This repository was archived by the owner on Apr 2, 2026. It is now read-only.
Repository navigation
Expand file tree
/
Copy pathrect.go
More file actions
665 lines (595 loc) · 15.8 KB
/
Copy pathrect.go
File metadata and controls
665 lines (595 loc) · 15.8 KB
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
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
package curve
import (
"iter"
"math"
"slices"
)
type Rect struct {
X0, Y0 float64
X1, Y1 float64
}
var _ ClosedShape = Rect{}
// NewRectFromPoints returns a rectangle with the extents of p0 and p1, ensuring that
// width and height are non-negative.
func NewRectFromPoints(p0, p1 Point) Rect {
return Rect{p0.X, p0.Y, p1.X, p1.Y}.Abs()
}
// NewRectFromOrigin returns a rectangle with the given size, extending to the right and
// down (for positive sizes) from the origin. Width and height are ensured to be
// non-negative.
func NewRectFromOrigin(origin Point, size Size) Rect {
return NewRectFromPoints(origin, origin.Translate(Vec2(size.AsVec2())))
}
// NewRectFromCenter returns a rectangle with the given size, centered around the center
// point.
func NewRectFromCenter(center Point, size Size) Rect {
return Rect{
X0: center.X - size.Width/2,
Y0: center.Y - size.Height/2,
X1: center.X + size.Width/2,
Y1: center.Y + size.Height/2,
}
}
// WithOrigin returns a new rectangle with the same size as r and a new origin.
func (r Rect) WithOrigin(origin Point) Rect {
return NewRectFromOrigin(origin, r.Size())
}
// WithSize returns a new rectangle with the same origin as r and a new size.
func (r Rect) WithSize(size Size) Rect {
return NewRectFromOrigin(r.Origin(), size)
}
// TODO(dh): Inset
// Abs returns a new rectangle with the same extents as r, but ensuring that width and
// height are non-negative.
func (r Rect) Abs() Rect {
return Rect{
X0: min(r.X0, r.X1),
Y0: min(r.Y0, r.Y1),
X1: max(r.X0, r.X1),
Y1: max(r.Y0, r.Y1),
}
}
func (r Rect) MinX() float64 { return min(r.X0, r.X1) }
func (r Rect) MaxX() float64 { return max(r.X0, r.X1) }
func (r Rect) MinY() float64 { return min(r.Y0, r.Y1) }
func (r Rect) MaxY() float64 { return max(r.Y0, r.Y1) }
// Origin returns the origin of the rectangle.
//
// This is the top left corner in a y-down space and with
// non-negative width and height.
func (r Rect) Origin() Point {
return Point{
X: r.X0,
Y: r.Y0,
}
}
// Width returns the rectangle's width, defined as X1 − X0. It may be negative.
func (r Rect) Width() float64 {
return r.X1 - r.X0
}
// Height returns the rectangle's heigth, defined as Y1 − Y0. It may be negative.
func (r Rect) Height() float64 {
return r.Y1 - r.Y0
}
func (r Rect) Size() Size {
return Size{
Width: r.Width(),
Height: r.Height(),
}
}
func (r Rect) Center() Point {
return Point{
X: 0.5 * (r.X0 + r.X1),
Y: 0.5 * (r.Y0 + r.Y1),
}
}
func (r Rect) Contains(pt Point) bool {
return pt.X >= r.X0 &&
pt.X < r.X1 &&
pt.Y >= r.Y0 &&
pt.Y < r.Y1
}
// Union returns the smallest rectangle enclosing r and o.
//
// Results are valid only if width and height are non-negative.
func (r Rect) Union(o Rect) Rect {
return Rect{
X0: min(r.X0, o.X0),
Y0: min(r.Y0, o.Y0),
X1: max(r.X1, o.X1),
Y1: max(r.Y1, o.Y1),
}
}
// UnionPoint computes the union with one point.
//
// This method includes the perimeter of zero-area rectangles.
// Thus, a succession of UnionPoint operations on a series of
// points yields their enclosing rectangle.
//
// Results are valid only if width and height are non-negative.
func (r Rect) UnionPoint(pt Point) Rect {
return Rect{
X0: min(r.X0, pt.X),
Y0: min(r.Y0, pt.Y),
X1: max(r.X1, pt.X),
Y1: max(r.Y1, pt.Y),
}
}
// Intersect returns the intersection of two rectangles.
//
// The result is zero-area if either input has negative width or
// height. The result always has non-negative width and height.
func (r Rect) Intersect(o Rect) Rect {
x0 := max(r.X0, o.X0)
y0 := max(r.Y0, o.Y0)
x1 := min(r.X1, o.X1)
y1 := min(r.Y1, o.Y1)
return Rect{
X0: x0,
Y0: y0,
X1: max(x0, x1),
Y1: max(y0, y1),
}
}
// Inflate expands a rectangle by a constant amount in both directions.
//
// The logic simply applies the amount in each direction. If rectangle
// area or added dimensions are negative, this could give odd results.
func (r Rect) Inflate(width, height float64) Rect {
return Rect{
X0: r.X0 - width,
Y0: r.Y0 - height,
X1: r.X1 + width,
Y1: r.Y1 + height,
}
}
// Round returns a new rectangle with each coordinate value rounded to the nearest
// integer.
func (r Rect) Round() Rect {
return Rect{
X0: math.Round(r.X0),
Y0: math.Round(r.Y0),
X1: math.Round(r.X1),
Y1: math.Round(r.Y1),
}
}
// Ceil returns a new rectangle with each coordinate value rounded to the least integer
// value greater than or equal to it.
func (r Rect) Ceil() Rect {
return Rect{
X0: math.Ceil(r.X0),
Y0: math.Ceil(r.Y0),
X1: math.Ceil(r.X1),
Y1: math.Ceil(r.Y1),
}
}
// Floor returns a new rectangle, with each coordinate value rounded down to the
// nearest integer.
func (r Rect) Floor() Rect {
return Rect{
X0: math.Floor(r.X0),
Y0: math.Floor(r.Y0),
X1: math.Floor(r.X1),
Y1: math.Floor(r.Y1),
}
}
// Expand returns a new rectangle, with each coordinate value rounded away from
// the center of the rectangle to the nearest integer, unless they are already
// an integer. That is to say this function will return the smallest possible
// rectangle with integer coordinates that is a superset of the input
// rectangle.
func (r Rect) Expand() Rect {
var x0, y0, x1, y1 float64
if r.X0 < r.X1 {
x0 = math.Floor(r.X0)
x1 = math.Ceil(r.X1)
} else {
x0 = math.Ceil(r.X0)
x1 = math.Floor(r.X1)
}
if r.Y0 < r.Y1 {
y0 = math.Floor(r.Y0)
y1 = math.Ceil(r.Y1)
} else {
y0 = math.Ceil(r.Y0)
y1 = math.Floor(r.Y1)
}
return Rect{
X0: x0,
Y0: y0,
X1: x1,
Y1: y1,
}
}
// Trunc returns a new rectangle, with each coordinate value rounded towards the
// center of the rectangle to the nearest integer, unless they are already an
// integer. That is to say this function will return the biggest possible
// rectangle with integer coordinates that is a subset of the input rectangle.
func (r Rect) Trunc() Rect {
var x0, y0, x1, y1 float64
if r.X0 < r.X1 {
x0 = math.Ceil(r.X0)
x1 = math.Floor(r.X1)
} else {
x0 = math.Floor(r.X0)
x1 = math.Ceil(r.X1)
}
if r.Y0 < r.Y1 {
y0 = math.Ceil(r.Y0)
y1 = math.Floor(r.Y1)
} else {
y0 = math.Floor(r.Y0)
y1 = math.Ceil(r.Y1)
}
return Rect{
X0: x0,
Y0: y0,
X1: x1,
Y1: y1,
}
}
// ScaleFromOrigin scales the rectangle by the factor f with respect to the
// origin (the point (0, 0)).
func (r Rect) ScaleFromOrigin(f float64) Rect {
return Rect{
X0: r.X0 * f,
Y0: r.Y0 * f,
X1: r.X1 * f,
Y1: r.Y1 * f,
}
}
// AspectRatio returns the aspect ratio of the rectangle.
//
// This is defined as the width divided by the height. It measures the
// "squareness" of the rectangle (a value of 1 is square).
//
// If the height is 0 the output will be "sign(x1 - x0) * infinity".
//
// If the width and height are 0, the result will be NaN.
func (r Rect) AspectRatio() float64 {
return r.Size().AspectRatio()
}
func (r Rect) IsInf() bool {
return math.IsInf(r.X0, 0) ||
math.IsInf(r.X1, 0) ||
math.IsInf(r.Y0, 0) ||
math.IsInf(r.Y1, 0)
}
func (r Rect) IsNaN() bool {
return math.IsNaN(r.X0) ||
math.IsNaN(r.X1) ||
math.IsNaN(r.Y0) ||
math.IsNaN(r.Y1)
}
func (r Rect) Translate(v Vec2) Rect {
return Rect{
X0: r.X0 + v.X,
Y0: r.Y0 + v.Y,
X1: r.X1 + v.X,
Y1: r.Y1 + v.Y,
}
}
func (r Rect) Area() float64 {
return r.Width() * r.Height()
}
func (r Rect) BoundingBox() Rect {
return r.Abs()
}
func (r Rect) Perimeter(accuracy float64) float64 {
return 2 * (math.Abs(r.Width()) + math.Abs(r.Height()))
}
func (r Rect) Winding(pt Point) int {
// Note: this function is carefully designed so that if the plane is
// tiled with rectangles, the winding number will be nonzero for exactly
// one of them.
xmin := min(r.X0, r.X1)
xmax := max(r.X0, r.X1)
ymin := min(r.Y0, r.Y1)
ymax := max(r.Y0, r.Y1)
if pt.X >= xmin && pt.X < xmax && pt.Y >= ymin && pt.Y < ymax {
if r.X1 > r.X0 != (r.Y1 > r.Y0) {
return -1
} else {
return 1
}
} else {
return 0
}
}
func (r Rect) Path(tolerance float64) BezPath { return slices.Collect(r.PathElements(tolerance)) }
func (r Rect) PathElements(tolerance float64) iter.Seq[PathElement] {
return func(yield func(PathElement) bool) {
_ = yield(MoveTo(Pt(r.X0, r.Y0))) &&
yield(LineTo(Pt(r.X1, r.Y0))) &&
yield(LineTo(Pt(r.X1, r.Y1))) &&
yield(LineTo(Pt(r.X0, r.Y1))) &&
yield(ClosePath())
}
}
// RoundedRect creates a new [RoundedRect] from this rectangle and the provided
// corner radii.
func (r Rect) RoundedRect(radii RoundedRectRadii) RoundedRect {
r = r.Abs()
shortestSide := min(r.Width(), r.Height())
radii = radii.Abs().Clamp(shortestSide / 2)
return RoundedRect{
Rect: r,
Radii: radii,
}
}
// ContainedRectWithAspectRatio returns the largest possible rectangle that is
// fully contained in this rectangle, with the given aspect ratio.
//
// The aspect ratio is specified fractionally, as width / height.
//
// The resulting rectangle will be centered if it is smaller than the input
// rectangle.
func (r Rect) ContainedRectWithAspectRatio(aspectRatio float64) Rect {
width, height := r.Width(), r.Height()
rAspect := width / height
// TODO the parameter 1e-9 was chosen quickly and may not be optimal.
if math.Abs(rAspect-aspectRatio) < 1e-9 {
return r
} else if math.Abs(rAspect) < math.Abs(aspectRatio) {
// shrink y to fit
newHeight := width / aspectRatio
gap := (height - newHeight) * 0.5
y0 := r.Y0 + gap
y1 := r.Y1 - gap
return Rect{r.X0, y0, r.X1, y1}
} else {
// shrink x to fit
newWidth := height * aspectRatio
gap := (width - newWidth) * 0.5
x0 := r.X0 + gap
x1 := r.X1 - gap
return Rect{x0, r.Y0, x1, r.Y1}
}
}
type RoundedRect struct {
Rect
Radii RoundedRectRadii
}
var _ ClosedShape = RoundedRect{}
func NewRoundedRect(x0, y0, x1, y1, radius float64) RoundedRect {
return RoundedRect{
Rect{x0, y0, x1, y1},
RoundedRectRadii{radius, radius, radius, radius},
}
}
func (r RoundedRect) Area() float64 {
// A corner is a quarter-circle, i.e.
// .............#
// . ######
// . #########
// . ###########
// . ############
// .#############
// ##############
// |-----r------|
// For each corner, we need to subtract the square that bounds this
// quarter-circle, and add back in the area of quarter circle.
corner := func(radius float64) float64 {
return (math.Pi/4 - 1) * radius * radius
}
// Start with the area of the bounding rectangle. For each corner,
// subtract the area of the corner under the quarter-circle, and add
// back the area of the quarter-circle.
return r.Rect.Area() +
corner(r.Radii.TopLeft) +
corner(r.Radii.TopRight) +
corner(r.Radii.BottomRight) +
corner(r.Radii.BottomLeft)
}
func dropFirst[T any](seq iter.Seq[T]) iter.Seq[T] {
return func(yield func(T) bool) {
first := true
for el := range seq {
if first {
first = false
continue
}
if !yield(el) {
break
}
}
}
}
func (r RoundedRect) Path(tolerance float64) BezPath {
return slices.Collect(r.PathElements(tolerance))
}
func (r RoundedRect) PathElements(tolerance float64) iter.Seq[PathElement] {
buildArcIter := func(i int, center Point, ellipseRadii Vec2) iter.Seq[PathElement] {
a := Arc{
Center: center,
Radii: ellipseRadii,
StartAngle: math.Pi / 2 * float64(i),
SweepAngle: math.Pi / 2,
XRotation: 0.0,
}
return dropFirst(a.PathElements(tolerance))
}
arcs := [...]iter.Seq[PathElement]{
buildArcIter(
2,
Point{
X: r.Rect.X0 + r.Radii.TopLeft,
Y: r.Rect.Y0 + r.Radii.TopLeft,
},
Vec2{
X: r.Radii.TopLeft,
Y: r.Radii.TopLeft,
},
),
buildArcIter(
3,
Point{
X: r.Rect.X1 - r.Radii.TopRight,
Y: r.Rect.Y0 + r.Radii.TopRight,
},
Vec2{
X: r.Radii.TopRight,
Y: r.Radii.TopRight,
},
),
buildArcIter(
0,
Point{
X: r.Rect.X1 - r.Radii.BottomRight,
Y: r.Rect.Y1 - r.Radii.BottomRight,
},
Vec2{
X: r.Radii.BottomRight,
Y: r.Radii.BottomRight,
},
),
buildArcIter(
1,
Point{
X: r.Rect.X0 + r.Radii.BottomLeft,
Y: r.Rect.Y1 - r.Radii.BottomLeft,
},
Vec2{
X: r.Radii.BottomLeft,
Y: r.Radii.BottomLeft,
},
),
}
rect := []PathElement{
LineTo(Pt(
r.Rect.X1-r.Radii.TopRight,
r.Rect.Y0,
)),
LineTo(Pt(
r.Rect.X1,
r.Rect.Y1-r.Radii.BottomRight,
)),
LineTo(Pt(
r.Rect.X0+r.Radii.BottomLeft,
r.Rect.Y1,
)),
ClosePath(),
}
return func(yield func(PathElement) bool) {
e := MoveTo(Pt(
r.Rect.X0,
r.Rect.Y0+r.Radii.TopLeft,
))
if !yield(e) {
return
}
// Generate the arc curve elements.
// When we've reached the end of the arc, add a line towards next arc.
for i, arc := range arcs {
for e := range arc {
if !yield(e) {
return
}
}
e := rect[i]
if !yield(e) {
return
}
}
}
}
func (r RoundedRect) Perimeter(accuracy float64) float64 {
corner := func(radius float64) float64 {
return (-2.0 + math.Pi/2) * radius * radius
}
// Start with the full perimeter. For each corner, subtract the
// border surrounding the rounded corner and add the quarter-circle
// perimeter.
return r.Rect.Perimeter(1.0) +
corner(r.Radii.TopLeft) +
corner(r.Radii.TopRight) +
corner(r.Radii.BottomRight) +
corner(r.Radii.BottomLeft)
}
func (rr RoundedRect) Winding(pt Point) int {
center := rr.Center()
// 1. Translate the point relative to the center of the rectangle.
pt.X -= center.X
pt.Y -= center.Y
// 2. Pick a radius value to use based on which quadrant the point is
// in.
var radius float64
switch {
case pt.X < 0.0 && pt.Y < 0.0:
radius = rr.Radii.TopLeft
case pt.X >= 0.0 && pt.Y < 0.0:
radius = rr.Radii.TopRight
case pt.X >= 0.0 && pt.Y >= 0.0:
radius = rr.Radii.BottomRight
case pt.X < 0.0 && pt.Y >= 0.0:
radius = rr.Radii.BottomLeft
}
// 3. This is the width and height of a rectangle with one corner at
// the center of the rounded rectangle, and another corner at the
// center of the relevant corner circle.
insideHalfWidth := max(rr.Width()/2.0-radius, 0)
insideHalfHeight := max(rr.Height()/2.0-radius, 0)
// 4. Three things are happening here.
//
// First, the x- and y-values are being reflected into the positive
// (bottom-right quadrant). The radius has already been determined,
// so it doesn't matter what quadrant is used.
//
// After reflecting, the points are clamped so that their x- and y-
// values can't be lower than the x- and y- values of the center of
// the corner circle, and the coordinate system is transformed
// again, putting (0, 0) at the center of the corner circle.
px := max(math.Abs(pt.X)-insideHalfWidth, 0.0)
py := max(math.Abs(pt.Y)-insideHalfHeight, 0.0)
// 5. The transforms above clamp all input points such that they will
// be inside the rounded rectangle if the corresponding output point
// (px, py) is inside a circle centered around the origin with the
// given radius.
inside := px*px+py*py <= radius*radius
if inside {
return 1
} else {
return 0
}
}
var _ Shape = RoundedRect{}
func (r RoundedRect) IsInf() bool {
return r.Rect.IsInf() || r.Radii.IsInf()
}
func (r RoundedRect) IsNaN() bool {
return r.Rect.IsNaN() || r.Radii.IsNaN()
}
type RoundedRectRadii struct {
TopLeft float64
TopRight float64
BottomRight float64
BottomLeft float64
}
func (r RoundedRectRadii) Abs() RoundedRectRadii {
return RoundedRectRadii{
TopLeft: math.Abs(r.TopLeft),
TopRight: math.Abs(r.TopRight),
BottomLeft: math.Abs(r.BottomLeft),
BottomRight: math.Abs(r.BottomRight),
}
}
func (r RoundedRectRadii) Clamp(max float64) RoundedRectRadii {
return RoundedRectRadii{
TopLeft: min(r.TopLeft, max),
TopRight: min(r.TopRight, max),
BottomLeft: min(r.BottomLeft, max),
BottomRight: min(r.BottomRight, max),
}
}
func (r RoundedRectRadii) IsInf() bool {
return math.IsInf(r.TopLeft, 0) ||
math.IsInf(r.TopRight, 0) ||
math.IsInf(r.BottomRight, 0) ||
math.IsInf(r.BottomLeft, 0)
}
func (r RoundedRectRadii) IsNaN() bool {
return math.IsNaN(r.TopLeft) ||
math.IsNaN(r.TopRight) ||
math.IsNaN(r.BottomRight) ||
math.IsNaN(r.BottomLeft)
}