--- a/pkg/octree/vertex.go	Wed Sep 26 09:49:00 2018 +0200
+++ b/pkg/octree/vertex.go	Wed Sep 26 12:21:12 2018 +0200
@@ -22,6 +22,19 @@
 
 	LineStringZ      []Vertex
 	MultiLineStringZ []LineStringZ
+
+	Box2D struct {
+		X1 float64
+		Y1 float64
+		X2 float64
+		Y2 float64
+	}
+
+	Plane2D struct {
+		A float64
+		B float64
+		C float64
+	}
 )
 
 const (
@@ -297,3 +310,75 @@
 
 	return buf.Bytes()
 }
+
+func (a Box2D) Intersects(b Box2D) bool {
+	return !(a.X2 < a.X1 || a.X2 < b.X1 ||
+		a.Y2 < a.Y1 || a.Y2 < b.Y1)
+}
+
+func (a Box2D) Mid() (float64, float64) {
+	return (a.X2-a.X1)*0.5 + a.X1, (a.Y2-a.Y1)*0.5 + a.Y1
+}
+
+func (a Box2D) Xi(i int) float64 {
+	if i == 0 {
+		return a.X1
+	}
+	return a.X2
+}
+
+func (a Box2D) Yi(i int) float64 {
+	if i == 0 {
+		return a.Y1
+	}
+	return a.Y2
+}
+
+func NewPlane2D(x1, y1, x2, y2 float64) Plane2D {
+	a := x2 - x1
+	b := y2 - y1
+
+	l := math.Sqrt(a*a + b*b)
+	a /= l
+	b /= l
+
+	// a*x1 + b*y1 + c = 0
+	c := -(a*x1 + b*y1)
+	return Plane2D{a, b, c}
+}
+
+func (p Plane2D) Eval(x, y float64) float64 {
+	return p.A*x + p.B*y + p.C
+}
+
+const epsPlane = 1e-5
+
+func sides(s int, x float64) int {
+	if math.Signbit(x) {
+		return s | 2
+	}
+	return s | 1
+}
+
+const eps = 1e-05
+
+func (a Box2D) IntersectsPlane(p Plane2D) bool {
+	var s int
+	for i := 0; i < 2; i++ {
+		x := a.Xi(i)
+		for j := 0; j < 2; j++ {
+			y := a.Yi(j)
+			v := p.Eval(x, y)
+			if math.Abs(v) < epsPlane {
+				//log.Printf("on line")
+				return true
+			}
+			if s = sides(s, v); s == 3 {
+				//log.Printf("... on both sides (djt)")
+				return true
+			}
+		}
+	}
+	//log.Printf("side: %d\n", s)
+	return false
+}