added stereographic_extrude

README.md

@@ -44,6 +44,7 @@ Some modules may depend on other modules. For example, the `polyline2d` module d
 
 - Other
     - [box_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-box_extrude.html)
+    - [stereographic_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-stereographic_extrude.html)
 
 ## About dotSCAD
 

docs/lib-stereographic_extrude.md

@@ -0,0 +1,31 @@
+# stereographic_extrude
+
+Takes a 2D polygon as input and extends it onto a sphere. If you light up a lamp on the north pole of the sphere, the shadow will return to the original 2D polygon. For more information, take a look at [Stereographic projection](https://en.wikipedia.org/wiki/Stereographic_projection).
+
+The 2D polygon should center at the origin and you have to determine the side length of a square which can cover the 2D polygon. Because the 2D polygon will be extended onto a sphere, you can use `$fa`, `$fs` or `$fn` to controll the sphere resolution.
+
+## Parameters
+
+- `shadow_side_leng` : The side length of a square which can cover the 2D polygon.
+- `$fa`, `$fs`, `$fn` : Check [the sphere module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Primitive_Solids#sphere for more details.
+
+
+## Examples
+    
+	dimension = 100;
+	
+	render() stereographic_extrude(shadow_side_leng = dimension)
+	   text(
+            "M", size = dimension, 
+            valign = "center", halign = "center"
+       );
+	   
+	color("black") 
+	   text(
+            "M", size = dimension, 
+            valign = "center", halign = "center"
+       );
+
+![stereographic_extrude](images/lib-stereographic_extrude-1.JPG)
+
+For more advanced examples, take a look at [my stereographic_projection collection](https://www.thingiverse.com/JustinSDK/collections/stereographic-projection).

src/stereographic_extrude.scad

@@ -0,0 +1,35 @@
+/**
+* stereographic_extrude.scad
+*
+* Takes a 2D polygon as input and extends it onto a sphere. 
+* If you light up a lamp on the north pole of the sphere, the 
+* shadow will return to the original 2D polygon. For more 
+* information, take a look at [Stereographic projection](https://en.wikipedia.org/wiki/Stereographic_projection).
+*
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-stereographic_extrude.html
+*
+**/
+
+module stereographic_extrude(shadow_side_leng) {
+    half_side_length = shadow_side_leng / 2;
+    outer_sphere_r = half_side_length / 3;
+    a = atan(sqrt(2) * half_side_length / (2 * outer_sphere_r));
+    inner_sphere_r = outer_sphere_r * sin(a);
+    
+    intersection() { 
+        translate([0, 0, outer_sphere_r]) difference() {
+            sphere(outer_sphere_r);
+            sphere(outer_sphere_r / 2 + inner_sphere_r / 2);
+            
+            translate([0, 0, outer_sphere_r / 2]) 
+                linear_extrude(outer_sphere_r) 
+                    circle(inner_sphere_r * cos(a));
+        }
+     
+        linear_extrude(outer_sphere_r * 2, scale = 0.01) 
+            children();
+    }
+}