1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
|
<!doctype html>
<meta charset=utf-8>
<script src='/resources/testharness.js'></script>
<script src='/resources/testharnessreport.js'></script>
<script src='../testcommon.js'></script>
<div id='log'></div>
<script type='text/javascript'>
'use strict';
// We don't have an official spec to define the distance between two transform
// lists, but we still need this for DevTools, so Gecko and Servo backend use
// the similar rules to define the distance. If there is a spec for it, we have
// to update this test file.
const EPSILON = 0.00001;
// |v| should be a unit vector (i.e. having length 1)
function getQuaternion(v, angle) {
return [
v[0] * Math.sin(angle / 2.0),
v[1] * Math.sin(angle / 2.0),
v[2] * Math.sin(angle / 2.0),
Math.cos(angle / 2.0)
];
}
function computeRotateDistance(q1, q2) {
const dot = q1.reduce((sum, e, i) => sum + e * q2[i], 0);
return Math.acos(Math.min(Math.max(dot, -1.0), 1.0)) * 2.0;
}
function createMatrixFromArray(array) {
return (array.length === 16 ? 'matrix3d' : 'matrix') + `(${array.join()})`;
}
function rotate3dToMatrix(x, y, z, radian) {
var sc = Math.sin(radian / 2) * Math.cos(radian / 2);
var sq = Math.sin(radian / 2) * Math.sin(radian / 2);
// Normalize the vector.
var length = Math.sqrt(x*x + y*y + z*z);
x /= length;
y /= length;
z /= length;
return [
1 - 2 * (y*y + z*z) * sq,
2 * (x * y * sq + z * sc),
2 * (x * z * sq - y * sc),
0,
2 * (x * y * sq - z * sc),
1 - 2 * (x*x + z*z) * sq,
2 * (y * z * sq + x * sc),
0,
2 * (x * z * sq + y * sc),
2 * (y * z * sq - x * sc),
1 - 2 * (x*x + y*y) * sq,
0,
0,
0,
0,
1
];
}
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform', 'none', 'none');
assert_equals(dist, 0, 'distance of translate');
}, 'Test distance of none and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform', 'translate(100px)', 'none');
assert_equals(dist, 100, 'distance of translate');
}, 'Test distance of translate function and none');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform', 'translate(100px)', 'translate(200px)');
assert_equals(dist, 200 - 100, 'distance of translate');
}, 'Test distance of translate functions');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform', 'translate3d(100px, 0, 50px)', 'none');
assert_equals(dist, Math.sqrt(100 * 100 + 50 * 50),
'distance of translate3d');
}, 'Test distance of translate3d function and none');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform',
'translate3d(100px, 0, 50px)',
'translate3d(200px, 80px, 0)');
assert_equals(dist, Math.sqrt(100 * 100 + 80 * 80 + 50 * 50),
'distance of translate');
}, 'Test distance of translate3d functions');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform', 'scale(1.5)', 'none');
assert_equals(dist, Math.sqrt(0.5 * 0.5 + 0.5 * 0.5), 'distance of scale');
}, 'Test distance of scale function and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform', 'scale(1.5)', 'scale(2.0)');
assert_equals(dist, Math.sqrt(0.5 * 0.5 + 0.5 * 0.5), 'distance of scale');
}, 'Test distance of scale functions');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'scale3d(1.5, 1.5, 1.5)',
'none');
assert_equals(dist,
Math.sqrt(0.5 * 0.5 + 0.5 * 0.5 + 0.5 * 0.5),
'distance of scale3d');
}, 'Test distance of scale3d function and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'scale3d(1.5, 1.5, 1.5)',
'scale3d(2.0, 2.0, 1.0)');
assert_equals(dist,
Math.sqrt(0.5 * 0.5 + 0.5 * 0.5 + 0.5 * 0.5),
'distance of scale3d');
}, 'Test distance of scale3d functions');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform', 'rotate(45deg)', 'rotate(90deg)');
assert_approx_equals(dist, Math.PI / 2.0 - Math.PI / 4.0, EPSILON, 'distance of rotate');
}, 'Test distance of rotate functions');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform', 'rotate(45deg)', 'none');
assert_approx_equals(dist, Math.PI / 4.0, EPSILON, 'distance of rotate');
}, 'Test distance of rotate function and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'rotate3d(0, 1, 0, 90deg)',
'none');
assert_approx_equals(dist, Math.PI / 2, EPSILON, 'distance of rotate3d');
}, 'Test distance of rotate3d function and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'rotate3d(0, 0, 1, 90deg)',
'rotate3d(1, 0, 0, 90deg)');
let q1 = getQuaternion([0, 0, 1], Math.PI / 2.0);
let q2 = getQuaternion([1, 0, 0], Math.PI / 2.0);
assert_approx_equals(dist, computeRotateDistance(q1, q2), EPSILON, 'distance of rotate3d');
}, 'Test distance of rotate3d functions');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'rotate3d(0, 0, 1, 90deg)',
'rotate3d(0, 0, 0, 90deg)');
assert_approx_equals(dist, Math.PI / 2, EPSILON, 'distance of rotate3d');
}, 'Test distance of rotate3d functions whose direction vector cannot be ' +
'normalized');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform', 'skew(1rad, 0.5rad)', 'none');
assert_approx_equals(dist, Math.sqrt(1 * 1 + 0.5 * 0.5), EPSILON, 'distance of skew');
}, 'Test distance of skew function and none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'skew(1rad, 0.5rad)',
'skew(-1rad, 0)');
assert_approx_equals(dist, Math.sqrt(2 * 2 + 0.5 * 0.5), EPSILON, 'distance of skew');
}, 'Test distance of skew functions');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'perspective(128px)',
'none');
assert_equals(dist, Infinity, 'distance of perspective');
}, 'Test distance of perspective function and none');
test(function(t) {
var target = addDiv(t);
// perspective(0) is treated as perspective(inf) because perspective length
// should be greater than or equal to zero.
var dist = getDistance(target, 'transform',
'perspective(128px)',
'perspective(0)');
assert_equals(dist, 128, 'distance of perspective');
}, 'Test distance of perspective function and an invalid perspective');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'perspective(128px)',
'perspective(1024px)');
assert_equals(dist, 1024 - 128, 'distance of perspective');
}, 'Test distance of perspective functions');
test(function(t) {
var target = addDiv(t);
var sin_30 = Math.sin(Math.PI / 6);
var cos_30 = Math.cos(Math.PI / 6);
// matrix => translate(100, 0) rotate(30deg).
var matrix = createMatrixFromArray([ cos_30, sin_30,
-sin_30, cos_30,
100, 0 ]);
var dist = getDistance(target, 'transform', matrix, 'none');
assert_approx_equals(dist,
Math.sqrt(100 * 100 + (Math.PI / 6) * (Math.PI / 6)),
EPSILON,
'distance of matrix');
}, 'Test distance of matrix function and none');
test(function(t) {
var target = addDiv(t);
var sin_30 = Math.sin(Math.PI / 6);
var cos_30 = Math.cos(Math.PI / 6);
// matrix1 => translate(100, 0) rotate(30deg).
var matrix1 = createMatrixFromArray([ cos_30, sin_30,
-sin_30, cos_30,
100, 0 ]);
// matrix2 => translate(0, 100) scale(0.5).
var matrix2 = createMatrixFromArray([ 0.5, 0, 0, 0.5, 0, 100 ]);
var dist = getDistance(target, 'transform', matrix1, matrix2);
assert_approx_equals(dist,
Math.sqrt(100 * 100 + 100 * 100 + // translate
(Math.PI / 6) * (Math.PI / 6) + // rotate
0.5 * 0.5 + 0.5 * 0.5), // scale
EPSILON,
'distance of matrix');
}, 'Test distance of matrix functions');
test(function(t) {
var target = addDiv(t);
var matrix = createMatrixFromArray(rotate3dToMatrix(0, 1, 0, Math.PI / 6));
var dist = getDistance(target, 'transform', matrix, 'none');
assert_approx_equals(dist, Math.PI / 6, EPSILON, 'distance of matrix3d');
}, 'Test distance of matrix3d function and none');
test(function(t) {
var target = addDiv(t);
// matrix1 => rotate3d(0, 1, 0, 30deg).
var matrix1 = createMatrixFromArray(rotate3dToMatrix(0, 1, 0, Math.PI / 6));
// matrix1 => translate3d(100, 0, 0) scale3d(0.5, 0.5, 0.5).
var matrix2 = createMatrixFromArray([ 0.5, 0, 0, 0,
0, 0.5, 0, 0,
0, 0, 0.5, 0,
100, 0, 0, 1 ]);
var dist = getDistance(target, 'transform', matrix1, matrix2);
assert_approx_equals(dist,
Math.sqrt(100 * 100 + // translate
0.5 * 0.5 * 3 + // scale
(Math.PI / 6) * (Math.PI / 6)), // rotate
EPSILON,
'distance of matrix');
}, 'Test distance of matrix3d functions');
test(function(t) {
var target = addDiv(t);
var cos_180 = Math.cos(Math.PI);
var sin_180 = Math.sin(Math.PI);
// matrix1 => translate3d(100px, 50px, -10px) skew(45deg).
var matrix1 = createMatrixFromArray([ 1, 0, 0, 0,
Math.tan(Math.PI/4.0), 1, 0, 0,
0, 0, 1, 0,
100, 50, -10, 1]);
// matrix2 => translate3d(1000px, 0, 0) rotate3d(1, 0, 0, 180deg).
var matrix2 = createMatrixFromArray([ 1, 0, 0, 0,
0, cos_180, sin_180, 0,
0, -sin_180, cos_180, 0,
1000, 0, 0, 1 ]);
var dist = getDistance(target, 'transform', matrix1, matrix2);
assert_approx_equals(dist,
Math.sqrt(900 * 900 + 50 * 50 + 10 * 10 + // translate
Math.PI * Math.PI + // rotate
(Math.PI / 4) * (Math.PI / 4)), // skew angle
EPSILON,
'distance of matrix');
}, 'Test distance of matrix3d functions with skew factors');
test(function(t) {
var target = addDiv(t);
var dist =
getDistance(target, 'transform',
'rotate(180deg) translate(1000px)',
'rotate(360deg) translate(0px)');
assert_approx_equals(dist, Math.sqrt(1000 * 1000 + Math.PI * Math.PI), EPSILON,
'distance of transform lists');
}, 'Test distance of transform lists');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'translate(100px) rotate(180deg)',
'translate(50px) rotate(90deg) scale(5) skew(1rad)');
assert_approx_equals(dist,
Math.sqrt(50 * 50 +
Math.PI / 2 * Math.PI / 2 +
4 * 4 * 2 +
1 * 1),
EPSILON,
'distance of transform lists');
}, 'Test distance of transform lists where one has extra items');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'translate(1000px) rotate3d(1, 0, 0, 180deg)',
'translate(1000px) scale3d(2.5, 0.5, 1)');
assert_equals(dist, Math.sqrt(Math.PI * Math.PI + 1.5 * 1.5 + 0.5 * 0.5),
'distance of transform lists');
}, 'Test distance of mismatched transform lists');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'transform',
'translate(100px) skew(1rad)',
'translate(1000px) rotate3d(0, 1, 0, -2rad)');
assert_approx_equals(dist,
Math.sqrt(900 * 900 + 1 * 1 + 2 * 2),
EPSILON,
'distance of transform lists');
}, 'Test distance of mismatched transform lists with skew function');
// Individual transforms
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'translate', '50px', 'none');
assert_equals(dist, Math.sqrt(50 * 50), 'distance of 2D translate and none');
}, 'Test distance of 2D translate property with none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'translate', '10px 30px', '50px');
assert_equals(dist, Math.sqrt(40 * 40 + 30 * 30), 'distance of 2D translate');
}, 'Test distance of 2D translate property');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'translate', '10px 30px 50px', '50px');
assert_equals(dist, Math.sqrt(40 * 40 + 30 * 30 + 50 * 50),
'distance of 3D translate');
}, 'Test distance of 3D translate property');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'scale', '2', 'none');
assert_equals(dist, Math.sqrt(1 + 1), 'distance of 2D scale and none');
}, 'Test distance of 2D scale property with none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'scale', '3', '1 1');
assert_equals(dist, Math.sqrt(2 * 2 + 2 * 2), 'distance of 2D scale');
}, 'Test distance of 2D scale property');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'scale', '3 2 2', '1 1');
assert_equals(dist, Math.sqrt(2 * 2 + 1 * 1 + 1 * 1),
'distance of 3D scale');
}, 'Test distance of 3D scale property');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'rotate', '180deg', 'none');
assert_equals(dist, Math.PI, 'distance of 2D rotate and none');
}, 'Test distance of 2D rotate property with none');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'rotate', '180deg', '90deg');
assert_equals(dist, Math.PI / 2.0, 'distance of 2D rotate');
}, 'Test distance of 2D rotate property');
test(function(t) {
var target = addDiv(t);
var dist = getDistance(target, 'rotate', 'z 90deg', 'x 90deg');
let q1 = getQuaternion([0, 0, 1], Math.PI / 2.0);
let q2 = getQuaternion([1, 0, 0], Math.PI / 2.0);
assert_approx_equals(dist, computeRotateDistance(q1, q2), EPSILON,
'distance of 3D rotate');
}, 'Test distance of 3D rotate property');
</script>
</html>
|
