package main

import(
	"fmt";
	"math";
)

type Point interface {
	DistanceFromPoint(point Point) float64;
	DistanceFromCartesian(x, y float64) float64;
	DistanceFromPolar(r, θ float64) float64;
}

type cartesian struct { x, y float64 }

func (self cartesian) DistanceFromPoint(other Point) float64 {
	return other.DistanceFromCartesian(self.x, self.y);
}

func (self cartesian) DistanceFromCartesian(x, y float64) float64 {
	dx := math.Fabs(self.x - x);
	dy := math.Fabs(self.y - y);
	return math.Sqrt(dx*dx + dy*dy);
}

func (self cartesian) DistanceFromPolar(r, θ float64) float64 {
	x := r * math.Cos(θ);
	y := r * math.Sin(θ);
	return self.DistanceFromCartesian(x, y);
}

type polar struct { r, θ float64 }

func (self polar) DistanceFromPoint(other Point) float64 {
	return other.DistanceFromPolar(self.r, self.θ);
}

func (self polar) DistanceFromCartesian(x, y float64) (result float64) {
	r := math.Sqrt(x*x + y*y);
	θ := math.Atan(y/x);
	return self.DistanceFromPolar(r, θ);
}

func (self polar) DistanceFromPolar(r, θ float64) float64 {
	return math.Sqrt(
		(self.r * self.r)
		+ (r * r)
		- (2 * self.r * r * math.Cos(θ - self.θ)));
}

func main() {
	a := cartesian{1,1};
	b := polar{1,math.Pi/2};
	fmt.Println(a.DistanceFromPoint(b));
}