1
// Copyright 2008 The Closure Library Authors. All Rights Reserved.
2
//
3
// Licensed under the Apache License, Version 2.0 (the "License");
4
// you may not use this file except in compliance with the License.
5
// You may obtain a copy of the License at
6
//
7
//      http://www.apache.org/licenses/LICENSE-2.0
8
//
9
// Unless required by applicable law or agreed to in writing, software
10
// distributed under the License is distributed on an "AS-IS" BASIS,
11
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12
// See the License for the specific language governing permissions and
13
// limitations under the License.
14

15

16
/**
17
 * @fileoverview Provides an object representation of an AffineTransform and
18
 * methods for working with it.
19
 */
20

21

22
goog.provide('goog.graphics.AffineTransform');
23

24

25

26
/**
27
 * Creates a 2D affine transform. An affine transform performs a linear
28
 * mapping from 2D coordinates to other 2D coordinates that preserves the
29
 * "straightness" and "parallelness" of lines.
30
 *
31
 * Such a coordinate transformation can be represented by a 3 row by 3 column
32
 * matrix with an implied last row of [ 0 0 1 ]. This matrix transforms source
33
 * coordinates (x,y) into destination coordinates (x',y') by considering them
34
 * to be a column vector and multiplying the coordinate vector by the matrix
35
 * according to the following process:
36
 * <pre>
37
 *      [ x']   [  m00  m01  m02  ] [ x ]   [ m00x + m01y + m02 ]
38
 *      [ y'] = [  m10  m11  m12  ] [ y ] = [ m10x + m11y + m12 ]
39
 *      [ 1 ]   [   0    0    1   ] [ 1 ]   [         1         ]
40
 * </pre>
41
 *
42
 * This class is optimized for speed and minimizes calculations based on its
43
 * knowledge of the underlying matrix (as opposed to say simply performing
44
 * matrix multiplication).
45
 *
46
 * @param {number=} opt_m00 The m00 coordinate of the transform.
47
 * @param {number=} opt_m10 The m10 coordinate of the transform.
48
 * @param {number=} opt_m01 The m01 coordinate of the transform.
49
 * @param {number=} opt_m11 The m11 coordinate of the transform.
50
 * @param {number=} opt_m02 The m02 coordinate of the transform.
51
 * @param {number=} opt_m12 The m12 coordinate of the transform.
52
 * @constructor
53
 * @final
54
 */
55
goog.graphics.AffineTransform = function(
56
    opt_m00, opt_m10, opt_m01, opt_m11, opt_m02, opt_m12) {
57
  if (arguments.length == 6) {
58
    this.setTransform(
59
        /** @type {number} */ (opt_m00),
60
        /** @type {number} */ (opt_m10),
61
        /** @type {number} */ (opt_m01),
62
        /** @type {number} */ (opt_m11),
63
        /** @type {number} */ (opt_m02),
64
        /** @type {number} */ (opt_m12));
65
  } else if (arguments.length != 0) {
66
    throw Error('Insufficient matrix parameters');
67
  } else {
68
    this.m00_ = this.m11_ = 1;
69
    this.m10_ = this.m01_ = this.m02_ = this.m12_ = 0;
70
  }
71
};
72

73

74
/**
75
 * @return {boolean} Whether this transform is the identity transform.
76
 */
77
goog.graphics.AffineTransform.prototype.isIdentity = function() {
78
  return this.m00_ == 1 && this.m10_ == 0 && this.m01_ == 0 && this.m11_ == 1 &&
79
      this.m02_ == 0 && this.m12_ == 0;
80
};
81

82

83
/**
84
 * @return {!goog.graphics.AffineTransform} A copy of this transform.
85
 */
86
goog.graphics.AffineTransform.prototype.clone = function() {
87
  return new goog.graphics.AffineTransform(
88
      this.m00_, this.m10_, this.m01_, this.m11_, this.m02_, this.m12_);
89
};
90

91

92
/**
93
 * Sets this transform to the matrix specified by the 6 values.
94
 *
95
 * @param {number} m00 The m00 coordinate of the transform.
96
 * @param {number} m10 The m10 coordinate of the transform.
97
 * @param {number} m01 The m01 coordinate of the transform.
98
 * @param {number} m11 The m11 coordinate of the transform.
99
 * @param {number} m02 The m02 coordinate of the transform.
100
 * @param {number} m12 The m12 coordinate of the transform.
101
 * @return {!goog.graphics.AffineTransform} This affine transform.
102
 */
103
goog.graphics.AffineTransform.prototype.setTransform = function(
104
    m00, m10, m01, m11, m02, m12) {
105
  if (!goog.isNumber(m00) || !goog.isNumber(m10) || !goog.isNumber(m01) ||
106
      !goog.isNumber(m11) || !goog.isNumber(m02) || !goog.isNumber(m12)) {
107
    throw Error('Invalid transform parameters');
108
  }
109
  this.m00_ = m00;
110
  this.m10_ = m10;
111
  this.m01_ = m01;
112
  this.m11_ = m11;
113
  this.m02_ = m02;
114
  this.m12_ = m12;
115
  return this;
116
};
117

118

119
/**
120
 * Sets this transform to be identical to the given transform.
121
 *
122
 * @param {!goog.graphics.AffineTransform} tx The transform to copy.
123
 * @return {!goog.graphics.AffineTransform} This affine transform.
124
 */
125
goog.graphics.AffineTransform.prototype.copyFrom = function(tx) {
126
  this.m00_ = tx.m00_;
127
  this.m10_ = tx.m10_;
128
  this.m01_ = tx.m01_;
129
  this.m11_ = tx.m11_;
130
  this.m02_ = tx.m02_;
131
  this.m12_ = tx.m12_;
132
  return this;
133
};
134

135

136
/**
137
 * Concatenates this transform with a scaling transformation.
138
 *
139
 * @param {number} sx The x-axis scaling factor.
140
 * @param {number} sy The y-axis scaling factor.
141
 * @return {!goog.graphics.AffineTransform} This affine transform.
142
 */
143
goog.graphics.AffineTransform.prototype.scale = function(sx, sy) {
144
  this.m00_ *= sx;
145
  this.m10_ *= sx;
146
  this.m01_ *= sy;
147
  this.m11_ *= sy;
148
  return this;
149
};
150

151

152
/**
153
 * Pre-concatenates this transform with a scaling transformation,
154
 * i.e. calculates the following matrix product:
155
 *
156
 * <pre>
157
 * [sx  0 0] [m00 m01 m02]
158
 * [ 0 sy 0] [m10 m11 m12]
159
 * [ 0  0 1] [  0   0   1]
160
 * </pre>
161
 *
162
 * @param {number} sx The x-axis scaling factor.
163
 * @param {number} sy The y-axis scaling factor.
164
 * @return {!goog.graphics.AffineTransform} This affine transform.
165
 */
166
goog.graphics.AffineTransform.prototype.preScale = function(sx, sy) {
167
  this.m00_ *= sx;
168
  this.m01_ *= sx;
169
  this.m02_ *= sx;
170
  this.m10_ *= sy;
171
  this.m11_ *= sy;
172
  this.m12_ *= sy;
173
  return this;
174
};
175

176

177
/**
178
 * Concatenates this transform with a translate transformation.
179
 *
180
 * @param {number} dx The distance to translate in the x direction.
181
 * @param {number} dy The distance to translate in the y direction.
182
 * @return {!goog.graphics.AffineTransform} This affine transform.
183
 */
184
goog.graphics.AffineTransform.prototype.translate = function(dx, dy) {
185
  this.m02_ += dx * this.m00_ + dy * this.m01_;
186
  this.m12_ += dx * this.m10_ + dy * this.m11_;
187
  return this;
188
};
189

190

191
/**
192
 * Pre-concatenates this transform with a translate transformation,
193
 * i.e. calculates the following matrix product:
194
 *
195
 * <pre>
196
 * [1 0 dx] [m00 m01 m02]
197
 * [0 1 dy] [m10 m11 m12]
198
 * [0 0  1] [  0   0   1]
199
 * </pre>
200
 *
201
 * @param {number} dx The distance to translate in the x direction.
202
 * @param {number} dy The distance to translate in the y direction.
203
 * @return {!goog.graphics.AffineTransform} This affine transform.
204
 */
205
goog.graphics.AffineTransform.prototype.preTranslate = function(dx, dy) {
206
  this.m02_ += dx;
207
  this.m12_ += dy;
208
  return this;
209
};
210

211

212
/**
213
 * Concatenates this transform with a rotation transformation around an anchor
214
 * point.
215
 *
216
 * @param {number} theta The angle of rotation measured in radians.
217
 * @param {number} x The x coordinate of the anchor point.
218
 * @param {number} y The y coordinate of the anchor point.
219
 * @return {!goog.graphics.AffineTransform} This affine transform.
220
 */
221
goog.graphics.AffineTransform.prototype.rotate = function(theta, x, y) {
222
  return this.concatenate(
223
      goog.graphics.AffineTransform.getRotateInstance(theta, x, y));
224
};
225

226

227
/**
228
 * Pre-concatenates this transform with a rotation transformation around an
229
 * anchor point.
230
 *
231
 * @param {number} theta The angle of rotation measured in radians.
232
 * @param {number} x The x coordinate of the anchor point.
233
 * @param {number} y The y coordinate of the anchor point.
234
 * @return {!goog.graphics.AffineTransform} This affine transform.
235
 */
236
goog.graphics.AffineTransform.prototype.preRotate = function(theta, x, y) {
237
  return this.preConcatenate(
238
      goog.graphics.AffineTransform.getRotateInstance(theta, x, y));
239
};
240

241

242
/**
243
 * Concatenates this transform with a shear transformation.
244
 *
245
 * @param {number} shx The x shear factor.
246
 * @param {number} shy The y shear factor.
247
 * @return {!goog.graphics.AffineTransform} This affine transform.
248
 */
249
goog.graphics.AffineTransform.prototype.shear = function(shx, shy) {
250
  var m00 = this.m00_;
251
  var m10 = this.m10_;
252
  this.m00_ += shy * this.m01_;
253
  this.m10_ += shy * this.m11_;
254
  this.m01_ += shx * m00;
255
  this.m11_ += shx * m10;
256
  return this;
257
};
258

259

260
/**
261
 * Pre-concatenates this transform with a shear transformation.
262
 * i.e. calculates the following matrix product:
263
 *
264
 * <pre>
265
 * [  1 shx 0] [m00 m01 m02]
266
 * [shy   1 0] [m10 m11 m12]
267
 * [  0   0 1] [  0   0   1]
268
 * </pre>
269
 *
270
 * @param {number} shx The x shear factor.
271
 * @param {number} shy The y shear factor.
272
 * @return {!goog.graphics.AffineTransform} This affine transform.
273
 */
274
goog.graphics.AffineTransform.prototype.preShear = function(shx, shy) {
275
  var m00 = this.m00_;
276
  var m01 = this.m01_;
277
  var m02 = this.m02_;
278
  this.m00_ += shx * this.m10_;
279
  this.m01_ += shx * this.m11_;
280
  this.m02_ += shx * this.m12_;
281
  this.m10_ += shy * m00;
282
  this.m11_ += shy * m01;
283
  this.m12_ += shy * m02;
284
  return this;
285
};
286

287

288
/**
289
 * @return {string} A string representation of this transform. The format of
290
 *     of the string is compatible with SVG matrix notation, i.e.
291
 *     "matrix(a,b,c,d,e,f)".
292
 * @override
293
 */
294
goog.graphics.AffineTransform.prototype.toString = function() {
295
  return 'matrix(' +
296
      [this.m00_, this.m10_, this.m01_, this.m11_, this.m02_, this.m12_].join(
297
          ',') +
298
      ')';
299
};
300

301

302
/**
303
 * @return {number} The scaling factor in the x-direction (m00).
304
 */
305
goog.graphics.AffineTransform.prototype.getScaleX = function() {
306
  return this.m00_;
307
};
308

309

310
/**
311
 * @return {number} The scaling factor in the y-direction (m11).
312
 */
313
goog.graphics.AffineTransform.prototype.getScaleY = function() {
314
  return this.m11_;
315
};
316

317

318
/**
319
 * @return {number} The translation in the x-direction (m02).
320
 */
321
goog.graphics.AffineTransform.prototype.getTranslateX = function() {
322
  return this.m02_;
323
};
324

325

326
/**
327
 * @return {number} The translation in the y-direction (m12).
328
 */
329
goog.graphics.AffineTransform.prototype.getTranslateY = function() {
330
  return this.m12_;
331
};
332

333

334
/**
335
 * @return {number} The shear factor in the x-direction (m01).
336
 */
337
goog.graphics.AffineTransform.prototype.getShearX = function() {
338
  return this.m01_;
339
};
340

341

342
/**
343
 * @return {number} The shear factor in the y-direction (m10).
344
 */
345
goog.graphics.AffineTransform.prototype.getShearY = function() {
346
  return this.m10_;
347
};
348

349

350
/**
351
 * Concatenates an affine transform to this transform.
352
 *
353
 * @param {!goog.graphics.AffineTransform} tx The transform to concatenate.
354
 * @return {!goog.graphics.AffineTransform} This affine transform.
355
 */
356
goog.graphics.AffineTransform.prototype.concatenate = function(tx) {
357
  var m0 = this.m00_;
358
  var m1 = this.m01_;
359
  this.m00_ = tx.m00_ * m0 + tx.m10_ * m1;
360
  this.m01_ = tx.m01_ * m0 + tx.m11_ * m1;
361
  this.m02_ += tx.m02_ * m0 + tx.m12_ * m1;
362

363
  m0 = this.m10_;
364
  m1 = this.m11_;
365
  this.m10_ = tx.m00_ * m0 + tx.m10_ * m1;
366
  this.m11_ = tx.m01_ * m0 + tx.m11_ * m1;
367
  this.m12_ += tx.m02_ * m0 + tx.m12_ * m1;
368
  return this;
369
};
370

371

372
/**
373
 * Pre-concatenates an affine transform to this transform.
374
 *
375
 * @param {!goog.graphics.AffineTransform} tx The transform to preconcatenate.
376
 * @return {!goog.graphics.AffineTransform} This affine transform.
377
 */
378
goog.graphics.AffineTransform.prototype.preConcatenate = function(tx) {
379
  var m0 = this.m00_;
380
  var m1 = this.m10_;
381
  this.m00_ = tx.m00_ * m0 + tx.m01_ * m1;
382
  this.m10_ = tx.m10_ * m0 + tx.m11_ * m1;
383

384
  m0 = this.m01_;
385
  m1 = this.m11_;
386
  this.m01_ = tx.m00_ * m0 + tx.m01_ * m1;
387
  this.m11_ = tx.m10_ * m0 + tx.m11_ * m1;
388

389
  m0 = this.m02_;
390
  m1 = this.m12_;
391
  this.m02_ = tx.m00_ * m0 + tx.m01_ * m1 + tx.m02_;
392
  this.m12_ = tx.m10_ * m0 + tx.m11_ * m1 + tx.m12_;
393
  return this;
394
};
395

396

397
/**
398
 * Transforms an array of coordinates by this transform and stores the result
399
 * into a destination array.
400
 *
401
 * @param {!Array<number>} src The array containing the source points
402
 *     as x, y value pairs.
403
 * @param {number} srcOff The offset to the first point to be transformed.
404
 * @param {!Array<number>} dst The array into which to store the transformed
405
 *     point pairs.
406
 * @param {number} dstOff The offset of the location of the first transformed
407
 *     point in the destination array.
408
 * @param {number} numPts The number of points to transform.
409
 */
410
goog.graphics.AffineTransform.prototype.transform = function(
411
    src, srcOff, dst, dstOff, numPts) {
412
  var i = srcOff;
413
  var j = dstOff;
414
  var srcEnd = srcOff + 2 * numPts;
415
  while (i < srcEnd) {
416
    var x = src[i++];
417
    var y = src[i++];
418
    dst[j++] = x * this.m00_ + y * this.m01_ + this.m02_;
419
    dst[j++] = x * this.m10_ + y * this.m11_ + this.m12_;
420
  }
421
};
422

423

424
/**
425
 * @return {number} The determinant of this transform.
426
 */
427
goog.graphics.AffineTransform.prototype.getDeterminant = function() {
428
  return this.m00_ * this.m11_ - this.m01_ * this.m10_;
429
};
430

431

432
/**
433
 * Returns whether the transform is invertible. A transform is not invertible
434
 * if the determinant is 0 or any value is non-finite or NaN.
435
 *
436
 * @return {boolean} Whether the transform is invertible.
437
 */
438
goog.graphics.AffineTransform.prototype.isInvertible = function() {
439
  var det = this.getDeterminant();
440
  return isFinite(det) && isFinite(this.m02_) && isFinite(this.m12_) &&
441
      det != 0;
442
};
443

444

445
/**
446
 * @return {!goog.graphics.AffineTransform} An AffineTransform object
447
 *     representing the inverse transformation.
448
 */
449
goog.graphics.AffineTransform.prototype.createInverse = function() {
450
  var det = this.getDeterminant();
451
  return new goog.graphics.AffineTransform(
452
      this.m11_ / det, -this.m10_ / det, -this.m01_ / det, this.m00_ / det,
453
      (this.m01_ * this.m12_ - this.m11_ * this.m02_) / det,
454
      (this.m10_ * this.m02_ - this.m00_ * this.m12_) / det);
455
};
456

457

458
/**
459
 * Creates a transform representing a scaling transformation.
460
 *
461
 * @param {number} sx The x-axis scaling factor.
462
 * @param {number} sy The y-axis scaling factor.
463
 * @return {!goog.graphics.AffineTransform} A transform representing a scaling
464
 *     transformation.
465
 */
466
goog.graphics.AffineTransform.getScaleInstance = function(sx, sy) {
467
  return new goog.graphics.AffineTransform().setToScale(sx, sy);
468
};
469

470

471
/**
472
 * Creates a transform representing a translation transformation.
473
 *
474
 * @param {number} dx The distance to translate in the x direction.
475
 * @param {number} dy The distance to translate in the y direction.
476
 * @return {!goog.graphics.AffineTransform} A transform representing a
477
 *     translation transformation.
478
 */
479
goog.graphics.AffineTransform.getTranslateInstance = function(dx, dy) {
480
  return new goog.graphics.AffineTransform().setToTranslation(dx, dy);
481
};
482

483

484
/**
485
 * Creates a transform representing a shearing transformation.
486
 *
487
 * @param {number} shx The x-axis shear factor.
488
 * @param {number} shy The y-axis shear factor.
489
 * @return {!goog.graphics.AffineTransform} A transform representing a shearing
490
 *     transformation.
491
 */
492
goog.graphics.AffineTransform.getShearInstance = function(shx, shy) {
493
  return new goog.graphics.AffineTransform().setToShear(shx, shy);
494
};
495

496

497
/**
498
 * Creates a transform representing a rotation transformation.
499
 *
500
 * @param {number} theta The angle of rotation measured in radians.
501
 * @param {number} x The x coordinate of the anchor point.
502
 * @param {number} y The y coordinate of the anchor point.
503
 * @return {!goog.graphics.AffineTransform} A transform representing a rotation
504
 *     transformation.
505
 */
506
goog.graphics.AffineTransform.getRotateInstance = function(theta, x, y) {
507
  return new goog.graphics.AffineTransform().setToRotation(theta, x, y);
508
};
509

510

511
/**
512
 * Sets this transform to a scaling transformation.
513
 *
514
 * @param {number} sx The x-axis scaling factor.
515
 * @param {number} sy The y-axis scaling factor.
516
 * @return {!goog.graphics.AffineTransform} This affine transform.
517
 */
518
goog.graphics.AffineTransform.prototype.setToScale = function(sx, sy) {
519
  return this.setTransform(sx, 0, 0, sy, 0, 0);
520
};
521

522

523
/**
524
 * Sets this transform to a translation transformation.
525
 *
526
 * @param {number} dx The distance to translate in the x direction.
527
 * @param {number} dy The distance to translate in the y direction.
528
 * @return {!goog.graphics.AffineTransform} This affine transform.
529
 */
530
goog.graphics.AffineTransform.prototype.setToTranslation = function(dx, dy) {
531
  return this.setTransform(1, 0, 0, 1, dx, dy);
532
};
533

534

535
/**
536
 * Sets this transform to a shearing transformation.
537
 *
538
 * @param {number} shx The x-axis shear factor.
539
 * @param {number} shy The y-axis shear factor.
540
 * @return {!goog.graphics.AffineTransform} This affine transform.
541
 */
542
goog.graphics.AffineTransform.prototype.setToShear = function(shx, shy) {
543
  return this.setTransform(1, shy, shx, 1, 0, 0);
544
};
545

546

547
/**
548
 * Sets this transform to a rotation transformation.
549
 *
550
 * @param {number} theta The angle of rotation measured in radians.
551
 * @param {number} x The x coordinate of the anchor point.
552
 * @param {number} y The y coordinate of the anchor point.
553
 * @return {!goog.graphics.AffineTransform} This affine transform.
554
 */
555
goog.graphics.AffineTransform.prototype.setToRotation = function(theta, x, y) {
556
  var cos = Math.cos(theta);
557
  var sin = Math.sin(theta);
558
  return this.setTransform(
559
      cos, sin, -sin, cos, x - x * cos + y * sin, y - x * sin - y * cos);
560
};
561

562

563
/**
564
 * Compares two affine transforms for equality.
565
 *
566
 * @param {goog.graphics.AffineTransform} tx The other affine transform.
567
 * @return {boolean} whether the two transforms are equal.
568
 */
569
goog.graphics.AffineTransform.prototype.equals = function(tx) {
570
  if (this == tx) {
571
    return true;
572
  }
573
  if (!tx) {
574
    return false;
575
  }
576
  return this.m00_ == tx.m00_ && this.m01_ == tx.m01_ && this.m02_ == tx.m02_ &&
577
      this.m10_ == tx.m10_ && this.m11_ == tx.m11_ && this.m12_ == tx.m12_;
578
};
579

580