func pruneEdgeDuplicates(edges []math.Vec2) []math.Vec2 {
pruned := make([]math.Vec2, 0, len(edges))
last := math.Vec2{}
for i, v := range edges {
if i == 0 || last.Sub(v).Len() > 0.0001 {
pruned = append(pruned, v)
}
last = v
}
return pruned
}
func segment(penWidth, r float32, a, b, c math.Vec2, aIsLast bool, vsEdgePos []float32, fillEdge []math.Vec2) ([]float32, []math.Vec2) {
ba, ca := a.Sub(b), a.Sub(c)
baLen, caLen := ba.Len(), ca.Len()
baDir, caDir := ba.DivS(baLen), ca.DivS(caLen)
dp := baDir.Dot(caDir)
if dp < -0.99999 {
// Straight lines cause DBZs, special case
inner := a.Sub(caDir.Tangent().MulS(penWidth))
vsEdgePos = appendVec2(vsEdgePos, a, inner)
if fillEdge != nil /*&& i != 0*/ {
fillEdge = append(fillEdge, inner)
}
return vsEdgePos, fillEdge
}
α := math.Acosf(dp) / 2
// ╔═══════════════════════════╦════════════════╗
// ║ ║ ║
// ║ A ║ ║
// ║ ╱:╲ ║ ║
// ║ ╱α:α╲ ║ A ║
// ║ ╱ : ╲ ║ |╲ ║
// ║ ╱ . d . ╲ ║ |α╲ ║
// ║ . : . ║ | ╲ ║
// ║ .P : Q. ║ | ╲ ║
// ║ ╱ X ╲ ║ | ╲ ║
// ║ ╱ . ┊ . ╲ ║ | ╲ ║
// ║ ╱ . r . ╲ ║ | ╲ ║
// ║ ╱ . ┊ . ╲ ║ |┐ β╲ ║
// ║ B ┊ C ║ P————————X ║
// ║ ║ ║
// ║ ^ ║ ║
// ║ ┊v ║ ║
// ║ ┊ u ║ ║
// ║ ┊—————> ║ ║
// ║ ║ ║
// ╚═══════════════════════════╩════════════════╝
v := baDir.Add(caDir).Normalize()
u := v.Tangent()
//
// cos(2 • α) = dp
//
// cos⁻¹(dp)
// α = ───────────
// 2
//
// r
// sin(α) = ───
// d
//
// r
// d = ──────
// sin(α)
//
d := r / math.Sinf(α)
// X cannot be futher than half way along ab or ac
dMax := math.Minf(baLen, caLen) / (2 * math.Cosf(α))
if d > dMax {
// Adjust d and r to compensate
d = dMax
r = d * math.Sinf(α)
}
x := a.Sub(v.MulS(d))
convex := baDir.Tangent().Dot(caDir) <= 0
w := penWidth
β := math.Pi/2 - α
// Special case for convex vertices where the pen width is greater than
// the rounding. Without dealing with this, we'd end up with the inner
// vertices overlapping. Instead use a point calculated much the same as
// x, but using the pen width.
useFixedInnerPoint := convex && w > r
fixedInnerPoint := a.Sub(v.MulS(math.Minf(w/math.Sinf(α), dMax)))
// Concave vertices behave much the same as convex, but we have to flip
// β as the sweep is reversed and w as we're extruding.
if !convex {
w, β = -w, -β
}
steps := 1 + int(d*α)
if aIsLast {
// No curvy edge required for the last vertex.
// This is already done by the first vertex.
steps = 1
}
for j := 0; j < steps; j++ {
γ := float32(0)
if steps > 1 {
γ = math.Lerpf(-β, β, float32(j)/float32(steps-1))
}
dir := v.MulS(math.Cosf(γ)).Add(u.MulS(math.Sinf(γ)))
va := x.Add(dir.MulS(r))
vb := va.Sub(dir.MulS(w))
if useFixedInnerPoint {
vb = fixedInnerPoint
}
vsEdgePos = appendVec2(vsEdgePos, va, vb)
if fillEdge != nil {
fillEdge = append(fillEdge, vb)
}
}
return vsEdgePos, fillEdge
}
