geometry: implement `Point::dist` for 3D points

[nit.git] / lib / geometry / points_and_lines.nit

# This file is part of NIT (http://www.nitlanguage.org).
#
# Copyright 2014 Alexis Laferrière <alexis.laf@xymus.net>
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# Interfaces and classes to represent basic geometry needs.
module points_and_lines is serialize

import serialization

# 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

# 2D point with `x` and `z`
class Point[N: Numeric]
        super IPoint[N]

        redef var x: N = 0.0 is writable, optional
        redef var y: N = 0.0 is writable, optional
end

# Abstract 3d point, strongly linked to its implementation `Point3d`
interface IPoint3d[N: Numeric]
        super IPoint[N]

        # Depth coordinate
        fun z: N is abstract

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

        redef fun dist2(other)
        do return x.value_of(other.dist2_with_3d(self))

        redef fun dist2_with_2d(other)
        do return dist2_xy(other).add(z.mul(z))

        redef fun dist2_with_3d(other)
        do
                var dz = other.z.sub(z)
                var s = dist2_xy(other).add(dz.mul(dz))
                return x.value_of(s)
        end
end

# 3D point with `x`, `y` and `z`
class Point3d[N: Numeric]
        super IPoint3d[N]
        super Point[N]

        redef var z: N = 0.0 is writable, optional
end

# Abstract 2D line segment between two ordered points
interface ILine[N: Numeric]
        # The type of points that ends the segment
        type P: IPoint[N]

        # Point at the left-end of the segment
        fun point_left: P is abstract

        # Point at the right-end of the segment
        fun point_right: P is abstract

        redef fun to_s do return "{point_left}--{point_right}"
end

# 2D line segment between two ordered points
class Line[N: Numeric]
        super ILine[N]

        redef var point_left
        redef var point_right

        init
        do
                var a = point_left
                var b = point_right
                if a.x > b.x then
                        point_left = b
                        point_right = a
                end
        end
end

# Abstract 3D line segment between two ordered points
interface ILine3d[N: Numeric]
        super ILine[N]

        redef type P: IPoint3d[N]
end

# 3D line segment between two ordered points
class Line3d[N: Numeric]
        super Line[N]
        super ILine3d[N]
end