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

Signed-off-by: Alexis Laferrière <alexis.laf@xymus.net>

diff --git a/lib/geometry/points_and_lines.nit b/lib/geometry/points_and_lines.nit
index eef5606..16efae0 100644 (file)
--- a/lib/geometry/points_and_lines.nit
+++ b/lib/geometry/points_and_lines.nit
@@ -38,7 +38,16 @@ interface IPoint[N: Numeric]
        # assert p0.dist(p1).is_approx(3.6, 0.01)
        # ~~~
        #
-       # TODO 3D implementation.
+       # 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)
@@ -54,8 +63,28 @@ interface IPoint[N: Numeric]
        # assert p0.dist2(p1) == 13.0
        # ~~~
        #
-       # TODO 3D implementation.
+       # 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)
@@ -100,6 +129,19 @@ interface IPoint3d[N: Numeric]
        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`