310 }
michael@0 311
michael@0 312 void
michael@0 313 gfx3DMatrix::RotateY(double aTheta)
michael@0 314 {
michael@0 315 double cosTheta = FlushToZero(cos(aTheta));
michael@0 316 double sinTheta = FlushToZero(sin(aTheta));
michael@0 317
michael@0 318 float temp;
michael@0 319
michael@0 320 temp = _11;
michael@0 321 _11 = cosTheta * _11 + -sinTheta * _31;
michael@0 322 _31 = sinTheta * temp + cosTheta * _31;
michael@0 323
michael@0 324 temp = _12;
michael@0 325 _12 = cosTheta * _12 + -sinTheta * _32;
michael@0 326 _32 = sinTheta * temp + cosTheta * _32;
michael@0 327
michael@0 328 temp = _13;
michael@0 329 _13 = cosTheta * _13 + -sinTheta * _33;
michael@0 330 _33 = sinTheta * temp + cosTheta * _33;
michael@0 331
michael@0 332 temp = _14;
michael@0 333 _14 = cosTheta * _14 + -sinTheta * _34;
michael@0 334 _34 = sinTheta * temp + cosTheta * _34;
michael@0 335 }
michael@0 336
michael@0 337 void
michael@0 338 gfx3DMatrix::RotateZ(double aTheta)
michael@0 339 {
michael@0 340 double cosTheta = FlushToZero(cos(aTheta));
michael@0 341 double sinTheta = FlushToZero(sin(aTheta));
michael@0 342
michael@0 343 float temp;
michael@0 344
michael@0 345 temp = _11;
michael@0 346 _11 = cosTheta * _11 + sinTheta * _21;
michael@0 347 _21 = -sinTheta * temp + cosTheta * _21;
michael@0 348
michael@0 349 temp = _12;
michael@0 350 _12 = cosTheta * _12 + sinTheta * _22;
michael@0 351 _22 = -sinTheta * temp + cosTheta * _22;
michael@0 352
michael@0 353 temp = _13;
michael@0 354 _13 = cosTheta * _13 + sinTheta * _23;
michael@0 355 _23 = -sinTheta * temp + cosTheta * _23;
michael@0 356
michael@0 357 temp = _14;
michael@0 358 _14 = cosTheta * _14 + sinTheta * _24;
michael@0 359 _24 = -sinTheta * temp + cosTheta * _24;
michael@0 360 }
michael@0 361
michael@0 362 void
michael@0 363 gfx3DMatrix::PreMultiply(const gfx3DMatrix& aOther)
michael@0 364 {
michael@0 365 *this = aOther * (*this);
michael@0 366 }
michael@0 367
michael@0 368 void
michael@0 369 gfx3DMatrix::PreMultiply(const gfxMatrix& aOther)
michael@0 370 {
michael@0 371 gfx3DMatrix temp;
michael@0 372 temp._11 = aOther.xx * _11 + aOther.yx * _21;
michael@0 373 temp._21 = aOther.xy * _11 + aOther.yy * _21;
michael@0 374 temp._31 = _31;
michael@0 375 temp._41 = aOther.x0 * _11 + aOther.y0 * _21 + _41;
michael@0 376 temp._12 = aOther.xx * _12 + aOther.yx * _22;
michael@0 377 temp._22 = aOther.xy * _12 + aOther.yy * _22;
michael@0 378 temp._32 = _32;
michael@0 379 temp._42 = aOther.x0 * _12 + aOther.y0 * _22 + _42;
michael@0 380 temp._13 = aOther.xx * _13 + aOther.yx * _23;
michael@0 381 temp._23 = aOther.xy * _13 + aOther.yy * _23;
michael@0 382 temp._33 = _33;
michael@0 383 temp._43 = aOther.x0 * _13 + aOther.y0 * _23 + _43;
michael@0 384 temp._14 = aOther.xx * _14 + aOther.yx * _24;
michael@0 385 temp._24 = aOther.xy * _14 + aOther.yy * _24;
michael@0 386 temp._34 = _34;
michael@0 387 temp._44 = aOther.x0 * _14 + aOther.y0 * _24 + _44;
michael@0 388
michael@0 389 *this = temp;
michael@0 390 }
michael@0 391
michael@0 392 gfx3DMatrix
michael@0 393 gfx3DMatrix::Translation(float aX, float aY, float aZ)
michael@0 394 {
michael@0 395 gfx3DMatrix matrix;
michael@0 396
michael@0 397 matrix._41 = aX;
michael@0 398 matrix._42 = aY;
michael@0 399 matrix._43 = aZ;
michael@0 400 return matrix;
michael@0 401 }
michael@0 402
michael@0 403 gfx3DMatrix
michael@0 404 gfx3DMatrix::Translation(const gfxPoint3D& aPoint)
michael@0 405 {
michael@0 406 gfx3DMatrix matrix;
michael@0 407
michael@0 408 matrix._41 = aPoint.x;
michael@0 409 matrix._42 = aPoint.y;
michael@0 410 matrix._43 = aPoint.z;
michael@0 411 return matrix;
michael@0 412 }
michael@0 413
michael@0 414 gfx3DMatrix
michael@0 415 gfx3DMatrix::ScalingMatrix(float aFactor)
michael@0 416 {
michael@0 417 gfx3DMatrix matrix;
michael@0 418
michael@0 419 matrix._11 = matrix._22 = matrix._33 = aFactor;
michael@0 420 return matrix;
michael@0 421 }
michael@0 422
michael@0 423 gfx3DMatrix
michael@0 424 gfx3DMatrix::ScalingMatrix(float aX, float aY, float aZ)
michael@0 425 {
michael@0 426 gfx3DMatrix matrix;
michael@0 427
michael@0 428 matrix._11 = aX;
michael@0 429 matrix._22 = aY;
michael@0 430 matrix._33 = aZ;
michael@0 431
michael@0 432 return matrix;
michael@0 433 }
michael@0 434
michael@0 435 gfxFloat
michael@0 436 gfx3DMatrix::Determinant() const
michael@0 437 {
michael@0 438 return _14 * _23 * _32 * _41
michael@0 439 - _13 * _24 * _32 * _41
michael@0 440 - _14 * _22 * _33 * _41
michael@0 441 + _12 * _24 * _33 * _41
michael@0 442 + _13 * _22 * _34 * _41
michael@0 443 - _12 * _23 * _34 * _41
michael@0 444 - _14 * _23 * _31 * _42
michael@0 445 + _13 * _24 * _31 * _42
michael@0 446 + _14 * _21 * _33 * _42
michael@0 447 - _11 * _24 * _33 * _42
michael@0 448 - _13 * _21 * _34 * _42
michael@0 449 + _11 * _23 * _34 * _42
michael@0 450 + _14 * _22 * _31 * _43
michael@0 451 - _12 * _24 * _31 * _43
michael@0 452 - _14 * _21 * _32 * _43
michael@0 453 + _11 * _24 * _32 * _43
michael@0 454 + _12 * _21 * _34 * _43
michael@0 455 - _11 * _22 * _34 * _43
michael@0 456 - _13 * _22 * _31 * _44
michael@0 457 + _12 * _23 * _31 * _44
michael@0 458 + _13 * _21 * _32 * _44
michael@0 459 - _11 * _23 * _32 * _44
michael@0 460 - _12 * _21 * _33 * _44
michael@0 461 + _11 * _22 * _33 * _44;
michael@0 462 }
michael@0 463
michael@0 464 gfxFloat
michael@0 465 gfx3DMatrix::Determinant3x3() const
michael@0 466 {
michael@0 467 return _11 * (_22 * _33 - _23 * _32) +
michael@0 468 _12 * (_23 * _31 - _33 * _21) +
michael@0 469 _13 * (_21 * _32 - _22 * _31);
michael@0 470 }
michael@0 471
michael@0 472 gfx3DMatrix
michael@0 473 gfx3DMatrix::Inverse3x3() const
michael@0 474 {
michael@0 475 gfxFloat det = Determinant3x3();
michael@0 476 if (det == 0.0) {
michael@0 477 return *this;
michael@0 478 }
michael@0 479
michael@0 480 gfxFloat detInv = 1/det;
michael@0 481 gfx3DMatrix temp;
michael@0 482
michael@0 483 temp._11 = (_22 * _33 - _23 * _32) * detInv;
michael@0 484 temp._12 = (_13 * _32 - _12 * _33) * detInv;
michael@0 485 temp._13 = (_12 * _23 - _13 * _22) * detInv;
michael@0 486 temp._21 = (_23 * _31 - _33 * _21) * detInv;
michael@0 487 temp._22 = (_11 * _33 - _13 * _31) * detInv;
michael@0 488 temp._23 = (_13 * _21 - _11 * _23) * detInv;
michael@0 489 temp._31 = (_21 * _32 - _22 * _31) * detInv;
michael@0 490 temp._32 = (_31 * _12 - _11 * _32) * detInv;
michael@0 491 temp._33 = (_11 * _22 - _12 * _21) * detInv;
michael@0 492 return temp;
michael@0 493 }
michael@0 494
michael@0 495 bool
michael@0 496 gfx3DMatrix::IsSingular() const
michael@0 497 {
michael@0 498 return Determinant() == 0.0;
michael@0 499 }
michael@0 500
michael@0 501 gfx3DMatrix
michael@0 502 gfx3DMatrix::Inverse() const
michael@0 503 {
michael@0 504 if (TransposedVector(3) == gfxPointH3D(0, 0, 0, 1)) {
michael@0 505 /**
michael@0 506 * When the matrix contains no perspective, the inverse
michael@0 507 * is the same as the 3x3 inverse of the rotation components
michael@0 508 * multiplied by the inverse of the translation components.
michael@0 509 * Doing these steps separately is faster and more numerically
michael@0 510 * stable.
michael@0 511 *
michael@0 512 * Inverse of the translation matrix is just negating
michael@0 513 * the values.
michael@0 514 */
michael@0 515 gfx3DMatrix matrix3 = Inverse3x3();
michael@0 516 matrix3.Translate(gfxPoint3D(-_41, -_42, -_43));
michael@0 517 return matrix3;
michael@0 518 }
michael@0 519
michael@0 520 gfxFloat det = Determinant();
michael@0 521 if (det == 0.0) {
michael@0 522 return *this;
michael@0 523 }
michael@0 524
michael@0 525 gfx3DMatrix temp;
michael@0 526
michael@0 527 temp._11 = _23*_34*_42 - _24*_33*_42 +
michael@0 528 _24*_32*_43 - _22*_34*_43 -
michael@0 529 _23*_32*_44 + _22*_33*_44;
michael@0 530 temp._12 = _14*_33*_42 - _13*_34*_42 -
michael@0 531 _14*_32*_43 + _12*_34*_43 +
michael@0 532 _13*_32*_44 - _12*_33*_44;
michael@0 533 temp._13 = _13*_24*_42 - _14*_23*_42 +
michael@0 534 _14*_22*_43 - _12*_24*_43 -
michael@0 535 _13*_22*_44 + _12*_23*_44;
michael@0 536 temp._14 = _14*_23*_32 - _13*_24*_32 -
michael@0 537 _14*_22*_33 + _12*_24*_33 +
michael@0 538 _13*_22*_34 - _12*_23*_34;
michael@0 539 temp._21 = _24*_33*_41 - _23*_34*_41 -
michael@0 540 _24*_31*_43 + _21*_34*_43 +
michael@0 541 _23*_31*_44 - _21*_33*_44;
michael@0 542 temp._22 = _13*_34*_41 - _14*_33*_41 +
michael@0 543 _14*_31*_43 - _11*_34*_43 -
michael@0 544 _13*_31*_44 + _11*_33*_44;
michael@0 545 temp._23 = _14*_23*_41 - _13*_24*_41 -
michael@0 546 _14*_21*_43 + _11*_24*_43 +
michael@0 547 _13*_21*_44 - _11*_23*_44;
michael@0 548 temp._24 = _13*_24*_31 - _14*_23*_31 +
michael@0 549 _14*_21*_33 - _11*_24*_33 -
michael@0 550 _13*_21*_34 + _11*_23*_34;
michael@0 551 temp._31 = _22*_34*_41 - _24*_32*_41 +
michael@0 552 _24*_31*_42 - _21*_34*_42 -
michael@0 553 _22*_31*_44 + _21*_32*_44;
michael@0 554 temp._32 = _14*_32*_41 - _12*_34*_41 -
michael@0 555 _14*_31*_42 + _11*_34*_42 +
michael@0 556 _12*_31*_44 - _11*_32*_44;
michael@0 557 temp._33 = _12*_24*_41 - _14*_22*_41 +
michael@0 558 _14*_21*_42 - _11*_24*_42 -
michael@0 559 _12*_21*_44 + _11*_22*_44;
michael@0 560 temp._34 = _14*_22*_31 - _12*_24*_31 -
michael@0 561 _14*_21*_32 + _11*_24*_32 +
michael@0 562 _12*_21*_34 - _11*_22*_34;
michael@0 563 temp._41 = _23*_32*_41 - _22*_33*_41 -
michael@0 564 _23*_31*_42 + _21*_33*_42 +
michael@0 565 _22*_31*_43 - _21*_32*_43;
michael@0 566 temp._42 = _12*_33*_41 - _13*_32*_41 +
michael@0 567 _13*_31*_42 - _11*_33*_42 -
michael@0 568 _12*_31*_43 + _11*_32*_43;
michael@0 569 temp._43 = _13*_22*_41 - _12*_23*_41 -
michael@0 570 _13*_21*_42 + _11*_23*_42 +
michael@0 571 _12*_21*_43 - _11*_22*_43;
michael@0 572 temp._44 = _12*_23*_31 - _13*_22*_31 +
michael@0 573 _13*_21*_32 - _11*_23*_32 -
michael@0 574 _12*_21*_33 + _11*_22*_33;
michael@0 575
michael@0 576 temp /= det;
michael@0 577 return temp;
michael@0 578 }
michael@0 579
michael@0 580 gfx3DMatrix&
michael@0 581 gfx3DMatrix::Normalize()
michael@0 582 {
michael@0 583 for (int i = 0; i < 4; i++) {
michael@0 584 for (int j = 0; j < 4; j++) {
michael@0 585 (*this)[i][j] /= (*this)[3][3];
michael@0 586 }
michael@0 587 }
michael@0 588 return *this;
michael@0 589 }
michael@0 590
michael@0 591 gfx3DMatrix&
michael@0 592 gfx3DMatrix::Transpose()
michael@0 593 {
michael@0 594 *this = Transposed();
michael@0 595 return *this;
michael@0 596 }
michael@0 597
michael@0 598 gfx3DMatrix
michael@0 599 gfx3DMatrix::Transposed() const
michael@0 600 {
michael@0 601 gfx3DMatrix temp;
michael@0 602 for (int i = 0; i < 4; i++) {
michael@0 603 temp[i] = TransposedVector(i);
michael@0 604 }
michael@0 605 return temp;
michael@0 606 }
michael@0 607
michael@0 608 gfxPoint
michael@0 609 gfx3DMatrix::Transform(const gfxPoint& point) const
michael@0 610 {
michael@0 611 gfxPoint3D vec3d(point.x, point.y, 0);
michael@0 612 vec3d = Transform3D(vec3d);
michael@0 613 return gfxPoint(vec3d.x, vec3d.y);
michael@0 614 }
michael@0 615
michael@0 616 gfxPoint3D
michael@0 617 gfx3DMatrix::Transform3D(const gfxPoint3D& point) const
michael@0 618 {
michael@0 619 gfxFloat x = point.x * _11 + point.y * _21 + point.z * _31 + _41;
michael@0 620 gfxFloat y = point.x * _12 + point.y * _22 + point.z * _32 + _42;
michael@0 621 gfxFloat z = point.x * _13 + point.y * _23 + point.z * _33 + _43;
michael@0 622 gfxFloat w = point.x * _14 + point.y * _24 + point.z * _34 + _44;
michael@0 623
michael@0 624 x /= w;
michael@0 625 y /= w;
michael@0 626 z /= w;
michael@0 627
michael@0 628 return gfxPoint3D(x, y, z);
michael@0 629 }
michael@0 630
michael@0 631 gfxPointH3D
michael@0 632 gfx3DMatrix::Transform4D(const gfxPointH3D& aPoint) const
michael@0 633 {
michael@0 634 gfxFloat x = aPoint.x * _11 + aPoint.y * _21 + aPoint.z * _31 + aPoint.w * _41;
michael@0 635 gfxFloat y = aPoint.x * _12 + aPoint.y * _22 + aPoint.z * _32 + aPoint.w * _42;
michael@0 636 gfxFloat z = aPoint.x * _13 + aPoint.y * _23 + aPoint.z * _33 + aPoint.w * _43;
michael@0 637 gfxFloat w = aPoint.x * _14 + aPoint.y * _24 + aPoint.z * _34 + aPoint.w * _44;
michael@0 638
michael@0 639 return gfxPointH3D(x, y, z, w);
michael@0 640 }
michael@0 641
michael@0 642 gfxPointH3D
michael@0 643 gfx3DMatrix::TransposeTransform4D(const gfxPointH3D& aPoint) const
michael@0 644 {
michael@0 645 gfxFloat x = aPoint.x * _11 + aPoint.y * _12 + aPoint.z * _13 + aPoint.w * _14;
michael@0 646 gfxFloat y = aPoint.x * _21 + aPoint.y * _22 + aPoint.z * _23 + aPoint.w * _24;
michael@0 647 gfxFloat z = aPoint.x * _31 + aPoint.y * _32 + aPoint.z * _33 + aPoint.w * _34;
michael@0 648 gfxFloat w = aPoint.x * _41 + aPoint.y * _42 + aPoint.z * _43 + aPoint.w * _44;
michael@0 649
michael@0 650 return gfxPointH3D(x, y, z, w);
michael@0 651 }
michael@0 652
michael@0 653 gfxRect
michael@0 654 gfx3DMatrix::TransformBounds(const gfxRect& rect) const
michael@0 655 {
michael@0 656 gfxPoint points[4];
michael@0 657
michael@0 658 points[0] = Transform(rect.TopLeft());
michael@0 659 points[1] = Transform(gfxPoint(rect.X() + rect.Width(), rect.Y()));
michael@0 660 points[2] = Transform(gfxPoint(rect.X(), rect.Y() + rect.Height()));
michael@0 661 points[3] = Transform(gfxPoint(rect.X() + rect.Width(),
michael@0 662 rect.Y() + rect.Height()));
michael@0 663
michael@0 664 gfxFloat min_x, max_x;
michael@0 665 gfxFloat min_y, max_y;
michael@0 666
michael@0 667 min_x = max_x = points[0].x;
michael@0 668 min_y = max_y = points[0].y;
michael@0 669
michael@0 670 for (int i=1; i<4; i++) {
michael@0 671 min_x = min(points[i].x, min_x);
michael@0 672 max_x = max(points[i].x, max_x);
michael@0 673 min_y = min(points[i].y, min_y);
michael@0 674 max_y = max(points[i].y, max_y);
michael@0 675 }
michael@0 676
michael@0 677 return gfxRect(min_x, min_y, max_x - min_x, max_y - min_y);
michael@0 678 }
michael@0 679
michael@0 680 gfxQuad
michael@0 681 gfx3DMatrix::TransformRect(const gfxRect& aRect) const
michael@0 682 {
michael@0 683 gfxPoint points[4];
michael@0 684
michael@0 685 points[0] = Transform(aRect.TopLeft());
michael@0 686 points[1] = Transform(gfxPoint(aRect.X() + aRect.Width(), aRect.Y()));
michael@0 687 points[2] = Transform(gfxPoint(aRect.X() + aRect.Width(),
michael@0 688 aRect.Y() + aRect.Height()));
michael@0 689 points[3] = Transform(gfxPoint(aRect.X(), aRect.Y() + aRect.Height()));
michael@0 690
michael@0 691 // Could this ever result in lines that intersect? I don't think so.
michael@0 692 return gfxQuad(points[0], points[1], points[2], points[3]);
michael@0 693 }
michael@0 694
michael@0 695 bool
michael@0 696 gfx3DMatrix::Is2D() const
michael@0 697 {
michael@0 698 if (_13 != 0.0f || _14 != 0.0f ||
michael@0 699 _23 != 0.0f || _24 != 0.0f ||
michael@0 700 _31 != 0.0f || _32 != 0.0f || _33 != 1.0f || _34 != 0.0f ||
michael@0 701 _43 != 0.0f || _44 != 1.0f) {
michael@0 702 return false;
michael@0 703 }
michael@0 704 return true;
michael@0 705 }
michael@0 706
michael@0 707 bool
michael@0 708 gfx3DMatrix::Is2D(gfxMatrix* aMatrix) const
michael@0 709 {
michael@0 710 if (!Is2D()) {
michael@0 711 return false;
michael@0 712 }
michael@0 713 if (aMatrix) {
michael@0 714 aMatrix->xx = _11;
michael@0 715 aMatrix->yx = _12;
michael@0 716 aMatrix->xy = _21;
michael@0 717 aMatrix->yy = _22;
michael@0 718 aMatrix->x0 = _41;
michael@0 719 aMatrix->y0 = _42;
michael@0 720 }
michael@0 721 return true;
michael@0 722 }
michael@0 723
michael@0 724 bool
michael@0 725 gfx3DMatrix::CanDraw2D(gfxMatrix* aMatrix) const
michael@0 726 {
michael@0 727 if (_14 != 0.0f ||
michael@0 728 _24 != 0.0f ||
michael@0 729 _44 != 1.0f) {
michael@0 730 return false;
michael@0 731 }
michael@0 732 if (aMatrix) {
michael@0 733 aMatrix->xx = _11;
michael@0 734 aMatrix->yx = _12;
michael@0 735 aMatrix->xy = _21;
michael@0 736 aMatrix->yy = _22;
michael@0 737 aMatrix->x0 = _41;
michael@0 738 aMatrix->y0 = _42;
michael@0 739 }
michael@0 740 return true;
michael@0 741 }
michael@0 742
michael@0 743 gfx3DMatrix&
michael@0 744 gfx3DMatrix::ProjectTo2D()
michael@0 745 {
michael@0 746 _31 = 0.0f;
michael@0 747 _32 = 0.0f;
michael@0 748 _13 = 0.0f;
michael@0 749 _23 = 0.0f;
michael@0 750 _33 = 1.0f;
michael@0 751 _43 = 0.0f;
michael@0 752 _34 = 0.0f;
michael@0 753 return *this;
michael@0 754 }
michael@0 755
michael@0 756 gfxPoint gfx3DMatrix::ProjectPoint(const gfxPoint& aPoint) const
michael@0 757 {
michael@0 758 // Define a ray of the form P + Ut where t is a real number
michael@0 759 // w is assumed to always be 1 when transforming 3d points with our
michael@0 760 // 4x4 matrix.
michael@0 761 // p is our click point, q is another point on the same ray.
michael@0 762 //
michael@0 763 // Note: since the transformation is a general projective transformation and is not
michael@0 764 // necessarily affine, we can't just take a unit vector u, back-transform it, and use
michael@0 765 // it as unit vector on the back-transformed ray. Instead, we really must take two points
michael@0 766 // on the ray and back-transform them.
michael@0 767 gfxPoint3D p(aPoint.x, aPoint.y, 0);
michael@0 768 gfxPoint3D q(aPoint.x, aPoint.y, 1);
michael@0 769
michael@0 770 // Back transform the vectors (using w = 1) and normalize
michael@0 771 // back into 3d vectors by dividing by the w component.
michael@0 772 gfxPoint3D pback = Transform3D(p);
michael@0 773 gfxPoint3D qback = Transform3D(q);
michael@0 774 gfxPoint3D uback = qback - pback;
michael@0 775
michael@0 776 // Find the point where the back transformed line intersects z=0
michael@0 777 // and find t.
michael@0 778
michael@0 779 float t = -pback.z / uback.z;
michael@0 780
michael@0 781 gfxPoint result(pback.x + t*uback.x, pback.y + t*uback.y);
michael@0 782
michael@0 783 return result;
michael@0 784 }
michael@0 785
michael@0 786 gfxRect gfx3DMatrix::ProjectRectBounds(const gfxRect& aRect) const
michael@0 787 {
michael@0 788 gfxPoint points[4];
michael@0 789
michael@0 790 points[0] = ProjectPoint(aRect.TopLeft());
michael@0 791 points[1] = ProjectPoint(aRect.TopRight());
michael@0 792 points[2] = ProjectPoint(aRect.BottomLeft());
michael@0 793 points[3] = ProjectPoint(aRect.BottomRight());
michael@0 794
michael@0 795 gfxFloat min_x, max_x;
michael@0 796 gfxFloat min_y, max_y;
michael@0 797
michael@0 798 min_x = max_x = points[0].x;
michael@0 799 min_y = max_y = points[0].y;
michael@0 800
michael@0 801 for (int i=1; i<4; i++) {
michael@0 802 min_x = min(points[i].x, min_x);
michael@0 803 max_x = max(points[i].x, max_x);
michael@0 804 min_y = min(points[i].y, min_y);
michael@0 805 max_y = max(points[i].y, max_y);
michael@0 806 }
michael@0 807
michael@0 808 return gfxRect(min_x, min_y, max_x - min_x, max_y - min_y);
michael@0 809 }
michael@0 810
michael@0 811 gfxRect gfx3DMatrix::UntransformBounds(const gfxRect& aRect, const gfxRect& aChildBounds) const
michael@0 812 {
michael@0 813 if (Is2D()) {
michael@0 814 return Inverse().TransformBounds(aRect);
michael@0 815 }
michael@0 816 gfxRect bounds = TransformBounds(aChildBounds);
michael@0 817
michael@0 818 gfxRect rect = aRect.Intersect(bounds);
michael@0 819
michael@0 820 return Inverse().ProjectRectBounds(rect);
michael@0 821 }
michael@0 822
michael@0 823 bool gfx3DMatrix::UntransformPoint(const gfxPoint& aPoint, const gfxRect& aChildBounds, gfxPoint* aOut) const
michael@0 824 {
michael@0 825 if (Is2D()) {
michael@0 826 *aOut = Inverse().Transform(aPoint);
michael@0 827 return true;
michael@0 828 }
michael@0 829 gfxRect bounds = TransformBounds(aChildBounds);
michael@0 830
michael@0 831 if (!bounds.Contains(aPoint)) {
michael@0 832 return false;
michael@0 833 }
michael@0 834
michael@0 835 *aOut = Inverse().ProjectPoint(aPoint);
michael@0 836 return true;
michael@0 837 }
michael@0 838
michael@0 839 gfxPoint3D gfx3DMatrix::GetNormalVector() const
michael@0 840 {
michael@0 841 // Define a plane in transformed space as the transformations
michael@0 842 // of 3 points on the z=0 screen plane.
michael@0 843 gfxPoint3D a = Transform3D(gfxPoint3D(0, 0, 0));
michael@0 844 gfxPoint3D b = Transform3D(gfxPoint3D(0, 1, 0));
michael@0 845 gfxPoint3D c = Transform3D(gfxPoint3D(1, 0, 0));
michael@0 846
michael@0 847 // Convert to two vectors on the surface of the plane.
michael@0 848 gfxPoint3D ab = b - a;
michael@0 849 gfxPoint3D ac = c - a;
michael@0 850
michael@0 851 return ac.CrossProduct(ab);
michael@0 852 }
michael@0 853
michael@0 854 bool gfx3DMatrix::IsBackfaceVisible() const
michael@0 855 {
michael@0 856 // Inverse()._33 < 0;
michael@0 857 gfxFloat det = Determinant();
michael@0 858 float _33 = _12*_24*_41 - _14*_22*_41 +
michael@0 859 _14*_21*_42 - _11*_24*_42 -
michael@0 860 _12*_21*_44 + _11*_22*_44;
michael@0 861 return (_33 * det) < 0;
michael@0 862 }
michael@0 863
michael@0 864 void gfx3DMatrix::NudgeToIntegers(void)
michael@0 865 {
michael@0 866 NudgeToInteger(&_11);
michael@0 867 NudgeToInteger(&_12);
michael@0 868 NudgeToInteger(&_13);
michael@0 869 NudgeToInteger(&_14);
michael@0 870 NudgeToInteger(&_21);
michael@0 871 NudgeToInteger(&_22);
michael@0 872 NudgeToInteger(&_23);
michael@0 873 NudgeToInteger(&_24);
michael@0 874 NudgeToInteger(&_31);
michael@0 875 NudgeToInteger(&_32);
michael@0 876 NudgeToInteger(&_33);
michael@0 877 NudgeToInteger(&_34);
michael@0 878 NudgeToInteger(&_41);
michael@0 879 NudgeToInteger(&_42);
michael@0 880 NudgeToInteger(&_43);
michael@0 881 NudgeToInteger(&_44);
michael@0 882 }

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