added shape_cyclicpolygon

README.md

@@ -83,6 +83,7 @@ Too many dependencies? Because OpenSCAD doesn't provide namespace management, I
 	- [shape_ellipse](https://openhome.cc/eGossip/OpenSCAD/lib-shape_ellipse.html)
     - [shape_square](https://openhome.cc/eGossip/OpenSCAD/lib-shape_square.html)
 	- [shape_trapezium](https://openhome.cc/eGossip/OpenSCAD/lib-shape_trapezium.html)
+	- [shape_cyclicpolygon](https://openhome.cc/eGossip/OpenSCAD/lib-shape_cyclicpolygon.html)
     - [shape_pentagram](https://openhome.cc/eGossip/OpenSCAD/lib-shape_pentagram.html)	
 	- [shape_superformula](https://openhome.cc/eGossip/OpenSCAD/lib-shape_superformula.html)	
 

docs/lib-shape_cyclicpolygon.md

@@ -0,0 +1,58 @@
+# shape_cyclicpolygon
+
+Returns shape points of a regular cyclic polygon. They can be used with xxx_extrude modules of dotSCAD. The shape points can be also used with the built-in polygon module. 
+
+## Parameters
+
+- `sides` : The radius of the circle.
+- `circle_r` : The radius of the circumcircle.
+- `$fa`, `$fs`, `$fn` : Check [the circle module](https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Using_the_2D_Subsystem#circle) for more details.
+
+## Examples
+
+    include <shape_cyclicpolygon.scad>;
+
+    circle_r = 10;
+    corner_r = 3;
+
+    $fn = 24;
+
+    for(i = [0:2]) {
+        translate([i * circle_r * 2, 0, 0]) 
+            polygon(
+                shape_cyclicpolygon(
+                    sides = 3 + i, 
+                    circle_r = circle_r, 
+                    corner_r = corner_r
+                )
+            );
+    }
+
+    for(i = [0:2]) {
+        translate([i * circle_r * 2, -circle_r * 2, 0]) 
+            polygon(
+                shape_cyclicpolygon(
+                    sides = 4 + i, 
+                    circle_r = circle_r , 
+                    corner_r = corner_r
+                )
+            );
+    }
+
+![shape_cyclicpolygon](images/lib-shape_cyclicpolygon-1.JPG)
+
+    include <shape_cyclicpolygon.scad>;
+    include <rotate_p.scad>;
+    include <cross_sections.scad>;
+    include <polysections.scad>;
+    include <ring_extrude.scad>;
+
+    shape_pts = shape_cyclicpolygon(
+        sides = 5, 
+        circle_r = 10, 
+        corner_r = 3
+    );
+
+    ring_extrude(shape_pts, radius = 20, angle = 180, twist = 90);
+
+![shape_cyclicpolygon](images/lib-shape_cyclicpolygon-2.JPG)

src/shape_cyclicpolygon.scad

@@ -0,0 +1,55 @@
+/**
+* shape_cyclicpolygon.scad
+*
+* Returns shape points of a regular cyclic polygon.
+* They can be used with xxx_extrude modules of dotSCAD.
+* The shape points can be also used with the built-in polygon module.
+* 
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-shape_cyclicpolygon.html
+*
+**/
+
+include <__private__/__frags.scad>;
+include <__private__/__pie_for_rounding.scad>;
+
+function shape_cyclicpolygon(sides, circle_r, corner_r) =
+    let(
+        frag_a = 360 / sides,
+        corner_a = (180 - frag_a),
+        corner_circle_a = 180 - corner_a,
+        half_corner_circle_a = corner_circle_a / 2,
+        corner_circle_center = circle_r - corner_r / sin(corner_a / 2),
+        first_corner = [
+            for(
+                    pt = __pie_for_rounding(
+                        corner_r, 
+                        -half_corner_circle_a, 
+                        half_corner_circle_a, 
+                        __frags(corner_r) * corner_circle_a / 360
+                    )
+               )
+               [pt[0] + corner_circle_center, pt[1]]
+        ]
+
+    )
+    concat(
+        first_corner, 
+        [
+            for(side = [1:sides - 1])
+                for(pt = first_corner)
+                    let(
+                        a = frag_a * side,
+                        x = pt[0],
+                        y = pt[1],
+                        sina = sin(a),
+                        cosa = cos(a)
+                    )
+                    [
+                        x * cosa - y * sina,
+                        x * sina + y * cosa
+                    ]
+        ]
+    );