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gpu: handle rounding errors when splitting quads

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This CL handles rounding errors arising when splitting quads into linear
segments.
Rounding errors would lead to a pair of quad triplets (from,ctl,to) not
exactly matching.
ie: to(n-1) wouldn't exactly match from(n).

Signed-off-by: Sebastien Binet <s@sbinet.org>
This commit is contained in:
Sebastien Binet
2021-01-01 16:15:48 +00:00
committed by Elias Naur
parent 8676a73a91
commit 5045a9e877
1 changed files with 39 additions and 6 deletions
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gpu/stroke.go
+39 -6
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@@ -32,6 +32,15 @@ import (
"gioui.org/op/clip"
)
// strokeTolerance is used to reconcile rounding errors arising
// when splitting quads into smaller and smaller segments to approximate
// them into straight lines, and when joining back segments.
//
// The magic value of 0.01 was found by striking a compromise between
// aesthetic looking (curves did look like curves, even after linearization)
// and speed.
const strokeTolerance = 0.01
type strokeQuad struct {
contour uint32
quad ops.Quad
@@ -182,10 +191,9 @@ func (qs strokeQuads) offset(hw float32, stroke clip.StrokeStyle) (rhs, lhs stro
})
}
const tolerance = 0.01
for i, state := range states {
rhs = rhs.append(strokeQuadBezier(state, +hw, tolerance))
lhs = lhs.append(strokeQuadBezier(state, -hw, tolerance))
rhs = rhs.append(strokeQuadBezier(state, +hw, strokeTolerance))
lhs = lhs.append(strokeQuadBezier(state, -hw, strokeTolerance))
// join the current and next segments
if hasNext := i+1 < len(states); hasNext || closed {
@@ -263,6 +271,21 @@ func (qs strokeQuads) append(ps strokeQuads) strokeQuads {
case len(qs) == 0:
return ps
}
// Consolidate quads and smooth out rounding errors.
// We need to also check for the strokeTolerance to correctly handle
// join/cap points or on-purpose disjoint quads.
p0 := qs[len(qs)-1].quad.To
p1 := ps[0].quad.From
if p0 != p1 && lenPt(p0.Sub(p1)) < strokeTolerance {
qs = append(qs, strokeQuad{
quad: ops.Quad{
From: p0,
Ctrl: p0.Add(p1).Mul(0.5),
To: p1,
},
})
}
return append(qs, ps...)
}
@@ -402,7 +425,10 @@ func strokeQuadBezier(state strokeState, d, flatness float32) strokeQuads {
// flattenQuadBezier splits a Bézier quadratic curve into linear sub-segments,
// themselves also encoded as Bézier (degenerate, flat) quadratic curves.
func flattenQuadBezier(qs strokeQuads, p0, p1, p2 f32.Point, d, flatness float32) strokeQuads {
var t float32
var (
t float32
flat64 = float64(flatness)
)
for t < 1 {
s2 := float64((p2.X-p0.X)*(p1.Y-p0.Y) - (p2.Y-p0.Y)*(p1.X-p0.X))
den := math.Hypot(float64(p1.X-p0.X), float64(p1.Y-p0.Y))
@@ -411,7 +437,6 @@ func flattenQuadBezier(qs strokeQuads, p0, p1, p2 f32.Point, d, flatness float32
}
s2 /= den
flat64 := float64(flatness)
t = 2.0 * float32(math.Sqrt(flat64/3.0/math.Abs(s2)))
if t >= 1.0 {
break
@@ -425,7 +450,15 @@ func flattenQuadBezier(qs strokeQuads, p0, p1, p2 f32.Point, d, flatness float32
}
func (qs *strokeQuads) addLine(p0, ctrl, p1 f32.Point, t, d float32) {
p0 = p0.Add(strokePathNorm(p0, ctrl, p1, 0, d))
switch i := len(*qs); i {
case 0:
p0 = p0.Add(strokePathNorm(p0, ctrl, p1, 0, d))
default:
// Address possible rounding errors and use previous point.
p0 = (*qs)[i-1].quad.To
}
p1 = p1.Add(strokePathNorm(p0, ctrl, p1, 1, d))
*qs = append(*qs,