# Abstract 2d point, strongly linked to its implementation `Point`
interface IPoint[N: Numeric]

	# Horizontal coordinate
	fun x: N is abstract

	# Vertical coordinate
	fun y: N is abstract

	redef fun to_s do return "({x}, {y})"

	# Distance with `other`
	#
	# ~~~
	# var p0 = new Point[Float](0.0, 0.0)
	# var p1 = new Point[Float](2.0, 3.0)
	# assert p0.dist(p1).is_approx(3.6, 0.01)
	# ~~~
	#
	# If `self` or `other` are in 3D, the distance takes into account the 3 axes.
	# For a 2D point, the Z coordinate is considered to be 0.
	#
	# ~~~
	# var p2 = new Point3d[Float](0.0, 0.0, 0.0)
	# var p3 = new Point3d[Float](2.0, 3.0, 4.0)
	# var p4 = new Point[Float](2.0, 3.0)
	# assert p2.dist(p3).is_approx(5.385, 0.01)
	# assert p2.dist(p4).is_approx(3.606, 0.01)
	# ~~~
	fun dist(other: Point[Numeric]): N
	do
		return x.value_of(dist2(other).to_f.sqrt)
	end

	# Square of the distance with `other`
	#
	# May be used as an approximation to compare distance between two points.
	#
	# ~~~
	# var p0 = new Point[Float](0.0, 0.0)
	# var p1 = new Point[Float](2.0, 3.0)
	# assert p0.dist2(p1) == 13.0
	# ~~~
	#
	# If `self` or `other` are in 3D, the distance takes into account the 3 axes.
	# For a 2D point, the Z coordinate is considered to be 0.
	#
	# ~~~
	# var p2 = new Point3d[Float](0.0, 0.0, 0.0)
	# var p3 = new Point3d[Float](2.0, 3.0, 4.0)
	# var p4 = new Point[Float](2.0, 3.0)
	# assert p2.dist2(p3).is_approx(29.0, 0.01)
	# assert p2.dist2(p4).is_approx(13.0, 0.01)
	# assert p4.dist2(p2).is_approx(13.0, 0.01)
	# ~~~
	fun dist2(other: Point[Numeric]): N
	do return x.value_of(other.dist2_with_2d(self))

	private fun dist2_with_2d(other: IPoint[Numeric]): Numeric
	do return dist2_xy(other)

	private fun dist2_with_3d(other: IPoint3d[Numeric]): Numeric
	do return dist2_xy(other).add(other.z.mul(other.z))

	# Square of the distance with `other` on the X and Y axes
	private fun dist2_xy(other: IPoint[N]): N
	do
		var dx = other.x.sub(x)
		var dy = other.y.sub(y)
		var s = (dx.mul(dx)).add(dy.mul(dy))
		return x.value_of(s)
	end

	# Linear interpolation between `self` and `other` at `p` out of `1.0`
	#
	# ~~~
	# var p0 = new Point[Float](0.0, 0.0)
	# var p1 = new Point[Float](2.0, 3.0)
	# assert p0.lerp(p1, 0.0) == p0
	# assert p0.lerp(p1, 1.0) == p1
	# assert p0.lerp(p1, 0.5) == new Point[Float](1.0, 1.5)
	# ~~~
	#
	# TODO 3D implementation.
	fun lerp(other: Point[Numeric], p: Float): Point[N]
	do
		var xx = x.to_f + (other.x.to_f - x.to_f).to_f * p
		var yy = y.to_f + (other.y.to_f - y.to_f).to_f * p
		return new Point[N](x.value_of(xx), y.value_of(yy))
	end

	redef fun ==(o) do return o isa IPoint[Numeric] and o.x == x and o.y == y
end