--- a/pkg/octree/vertex.go	Fri Mar 01 11:06:27 2019 +0100
+++ b/pkg/octree/vertex.go	Fri Mar 01 15:33:27 2019 +0100
@@ -110,6 +110,89 @@
 	return math.Sqrt(v.Dot(v))
 }
 
+func area(a, b, c Vertex) float64 {
+	return (b.Y-a.Y)*(c.X-b.X) - (b.X-a.X)*(c.Y-b.Y)
+}
+
+func inCircle(a, b, c, p Vertex) bool {
+	dx := a.X - p.X
+	dy := a.Y - p.Y
+	ex := b.X - p.X
+	ey := b.Y - p.Y
+	fx := c.X - p.X
+	fy := c.Y - p.Y
+
+	ap := dx*dx + dy*dy
+	bp := ex*ex + ey*ey
+	cp := fx*fx + fy*fy
+
+	return dx*(ey*cp-bp*fy)-dy*(ex*cp-bp*fx)+ap*(ex*fy-ey*fx) < 0
+}
+
+func circumradius(a, b, c Vertex) float64 {
+	dx := b.X - a.X
+	dy := b.Y - a.Y
+	ex := c.X - a.X
+	ey := c.Y - a.Y
+
+	bl := dx*dx + dy*dy
+	cl := ex*ex + ey*ey
+	d := dx*ey - dy*ex
+
+	x := (ey*bl - dy*cl) * 0.5 / d
+	y := (dx*cl - ex*bl) * 0.5 / d
+
+	r := x*x + y*y
+
+	if bl == 0 || cl == 0 || d == 0 || r == 0 {
+		return infinity
+	}
+
+	return r
+}
+
+func circumcenter(a, b, c Vertex) Vertex {
+	dx := b.X - a.X
+	dy := b.Y - a.Y
+	ex := c.X - a.X
+	ey := c.Y - a.Y
+
+	bl := dx*dx + dy*dy
+	cl := ex*ex + ey*ey
+	d := dx*ey - dy*ex
+
+	x := a.X + (ey*bl-dy*cl)*0.5/d
+	y := a.Y + (dx*cl-ex*bl)*0.5/d
+
+	return Vertex{X: x, Y: y}
+}
+
+func polygonArea(points []Vertex) float64 {
+	var result float64
+	for i, p := range points {
+		q := points[(i+1)%len(points)]
+		result += (p.X - q.X) * (p.Y + q.Y)
+	}
+	return result / 2
+}
+
+func polygonPerimeter(points []Vertex) float64 {
+	if len(points) == 0 {
+		return 0
+	}
+	var result float64
+	q := points[len(points)-1]
+	for _, p := range points {
+		result += p.Distance2D(q)
+		q = p
+	}
+	return result
+}
+
+func (v Vertex) Distance2D(w Vertex) float64 {
+	return math.Hypot(v.X-w.X, v.Y-w.Y)
+}
+
 // Minimize adjust this vertex v to hold the minimum
 // values component-wise of v and w.
 func (v *Vertex) Minimize(w Vertex) {
@@ -138,6 +221,20 @@
 	}
 }
 
+func (v Vertex) SquaredDistance2D(w Vertex) float64 {
+	dx := v.X - w.X
+	dy := v.Y - w.Y
+	return dx*dx + dy*dy
+}
+
+// Sub2D returns (v - w) component-wise.
+func (v Vertex) Sub2D(w Vertex) Vertex {
+	return Vertex{
+		X: v.X - w.X,
+		Y: v.Y - w.Y,
+	}
+}
+
 // Sub returns (v - w) component-wise.
 func (v Vertex) Sub(w Vertex) Vertex {
 	return Vertex{