ref: b25af47c45adcaef27ae241623f40208c53a1866 gio/ui/paint/path.go -rw-r--r-- 7.6 KiB View raw
                                                                                
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
// SPDX-License-Identifier: Unlicense OR MIT

package paint

import (
	"encoding/binary"
	"math"
	"unsafe"

	"gioui.org/ui"
	"gioui.org/ui/f32"
	"gioui.org/ui/internal/opconst"
	"gioui.org/ui/internal/path"
)

// PathBuilder builds and adds a general ClipOp clip path
// from lines and curves.
// PathBuilder generates no garbage and can be used for
// dynamic paths; path data is stored directly in the Ops
// list supplied to Init.
type PathBuilder struct {
	ops       *ui.Ops
	firstVert int
	nverts    int
	maxy      float32
	pen       f32.Point
	bounds    f32.Rectangle
	hasBounds bool
}

// ClipOp sets the current clip path.
type ClipOp struct {
	bounds f32.Rectangle
}

func (p ClipOp) Add(o *ui.Ops) {
	data := make([]byte, opconst.TypeClipLen)
	data[0] = byte(opconst.TypeClip)
	bo := binary.LittleEndian
	bo.PutUint32(data[1:], math.Float32bits(p.bounds.Min.X))
	bo.PutUint32(data[5:], math.Float32bits(p.bounds.Min.Y))
	bo.PutUint32(data[9:], math.Float32bits(p.bounds.Max.X))
	bo.PutUint32(data[13:], math.Float32bits(p.bounds.Max.Y))
	o.Write(data)
}

// Init the builder and specify the operations list for
// storing the path data and final ClipOp.
func (p *PathBuilder) Init(ops *ui.Ops) {
	p.ops = ops
}

// MoveTo moves the pen to the given position.
func (p *PathBuilder) Move(to f32.Point) {
	p.end()
	to = to.Add(p.pen)
	p.maxy = to.Y
	p.pen = to
}

// end completes the current contour.
func (p *PathBuilder) end() {
	aux := p.ops.Aux()
	bo := binary.LittleEndian
	// Fill in maximal Y coordinates of the NW and NE corners.
	for i := p.firstVert; i < p.nverts; i++ {
		off := path.VertStride*i + int(unsafe.Offsetof(((*path.Vertex)(nil)).MaxY))
		bo.PutUint32(aux[off:], math.Float32bits(p.maxy))
	}
	p.firstVert = p.nverts
}

// Line records a line from the pen to end.
func (p *PathBuilder) Line(to f32.Point) {
	to = to.Add(p.pen)
	p.lineTo(to)
}

func (p *PathBuilder) lineTo(to f32.Point) {
	// Model lines as degenerate quadratic Béziers.
	p.quadTo(to.Add(p.pen).Mul(.5), to)
}

// Quad records a quadratic Bézier from the pen to end
// with the control point ctrl.
func (p *PathBuilder) Quad(ctrl, to f32.Point) {
	ctrl = ctrl.Add(p.pen)
	to = to.Add(p.pen)
	p.quadTo(ctrl, to)
}

func (p *PathBuilder) quadTo(ctrl, to f32.Point) {
	// Zero width curves don't contribute to stenciling.
	if p.pen.X == to.X && p.pen.X == ctrl.X {
		p.pen = to
		return
	}

	bounds := f32.Rectangle{
		Min: p.pen,
		Max: to,
	}.Canon()

	// If the curve contain areas where a vertical line
	// intersects it twice, split the curve in two x monotone
	// lower and upper curves. The stencil fragment program
	// expects only one intersection per curve.

	// Find the t where the derivative in x is 0.
	v0 := ctrl.Sub(p.pen)
	v1 := to.Sub(ctrl)
	d := v0.X - v1.X
	// t = v0 / d. Split if t is in ]0;1[.
	if v0.X > 0 && d > v0.X || v0.X < 0 && d < v0.X {
		t := v0.X / d
		ctrl0 := p.pen.Mul(1 - t).Add(ctrl.Mul(t))
		ctrl1 := ctrl.Mul(1 - t).Add(to.Mul(t))
		mid := ctrl0.Mul(1 - t).Add(ctrl1.Mul(t))
		p.simpleQuadTo(ctrl0, mid)
		p.simpleQuadTo(ctrl1, to)
		if mid.X > bounds.Max.X {
			bounds.Max.X = mid.X
		}
		if mid.X < bounds.Min.X {
			bounds.Min.X = mid.X
		}
	} else {
		p.simpleQuadTo(ctrl, to)
	}
	// Find the y extremum, if any.
	d = v0.Y - v1.Y
	if v0.Y > 0 && d > v0.Y || v0.Y < 0 && d < v0.Y {
		t := v0.Y / d
		y := (1-t)*(1-t)*p.pen.Y + 2*(1-t)*t*ctrl.Y + t*t*to.Y
		if y > bounds.Max.Y {
			bounds.Max.Y = y
		}
		if y < bounds.Min.Y {
			bounds.Min.Y = y
		}
	}
	p.expand(bounds)
}

// Cube records a cubic Bézier from the pen through
// two control points ending in to.
func (p *PathBuilder) Cube(ctrl0, ctrl1, to f32.Point) {
	ctrl0 = ctrl0.Add(p.pen)
	ctrl1 = ctrl1.Add(p.pen)
	to = to.Add(p.pen)
	// Set the maximum distance proportionally to the longest side
	// of the bounding rectangle.
	hull := f32.Rectangle{
		Min: p.pen,
		Max: ctrl0,
	}.Canon().Add(ctrl1).Add(to)
	l := hull.Dx()
	if h := hull.Dy(); h > l {
		l = h
	}
	p.approxCubeTo(0, l*0.001, ctrl0, ctrl1, to)
}

// approxCube approximates a cubic Bézier by a series of quadratic
// curves.
func (p *PathBuilder) approxCubeTo(splits int, maxDist float32, ctrl0, ctrl1, to f32.Point) int {
	// The idea is from
	// https://caffeineowl.com/graphics/2d/vectorial/cubic2quad01.html
	// where a quadratic approximates a cubic by eliminating its t³ term
	// from its polynomial expression anchored at the starting point:
	//
	// P(t) = pen + 3t(ctrl0 - pen) + 3t²(ctrl1 - 2ctrl0 + pen) + t³(to - 3ctrl1 + 3ctrl0 - pen)
	//
	// The control point for the new quadratic Q1 that shares starting point, pen, with P is
	//
	// C1 = (3ctrl0 - pen)/2
	//
	// The reverse cubic anchored at the end point has the polynomial
	//
	// P'(t) = to + 3t(ctrl1 - to) + 3t²(ctrl0 - 2ctrl1 + to) + t³(pen - 3ctrl0 + 3ctrl1 - to)
	//
	// The corresponding quadratic Q2 that shares the end point, to, with P has control
	// point
	//
	// C2 = (3ctrl1 - to)/2
	//
	// The combined quadratic Bézier, Q, shares both start and end points with its cubic
	// and use the midpoint between the two curves Q1 and Q2 as control point:
	//
	// C = (3ctrl0 - pen + 3ctrl1 - to)/4
	c := ctrl0.Mul(3).Sub(p.pen).Add(ctrl1.Mul(3)).Sub(to).Mul(1.0 / 4.0)
	const maxSplits = 32
	if splits >= maxSplits {
		p.quadTo(c, to)
		return splits
	}
	// The maximum distance between the cubic P and its approximation Q given t
	// can be shown to be
	//
	// d = sqrt(3)/36*|to - 3ctrl1 + 3ctrl0 - pen|
	//
	// To save a square root, compare d² with the squared tolerance.
	v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(p.pen)
	d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36)
	if d2 <= maxDist*maxDist {
		p.quadTo(c, to)
		return splits
	}
	// De Casteljau split the curve and approximate the halves.
	t := float32(0.5)
	c0 := p.pen.Add(ctrl0.Sub(p.pen).Mul(t))
	c1 := ctrl0.Add(ctrl1.Sub(ctrl0).Mul(t))
	c2 := ctrl1.Add(to.Sub(ctrl1).Mul(t))
	c01 := c0.Add(c1.Sub(c0).Mul(t))
	c12 := c1.Add(c2.Sub(c1).Mul(t))
	c0112 := c01.Add(c12.Sub(c01).Mul(t))
	splits++
	splits = p.approxCubeTo(splits, maxDist, c0, c01, c0112)
	splits = p.approxCubeTo(splits, maxDist, c12, c2, to)
	return splits
}

func (p *PathBuilder) expand(b f32.Rectangle) {
	if !p.hasBounds {
		p.hasBounds = true
		inf := float32(math.Inf(+1))
		p.bounds = f32.Rectangle{
			Min: f32.Point{X: inf, Y: inf},
			Max: f32.Point{X: -inf, Y: -inf},
		}
	}
	p.bounds = p.bounds.Union(b)
}

func (p *PathBuilder) vertex(cornerx, cornery int16, ctrl, to f32.Point) {
	p.nverts++
	v := path.Vertex{
		CornerX: cornerx,
		CornerY: cornery,
		FromX:   p.pen.X,
		FromY:   p.pen.Y,
		CtrlX:   ctrl.X,
		CtrlY:   ctrl.Y,
		ToX:     to.X,
		ToY:     to.Y,
	}
	data := make([]byte, path.VertStride+1)
	data[0] = byte(opconst.TypeAux)
	bo := binary.LittleEndian
	data[1] = byte(uint16(v.CornerX))
	data[2] = byte(uint16(v.CornerX) >> 8)
	data[3] = byte(uint16(v.CornerY))
	data[4] = byte(uint16(v.CornerY) >> 8)
	bo.PutUint32(data[5:], math.Float32bits(v.MaxY))
	bo.PutUint32(data[9:], math.Float32bits(v.FromX))
	bo.PutUint32(data[13:], math.Float32bits(v.FromY))
	bo.PutUint32(data[17:], math.Float32bits(v.CtrlX))
	bo.PutUint32(data[21:], math.Float32bits(v.CtrlY))
	bo.PutUint32(data[25:], math.Float32bits(v.ToX))
	bo.PutUint32(data[29:], math.Float32bits(v.ToY))
	p.ops.Write(data)
}

func (p *PathBuilder) simpleQuadTo(ctrl, to f32.Point) {
	if p.pen.Y > p.maxy {
		p.maxy = p.pen.Y
	}
	if ctrl.Y > p.maxy {
		p.maxy = ctrl.Y
	}
	if to.Y > p.maxy {
		p.maxy = to.Y
	}
	// NW.
	p.vertex(-1, 1, ctrl, to)
	// NE.
	p.vertex(1, 1, ctrl, to)
	// SW.
	p.vertex(-1, -1, ctrl, to)
	// SE.
	p.vertex(1, -1, ctrl, to)
	p.pen = to
}

// End the path and add the resulting ClipOp to
// the operation list passed to Init.
func (p *PathBuilder) End() {
	p.end()
	ClipOp{
		bounds: p.bounds,
	}.Add(p.ops)
}