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internal/stroke: tiny optimization to approxCubeTo

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Signed-off-by: Egon Elbre <egonelbre@gmail.com>
This commit is contained in:
Egon Elbre
2023-06-27 11:08:02 +03:00
committed by Elias Naur
parent b183774063
commit 0edc00a721
1 changed files with 6 additions and 5 deletions
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internal/stroke/stroke.go
+6 -5
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@@ -677,13 +677,14 @@ func SplitCubic(from, ctrl0, ctrl1, to f32.Point, quads []QuadSegment) []QuadSeg
if h := hull.Dy(); h > l {
l = h
}
approxCubeTo(&quads, 0, l*0.001, from, ctrl0, ctrl1, to)
maxDist := l * 0.001
approxCubeTo(&quads, 0, maxDist*maxDist, from, ctrl0, ctrl1, to)
return quads
}
// approxCubeTo approximates a cubic Bézier by a series of quadratic
// curves.
func approxCubeTo(quads *[]QuadSegment, splits int, maxDist float32, from, ctrl0, ctrl1, to f32.Point) int {
func approxCubeTo(quads *[]QuadSegment, splits int, maxDistSq float32, from, 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
@@ -722,7 +723,7 @@ func approxCubeTo(quads *[]QuadSegment, splits int, maxDist float32, from, ctrl0
// To save a square root, compare d² with the squared tolerance.
v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(from)
d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36)
if d2 <= maxDist*maxDist {
if d2 <= maxDistSq {
*quads = append(*quads, QuadSegment{From: from, Ctrl: c, To: to})
return splits
}
@@ -735,7 +736,7 @@ func approxCubeTo(quads *[]QuadSegment, splits int, maxDist float32, from, ctrl0
c12 := c1.Add(c2.Sub(c1).Mul(t))
c0112 := c01.Add(c12.Sub(c01).Mul(t))
splits++
splits = approxCubeTo(quads, splits, maxDist, from, c0, c01, c0112)
splits = approxCubeTo(quads, splits, maxDist, c0112, c12, c2, to)
splits = approxCubeTo(quads, splits, maxDistSq, from, c0, c01, c0112)
splits = approxCubeTo(quads, splits, maxDistSq, c0112, c12, c2, to)
return splits
}