Function flattenEllipticArc

path_util.go:345–385

(start Point, rx, ry, phi float64, large, sweep bool, end Point, tolerance float64)

}

func flattenEllipticArc(start Point, rx, ry, phi float64, large, sweep bool, end Point, tolerance float64) *Path {
	if Equal(rx, ry) {
		// circle
		r := rx
		cx, cy, theta0, theta1 := ellipseToCenter(start.X, start.Y, rx, ry, phi, large, sweep, end.X, end.Y)
		theta0 += phi
		theta1 += phi

		// draw line segments from arc+tolerance to arc+tolerance, touching arc-tolerance in between
		// we start and end at the arc itself
		dtheta := math.Abs(theta1 - theta0)
		thetaEnd := math.Acos((r - tolerance) / r)               // half angle of first/last segment
		thetaMid := math.Acos((r - tolerance) / (r + tolerance)) // half angle of middle segments
		n := math.Ceil((dtheta - thetaEnd*2.0) / (thetaMid * 2.0))

		// evenly space out points along arc
		ratio := dtheta / (thetaEnd*2.0 + thetaMid*2.0*n)
		thetaEnd *= ratio
		thetaMid *= ratio

		// adjust distance from arc to lower total deviation area, add points on the outer circle
		// of the tolerance since the middle of the line segment touches the inner circle and thus
		// even out. Ratio < 1 is when the line segments are shorter (and thus not touch the inner
		// tolerance circle).
		r += ratio * tolerance

		p := &Path{}
		p.MoveTo(start.X, start.Y)
		theta := thetaEnd + thetaMid
		for i := 0; i < int(n); i++ {
			t := theta0 + math.Copysign(theta, theta1-theta0)
			pos := PolarPoint(t, r).Add(Point{cx, cy})
			p.LineTo(pos.X, pos.Y)
			theta += 2.0 * thetaMid
		}
		p.LineTo(end.X, end.Y)
		return p
	}
	// TODO: (flatten ellipse) use direct algorithm
	return arcToCube(start, rx, ry, phi, large, sweep, end).Flatten(tolerance)
}

////////////////////////////////////////////////////////////////
// Béziers /////////////////////////////////////////////////////