package engine

import (
	"fmt"
	"image"
	"strconv"
)

// Int3 is a an element of int^3.
type Int3 struct {
	X, Y, Z int
}

// Pt3(x, y, z) is shorthand for Int3{x, y, z}.
func Pt3(x, y, z int) Int3 {
	return Int3{x, y, z}
}

// String returns a string representation of p like "(3,4,5)".
func (p Int3) String() string {
	return "(" + strconv.Itoa(p.X) + "," + strconv.Itoa(p.Y) + "," + strconv.Itoa(p.Z) + ")"
}

// XY applies the Z-forgetting projection. (It returns just X and Y.)
func (p Int3) XY() image.Point {
	return image.Point{p.X, p.Y}
}

// Add performs vector addition.
func (p Int3) Add(q Int3) Int3 {
	return Int3{p.X + q.X, p.Y + q.Y, p.Z + q.Z}
}

// Sub performs vector subtraction.
func (p Int3) Sub(q Int3) Int3 {
	return p.Add(q.Neg())
}

// CMul performs componentwise multiplication.
func (p Int3) CMul(q Int3) Int3 {
	return Int3{p.X * q.X, p.Y * q.Y, p.Z * q.Z}
}

// Mul performs scalar multiplication.
func (p Int3) Mul(k int) Int3 {
	return Int3{p.X * k, p.Y * k, p.Z * k}
}

// CDiv performs componentwise division.
func (p Int3) CDiv(q Int3) Int3 {
	return Int3{p.X / q.X, p.Y / q.Y, p.Z / q.Z}
}

// Div performs scalar division by k.
func (p Int3) Div(k int) Int3 {
	return Int3{p.X / k, p.Y / k, p.Z / k}
}

// Neg returns the vector pointing in the opposite direction.
func (p Int3) Neg() Int3 {
	return Int3{-p.X, -p.Y, -p.Z}
}

// Coord returns the components of the vector.
func (p Int3) Coord() (x, y, z int) {
	return p.X, p.Y, p.Z
}

// Sign returns a sign vector.
func (p Int3) Sign() Int3 {
	return Int3{sign(p.X), sign(p.Y), sign(p.Z)}
}

// Dot returns the dot product of the two vectors.
func (p Int3) Dot(q Int3) int {
	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
}

func sign(m int) int {
	if m == 0 {
		return 0
	}
	if m < 0 {
		return -1
	}
	return 1
}

func signf(m float64) float64 {
	if m == 0 {
		return 0
	}
	if m < 0 {
		return -1
	}
	return 1
}

// Float3 is an element of float64^3.
type Float3 struct {
	X, Y, Z float64
}

// String returns a string representation of p like "(3.0,4.0,5.0)".
func (p Float3) String() string {
	return fmt.Sprintf("(%f,%f,%f)", p.X, p.Y, p.Z)
}

// Add performs vector addition.
func (p Float3) Add(q Float3) Float3 {
	return Float3{p.X + q.X, p.Y + q.Y, p.Z + q.Z}
}

// Sub performs vector subtraction.
func (p Float3) Sub(q Float3) Float3 {
	return p.Add(q.Neg())
}

// CMul performs componentwise multiplication.
func (p Float3) CMul(q Float3) Float3 {
	return Float3{p.X * q.X, p.Y * q.Y, p.Z * q.Z}
}

// Mul performs scalar multiplication.
func (p Float3) Mul(k float64) Float3 {
	return Float3{p.X * k, p.Y * k, p.Z * k}
}

// CDiv performs componentwise division.
func (p Float3) CDiv(q Float3) Float3 {
	return Float3{p.X / q.X, p.Y / q.Y, p.Z / q.Z}
}

// Div performs scalar division by k.
func (p Float3) Div(k float64) Float3 {
	return Float3{p.X / k, p.Y / k, p.Z / k}
}

// Neg returns the vector pointing in the opposite direction.
func (p Float3) Neg() Float3 {
	return Float3{-p.X, -p.Y, -p.Z}
}

// Coord returns the components of the vector.
func (p Float3) Coord() (x, y, z float64) {
	return p.X, p.Y, p.Z
}

// Sign returns a sign vector.
func (p Float3) Sign() Float3 {
	return Float3{signf(p.X), signf(p.Y), signf(p.Z)}
}

// Dot returns the dot product of the two vectors.
func (p Float3) Dot(q Float3) float64 {
	return p.X*q.X + p.Y*q.Y + p.Z*q.Z
}