added bezier

README.md

@@ -23,3 +23,5 @@ I've been using OpenSCAD for years and created some funny things. Some of them i
 	- [hollow_out](https://openhome.cc/eGossip/OpenSCAD/lib-hollow_out.html)
 	- [bend](https://openhome.cc/eGossip/OpenSCAD/lib-bend.html)
 
+- Math
+    - [bezier](https://openhome.cc/eGossip/OpenSCAD/lib-bezier.html)

docs/lib-bezier.md

@@ -0,0 +1,28 @@
+# bezier
+
+Given a set of control points, the bezier function returns points of the Bézier path. Combined with the `polyline`, `polyline3d` or `hull_polyline3d` module defined in my lib-openscad, you can create a Bézier curve.
+
+## Parameters
+
+- `t_step` : The distance between two points of the Bézier path.
+- `points` : A set of `[x, y, z]` control points.
+
+## Examples
+
+If you have four control points and combine with the `hull_polyline3d` module:
+
+	t_step = 0.05;
+	width = 2;
+	
+	p0 = [0, 0, 0];
+	p1 = [40, 60, 35];
+	p2 = [-50, 90, 0];
+	p3 = [0, 200, -35];
+	
+	points = bezier(t_step, 
+	    [p0, p1, p2, p3]
+	);
+	
+	hull_polyline3d(points, width);      
+
+![bezier](images/lib-bezier-1.JPG)

src/bezier.scad

@@ -0,0 +1,46 @@
+/**
+* bezier.scad
+*
+* Given a set of control points, the bezier function returns points of the Bézier path. 
+* Combined with the polyline, polyline3d or hull_polyline3d module defined in my lib-openscad, 
+* you can create a Bézier curve.
+* 
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier.html
+*
+**/ 
+
+function _combi(r, n) = 
+    n == 0 ? 1 : (_combi(r, n - 1) * (r - n + 1) / n);
+        
+function bezier_coordinate(t, pn, n, i = 0) = 
+    i == n + 1 ? 0 : 
+        (_combi(n, i) * pn[i] * pow(1 - t, n - i) * pow(t, i) + 
+            bezier_coordinate(t, pn, n, i + 1));
+        
+function _bezier_point(t, points) = 
+    [
+        bezier_coordinate(
+            t, 
+            [points[0][0], points[1][0], points[2][0], points[3][0]], 
+            len(points) - 1
+        ),
+        bezier_coordinate(
+            t, 
+            [points[0][1], points[1][1], points[2][1], points[3][1]], 
+            len(points) - 1
+        ),
+        bezier_coordinate(
+            t, 
+            [points[0][2], points[1][2], points[2][2], points[3][2]], 
+            len(points) - 1
+        )
+    ];
+
+function bezier(t_step, points) = 
+    [
+        for(t = [0: t_step: 1 + t_step]) 
+            _bezier_point(t, points)
+    ];