--- a/pkg/octree/vertex.go	Mon Feb 25 17:02:33 2019 +0100
+++ b/pkg/octree/vertex.go	Mon Feb 25 18:21:33 2019 +0100
@@ -60,8 +60,54 @@
 		B float64
 		C float64
 	}
+
+	Plane3D struct {
+		A float64
+		B float64
+		C float64
+		D float64
+	}
 )
 
+func (t *Triangle) Plane3D() Plane3D {
+
+	v0 := t[1].Sub(t[0])
+	v1 := t[2].Sub(t[0])
+	n := v0.Cross(v1).Normalize()
+
+	// x*nx+ y*ny+ z*nz + d = 0
+	// d = - (x*nx+ y*ny + z*nz)
+	d := -t[0].Dot(n)
+	return Plane3D{
+		A: n.X,
+		B: n.Y,
+		C: n.Z,
+		D: d,
+	}
+}
+
+func (p Plane3D) Z(x, y float64) float64 {
+	// p.A*x + p.B*y + p.C*z + p.D = 0
+	return -(p.A*x + p.B*y + p.D) / p.C
+}
+
+func (v Vertex) Normalize() Vertex {
+	s := 1 / v.Length()
+	return Vertex{
+		X: s * v.X,
+		Y: s * v.Y,
+		Z: s * v.Z,
+	}
+}
+
+func (v Vertex) Dot(w Vertex) float64 {
+	return v.X*w.X + v.Y*w.Y + v.Z*w.Z
+}
+
+func (v Vertex) Length() float64 {
+	return math.Sqrt(v.Dot(v))
+}
+
 // Minimize adjust this vertex v to hold the minimum
 // values component-wise of v and w.
 func (v *Vertex) Minimize(w Vertex) {
@@ -166,6 +212,30 @@
 	return 0
 }
 
+func (v Vertex) Dot2(w Vertex) float64 {
+	return v.X*w.X + v.Y*w.Y
+}
+
+func (t *Triangle) Contains(x, y float64) bool {
+	v0 := t[2].Sub(t[0])
+	v1 := t[1].Sub(t[0])
+	v2 := Vertex{X: x, Y: y}.Sub(t[0])
+
+	dot00 := v0.Dot2(v0)
+	dot01 := v0.Dot2(v1)
+	dot02 := v0.Dot2(v2)
+	dot11 := v1.Dot2(v1)
+	dot12 := v1.Dot2(v2)
+
+	// Compute barycentric coordinates
+	invDenom := 1 / (dot00*dot11 - dot01*dot01)
+	u := (dot11*dot02 - dot01*dot12) * invDenom
+	v := (dot00*dot12 - dot01*dot02) * invDenom
+
+	// Check if point is in triangle
+	return u >= 0 && v >= 0 && u+v < 1
+}
+
 // IntersectHorizontal calculates the line string that
 // results when cutting a triangle a a certain height.
 // Can be empty (on intersection),
@@ -518,6 +588,11 @@
 		a.Y2 < a.Y1 || a.Y2 < b.Y1)
 }
 
+func (a Box2D) Contains(x, y float64) bool {
+	return a.X1 <= x && x <= a.X2 &&
+		a.Y1 <= y && y <= a.Y2
+}
+
 // Xi returns the i-th x component.
 func (a Box2D) Xi(i int) float64 {
 	if i == 0 {