added path_extend

docs/lib-path_extend.md

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+# path_extend
+
+It extends a 2D stroke along a path. This module is suitable for a path created by a continuous function. 
+
+It depends on the rotate_p function and the polytransversals module. Remember to include "rotate_p.scad" and "polytransversals.scad".
+
+When using this module, you should use points to represent the 2D stroke.
+
+## Parameters
+
+- `stroke_pts` : A list of points represent a stroke. See the example below.
+- `path_pts` : A list of points represent the path.
+
+## Examples
+
+	include <rotate_p.scad>;
+	include <polytransversals.scad>;
+	include <path_extend.scad>;
+	include <circle_path.scad>;
+	include <archimedean_spiral.scad>;
+	
+	$fn = 96;
+	
+	stroke1 = [[-5, 2.5], [-2.5, 0], [0, 2.5], [2.5, 0], [5, 2.5]];
+	path_pts1 = circle_path(50, 60);
+	path_extend(stroke1, path_pts1);
+	
+	stroke2 = [[-4, 0], [0, 4], [4, 0]];
+	pts_angles = archimedean_spiral(
+	    arm_distance = 17,
+	    init_angle = 180,
+	    point_distance = 5,
+	    num_of_points = 85 
+	); 
+	
+	translate([120, 0, 0]) 
+	    path_extend(
+	        stroke2, 
+	        [for(pa = pts_angles) pa[0]]
+	    );
+
+![path_extend](images/lib-path_extend-1.JPG)

src/path_extend.scad

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+/**
+* path_extend.scad
+*
+* It extends a 2D stroke along a path. 
+* This module is suitable for a path created by a continuous function.
+* It depends on the rotate_p function and the polytransversals module. 
+* Remember to include "rotate_p.scad" and "polytransversals.scad".
+*
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-path_extend.html
+*
+**/
+
+module path_extend(stroke_pts, path_pts) {
+    function length(p1, p2) = 
+        let(
+            x1 = p1[0],
+            y1 = p1[1],
+            x2 = p2[0],
+            y2 = p2[1]
+        ) sqrt(pow(x2 - x1, 2) + pow(y2 - y1, 2));
+
+    function az(p1, p2) = 
+        let(
+            x1 = p1[0],
+            y1 = p1[1],
+            x2 = p2[0],
+            y2 = p2[1]
+        ) -90 + atan2((y2 - y1), (x2 - x1));
+    
+    leng_path_pts = len(path_pts);
+
+    function first_stroke() =
+        let(
+            p1 = path_pts[0],
+            p2 = path_pts[1],
+            a = az(p1, p2)
+        )
+        [
+            for(p = stroke_pts)
+                rotate_p(p, a) + p1
+        ];    
+    
+    function stroke(p1, p2) =
+        let(
+            leng = length(p1, p2),
+            a = az(p1, p2)
+        )
+        [
+            for(p = stroke_pts)
+                rotate_p(p + [0, leng], a) + p1
+        ];
+        
+    function path_extend_inner(index) =
+        index == leng_path_pts ? [] :
+            concat(
+               [stroke(path_pts[index - 1], path_pts[index])],
+               path_extend_inner(index + 1)
+           );
+    
+    polytransversals(
+        concat([first_stroke()], path_extend_inner(1))
+    );
+}