package main

import (
	"math"
)

type Vector3 struct {
	X, Y, Z float64
}

func (u Vector3) Add(v Vector3) Vector3 {
	return Vector3{u.X + v.X, u.Y + v.Y, u.Z + v.Z}
}

func (u Vector3) Neg() Vector3 {
	return Vector3{-u.X, -u.Y, -u.Z}
}

func (u Vector3) Sub(v Vector3) Vector3 {
	return u.Add(v.Neg())
}

func (u Vector3) Scale(a float64) Vector3 {
	return Vector3{a * u.X, a * u.Y, a * u.Z}
}

func (u Vector3) Dot(v Vector3) float64 {
	return u.X*v.X + u.Y*v.Y + u.Z*v.Z
}

func (u Vector3) Cross(v Vector3) Vector3 {
	return Vector3{u.Y*v.Z - u.Z*v.Y, u.Z*v.X - u.X*v.Z, u.X*v.Y - u.Y*v.X}
}

func (u Vector3) LengthSquared() float64 {
	return u.Dot(u)
}

func (u Vector3) Length() float64 {
	return math.Sqrt(u.LengthSquared())
}

func (u Vector3) Normalized() Vector3 {
	return u.Scale(1.0 / u.Length())
}

func (u Vector3) Round() Vector3 {
	round := math.Round
	return Vector3{round(u.X), round(u.Y), round(u.Z)}
}

// i incident, n normal. Both vector should be normalized
func Reflect(i Vector3, n Vector3) Vector3 {
	y := i.Dot(n)
	return i.Add(n.Scale(2 * y))
}

// Todo : Refract

// Rodrigues' rotation formula. rotVector should be normalized
func rotate(u Vector3, rotVector Vector3, angle float64) Vector3 {
	cos, sin := math.Cos(angle), math.Sin(angle)
	vec1 := u.Scale(cos)
	vec2 := rotVector.Cross(u).Scale(sin)
	vec3 := rotVector.Scale(rotVector.Dot(u) * (1 - cos))
	return vec1.Add(vec2).Add(vec3)
}

func (v Vector3) Unpack() (float64, float64, float64) {
	return v.X, v.Y, v.Z
}