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internal/stroke: optimize SplitCubic

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│   sec/op    │   sec/op     vs base               │
SplitCubic/4-10    37.36n ± 0%   36.16n ± 0%  -3.21% (p=0.000 n=10)
SplitCubic/8-10    74.53n ± 0%   72.21n ± 0%  -3.12% (p=0.000 n=10)
SplitCubic/16-10   149.3n ± 1%   144.5n ± 0%  -3.22% (p=0.000 n=10)
SplitCubic/33-10   340.1n ± 0%   334.4n ± 0%  -1.65% (p=0.000 n=10)

Signed-off-by: Egon Elbre <egonelbre@gmail.com>
This commit is contained in:
Egon Elbre
2023-06-27 11:44:26 +03:00
committed by Elias Naur
parent 55404aec91
commit e5fe3a0732
1 changed files with 9 additions and 3 deletions
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internal/stroke/stroke.go
+9 -3
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@@ -709,7 +709,11 @@ func approxCubeTo(quads *[]QuadSegment, splits int, maxDistSq float32, from, ctr
// 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(from).Add(ctrl1.Mul(3)).Sub(to).Mul(1.0 / 4.0)
// using, q0 := 3ctrl0 - pen, q1 := 3ctrl1 - to
// C = (q0 + q1)/4
q0 := ctrl0.Mul(3).Sub(from)
q1 := ctrl1.Mul(3).Sub(to)
c := q0.Add(q1).Mul(1.0 / 4.0)
const maxSplits = 32
if splits >= maxSplits {
*quads = append(*quads, QuadSegment{From: from, Ctrl: c, To: to})
@@ -718,10 +722,12 @@ func approxCubeTo(quads *[]QuadSegment, splits int, maxDistSq float32, from, ctr
// 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|
// d = sqrt(3)/36 * |to - 3ctrl1 + 3ctrl0 - pen|
// reusing, q0 := 3ctrl0 - pen, q1 := 3ctrl1 - to
// d = sqrt(3)/36 * |-q1 + q0|
//
// To save a square root, compare d² with the squared tolerance.
v := to.Sub(ctrl1.Mul(3)).Add(ctrl0.Mul(3)).Sub(from)
v := q0.Sub(q1)
d2 := (v.X*v.X + v.Y*v.Y) * 3 / (36 * 36)
if d2 <= maxDistSq {
*quads = append(*quads, QuadSegment{From: from, Ctrl: c, To: to})