add vrn_sphere

src/experimental/note.md

@@ -6,4 +6,5 @@ new:
 
 - maze/mz_wang_tiles?
 - surface/sf_cylinder?
-- noise/worley_sphere?
+- noise/worley_sphere?
+- voronoi/vrn_sphere?

src/voronoi/_impl/_vrn_sphere_impl.scad

@@ -0,0 +1,7 @@
+function stereographic_proj_to_plane(point) =
+    let(n = 1 - point.z)
+    [point.x / n, point.y / n];
+
+function stereographic_proj_to_sphere(point) =
+    let(n = 1 + point.x ^ 2 + point.y ^ 2)
+    [2 * point.x / n, 2 * point.y / n, (-1 + point.x ^ 2 + point.y ^ 2) / n];

src/voronoi/vrn_sphere.scad

@@ -0,0 +1,38 @@
+use <_impl/_vrn_sphere_impl.scad>;
+use <vrn2_cells_from.scad>;
+
+function vrn_sphere(points) = 
+    let(
+	    r = norm(points[0]),
+	    plane_pts = [for(p = points) stereographic_proj_to_plane(p / r)],
+		inifinity = [4.5e8, 0],
+		vrn2_cells = vrn2_cells_from(concat(plane_pts, [inifinity]))
+	)
+    [
+		for(i = [0:len(vrn2_cells) - 2])
+		[for(p = vrn2_cells[i]) stereographic_proj_to_sphere(p) * r]
+	];
+	
+/*
+use <voronoi/vrn_sphere.scad>;
+use <fibonacci_lattice.scad>;
+use <polyline_join.scad>;
+
+n = 60;
+radius = 2;
+
+pts = fibonacci_lattice(n, radius);
+#for(p = pts) {
+    translate(p)
+        sphere(.05);
+}
+
+cells = vrn_sphere(pts);
+for(i = [0:len(cells) - 1]) {
+    cell = cells[i];
+
+    polyline_join(concat(cell, [cell[0]]))
+        sphere(.05);
+
+}
+*/