package main

import "math"

type vertex struct {
	x float64
	y float64
	z float64
}

func (v *vertex) minimize(w vertex) {
	if w.x < v.x {
		v.x = w.x
	}
	if w.y < v.y {
		v.y = w.y
	}
	if w.z < v.z {
		v.z = w.z
	}
}

func (v *vertex) maximize(w vertex) {
	if w.x > v.x {
		v.x = w.x
	}
	if w.y > v.y {
		v.y = w.y
	}
	if w.z > v.z {
		v.z = w.z
	}
}

type plane struct {
	a float64
	b float64
	c float64
	d float64
}

func (a vertex) cross(b vertex) vertex {
	return vertex{
		a.y*b.z - a.z*b.y,
		a.z*b.x - a.x*b.z,
		a.x*b.y - a.y*b.x,
	}
}

func (a vertex) sub(b vertex) vertex {
	return vertex{
		a.x - b.x,
		a.y - b.y,
		a.z - b.z,
	}
}

func (a vertex) scale(s float64) vertex {
	return vertex{
		s * a.x,
		s * a.y,
		s * a.z,
	}
}

func (a vertex) dot(b vertex) float64 {
	return a.x*b.x + a.y*b.y + a.z*b.z
}

func (a vertex) length() float64 {
	return math.Sqrt(a.x*a.x + a.y*a.y + a.z*a.z)
}

func newPlane(v1, v2, v3 vertex) plane {
	w1 := v2.sub(v1)
	w2 := v3.sub(v1)
	p := w1.cross(w2)
	p = p.scale(1 / p.length())

	// x*p.x + y*p.y + z*p.z + d = 0
	// d = -(x*p.x + y*p.y + z*p.z)
	d := -p.dot(v1)
	return plane{
		a: p.x,
		b: p.y,
		c: p.z,
		d: d,
	}
}

func (p plane) eval(v vertex) float64 {
	return p.a*v.x + p.b*v.y + p.c*v.z + p.d
}

func interpolate(v1, v2 vertex) func(vertex) vertex {
	return func(s vertex) vertex {
		return vertex{
			(v2.x-v1.x)*s.x + v1.x,
			(v2.y-v1.y)*s.y + v1.y,
			(v2.z-v1.z)*s.z + v1.z,
		}
	}
}

func (a vertex) less(b vertex) bool {
	return a.x < b.x || a.y < b.y || a.z < b.z
}