added bezier_smooth

README.md

@@ -65,6 +65,7 @@ Too many dependencies? Because OpenSCAD doesn't provide namespace management, I
     - [circle_path](https://openhome.cc/eGossip/OpenSCAD/lib-circle_path.html)
     - [bezier_curve](https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html)
 	- [bezier_surface](https://openhome.cc/eGossip/OpenSCAD/lib-bezier_surface.html)
+	- [bezier_smooth](https://openhome.cc/eGossip/OpenSCAD/lib-bezier_smooth.html)
     - [helix](https://openhome.cc/eGossip/OpenSCAD/lib-helix.html)
     - [golden_spiral](https://openhome.cc/eGossip/OpenSCAD/lib-golden_spiral.html)
     - [archimedean_spiral](https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral.html)

docs/lib-bezier_smooth.md

@@ -0,0 +1,59 @@
+# bezier_smooth
+
+Given a path, the bezier_smooth function uses bazier curves to smooth all corners. You can use it to create smoothier lines or rounded shapes.
+
+Dependencies: the `bezier_curve` function.
+
+## Parameters
+
+- `path_pts` : A list of points represent the path.
+- `round_d` : Used to create the other two control points at the corner.
+- `t_step` : The distance between two points of the Bézier path at the corner. It defaults to 0.1.
+- `closed` : It defaults to `false`. If you have a closed path, set it to `true`.
+
+## Examples
+
+	include <hull_polyline3d.scad>;
+	include <bezier_curve.scad>;
+	include <bezier_smooth.scad>;
+
+	width = 2;
+	round_d = 15;
+
+	path_pts = [
+		[0, 0, 0],
+		[40, 60, 10],
+		[-50, 90, 30],
+		[-10, -10, 50]
+	];
+
+	hull_polyline3d(
+		path_pts, width
+	);
+
+	smoothed_path_pts = bezier_smooth(path_pts, round_d);
+
+	color("red") translate([30, 0, 0]) hull_polyline3d(
+		smoothed_path_pts, width
+	);
+
+![bezier_smooth](images/lib-bezier_smooth-1.JPG)
+
+	include <bezier_curve.scad>;
+	include <bezier_smooth.scad>;
+
+	round_d = 10;
+
+	path_pts = [
+		[0, 0],
+		[40, 0],
+		[0, 60]
+	];
+
+	polygon(path_pts);
+
+	smoothed_path_pts = bezier_smooth(path_pts, round_d, closed = true);
+
+	translate([50, 0, 0]) polygon(smoothed_path_pts);
+
+![bezier_smooth](images/lib-bezier_smooth-2.JPG)

src/bezier_smooth.scad

@@ -0,0 +1,81 @@
+/**
+* bezier_smooth.scad
+*
+* Given a path, the bezier_smooth function uses bazier curves to smooth all corners. 
+* 
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-bezier_curve.html
+*
+**/ 
+
+include <__private__/__to3d.scad>;
+include <__private__/__to2d.scad>;
+
+function _ya_za(p1, p2) = 
+    let(
+        dx = p2[0] - p1[0],
+        dy = p2[1] - p1[1],
+        dz = p2[2] - p1[2],
+        za = atan2(dy, dx),
+        ya = atan2(dz, sqrt(pow(dx, 2) + pow(dy, 2)))
+    ) [ya, za];
+    
+function _corner_ctrl_pts(round_d, p1, p2, p3) =
+    let(
+        _ya_za_1 = _ya_za(p1, p2),
+        _ya_za_2 = _ya_za(p3, p2),
+        
+        dz1 = sin(_ya_za_1[0]) * round_d,
+        dxy1 = cos(_ya_za_1[0]) * round_d,
+        dy1 = sin(_ya_za_1[1]) * dxy1,
+        dx1 = cos(_ya_za_1[1]) * dxy1,
+        
+        dz2 = sin(_ya_za_2[0]) * round_d,
+        dxy2 = cos(_ya_za_2[0]) * round_d,
+        dy2 = sin(_ya_za_2[1]) * dxy2,
+        dx2 = cos(_ya_za_2[1]) * dxy2       
+    )
+    [
+        p2 - [dx1, dy1, dz1],
+        p2,
+        p2 - [dx2, dy2, dz2]
+    ];
+    
+    
+function _bezier_corner(t_step, p1, p2, p3) =
+    bezier_curve(t_step, _corner_ctrl_pts(round_d, p1, p2, p3));
+
+function _recursive_bezier_smooth(pts, round_d, t_step, leng, i = 0) =
+    i <= leng - 3 ? 
+        concat(
+            _bezier_corner(t_step, pts[i], pts[i + 1], pts[i + 2]), 
+            _recursive_bezier_smooth(pts, round_d, t_step, leng, i + 1)
+        )
+        : [];    
+    
+function bezier_smooth(path_pts, round_d, t_step = 0.1, closed = false) =
+    let(
+        pts = len(path_pts[0]) == 3 ? path_pts : [for(p = path_pts) __to3d(p)],
+        leng = len(pts),
+        middle_pts = _recursive_bezier_smooth(pts, round_d, t_step, leng),
+        pth_pts = closed ?
+            concat(
+                _recursive_bezier_smooth(
+                    [pts[leng - 1], pts[0], pts[1]],
+                    round_d, t_step, 3
+                ),
+                middle_pts,
+                _recursive_bezier_smooth(
+                    [pts[leng - 2], pts[leng - 1], pts[0]],
+                    round_d, t_step, 3
+                )  
+            ) :
+            concat(
+                [pts[0]],
+                middle_pts,
+                [pts[leng - 1]]
+            )
+    ) 
+    len(path_pts[0]) == 2 ? [for(p = pth_pts) __to2d(p)] : pth_pts;