func EdgeInterpolateAtDistance(ax s1.Angle, a, b Point, ab s1.Angle) Point {
axRad := ax.Radians()
abRad := ab.Radians()
f := math.Sin(axRad) / math.Sin(abRad)
e := math.Cos(axRad) - f*math.Cos(abRad)
v0 := a.Mul(e)
v1 := b.Mul(f)
return Point{v0.Add(v1).Normalize()}
}
// radiusToHeight converts an s1.Angle into the height of the cap.
func radiusToHeight(r s1.Angle) float64 {
if r.Radians() < 0 {
return emptyHeight
}
if r.Radians() >= math.Pi {
return fullHeight
}
// The height of the cap can be computed as 1 - cos(r), but this isn't very
// accurate for angles close to zero (where cos(r) is almost 1). The
// formula below has much better precision.
d := math.Sin(0.5 * r.Radians())
return 2 * d * d
}
func (p *Polygon) InternalClipPolyline(invert bool, a *Polyline, out *[]*Polyline, mergeRadius s1.Angle) {
// Clip the polyline A to the interior of this polygon.
// The resulting polyline(s) will be appended to "out".
// If invert is true, we clip A to the exterior of this polygon
// instead. Vertices will be dropped such that adjacent vertices
// will not be closer than "mergeRadius".
//
// We do the intersection/subtraction by walking the polyline edges.
// For each edge, we compute all intersections with the polygon
// boundary and sort them in increasing order of distance along that
// edge. We then divide the intersection points into pairs, and
// output a clipped polyline segment for each one.
// We keep track of whether we're inside or outside of the polygon
// at all times to decide which segments to output.
var intersections IntersectionSet
var vertices []Point
index := NewPolygonIndex(p, false)
n := a.NumVertices()
inside := p.ContainsPoint(a.Vertex(0)) != invert
for j := 0; j < n-1; j++ {
a0 := a.Vertex(j)
a1 := a.Vertex(j + 1)
ClipEdge(a0, a1, index, true, &intersections)
if inside {
intersections = append(intersections, FloatPointPair{0, a0})
}
inside = (len(intersections) & 1) != 0
if inside {
intersections = append(intersections, FloatPointPair{1, a1})
}
sort.Sort(intersections)
// At this point we have a sorted array of vertex pairs
// representing the edge(s) obtained after clipping (a0,a1)
// against the polygon.
for k := 0; k < len(intersections); k += 2 {
if intersections[k] == intersections[k+1] {
continue
}
v0 := intersections[k].second
v1 := intersections[k+1].second
// If the gap from the previous vertex to this one is
// large enough, start a new polyline.
if len(vertices) > 0 && vertices[len(vertices)-1].Angle(v0.Vector).Radians() > mergeRadius.Radians() {
*out = append(*out, PolylineFromPoints(vertices))
vertices = []Point{}
}
// Append this segment to the current polyline,
// ignoring any vertices that are too close to the
// previous vertex.
if len(vertices) == 0 {
vertices = append(vertices, v0)
}
if vertices[len(vertices)-1].Angle(v1.Vector).Radians() > mergeRadius.Radians() {
vertices = append(vertices, v1)
}
}
intersections = IntersectionSet{}
}
if len(vertices) > 0 {
*out = append(*out, PolylineFromPoints(vertices))
}
}