supported count_clockwise

docs/lib-golden_spiral.md

@@ -0,0 +1,68 @@
+# golden_spiral
+
+Gets all points and angles on the path of a golden spiral. The distance between two  points is almost constant. 
+
+It returns a vector of `[[x, y], angle]`. 
+
+## Parameters
+
+- `from` : If any ray from the origin intersects two successive turnings of the spiral, we'll have two points. The `arm_distance` is the distance between these two points.
+- `to` : In polar coordinates `(r, θ)` Archimedean spiral can be described by the equation `r = bθ ` where `θ` is measured in radians. For being consistent with OpenSCAD, the function here use degrees. The `init_angle` is which angle the first point want to start.
+- `point_distance` : Distance between two points on the path.
+- `rt_dir` : `"CT_CLK"` for counterclockwise. `"CLK"` for clockwise. The default value is `"CT_CLK"`.
+
+## Examples
+    
+	include <polyline2d.scad>;
+    include <archimedean_spiral.scad>;
+	
+	points_angles = archimedean_spiral(
+	    arm_distance = 10,
+	    init_angle = 180,
+	    point_distance = 5,
+	    num_of_points = 100 
+	); 
+	
+	points = [for(pa = points_angles) pa[0]];
+	
+	polyline2d(points, width = 1);
+
+
+![archimedean_spiral](images/lib-archimedean_spiral-1.JPG)
+	
+    include <archimedean_spiral.scad>;
+    
+	points_angles = archimedean_spiral(
+	    arm_distance = 10,  
+	    init_angle = 180, 
+	    point_distance = 5,
+	    num_of_points = 100 
+	); 
+	
+	for(pa = points_angles) {
+	    translate(pa[0]) 
+	        circle(2);
+	}
+
+![archimedean_spiral](images/lib-archimedean_spiral-2.JPG)
+
+    include <archimedean_spiral.scad>;
+    
+    t = "3.141592653589793238462643383279502884197169399375105820974944592307816406286";
+
+	points = archimedean_spiral(
+	    arm_distance = 15,
+	    init_angle = 450, 
+	    point_distance = 12, 
+	    num_of_points = len(t) 
+	); 
+	
+	for(i = [0: len(points) - 1]) {
+	    translate(points[i][0])          
+	        rotate(points[i][1] + 90)  
+	            text(t[i], valign = "center", halign = "center");
+	}
+
+![archimedean_spiral](images/lib-archimedean_spiral-3.JPG)
+
+

src/golden_spiral.scad

@@ -33,34 +33,43 @@ function _remove_same_pts(pts1, pts2) =
         concat(pts1, [for(i = [1:len(pts2) - 1]) pts2[i]]) : 
         concat(pts1, pts2);    
 
-function _golden_spiral_from_ls_or_eql_to(from, to, point_distance ) = 
+function _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) = 
     let(
         f1 = _fast_fibonacci(from),
         f2 = _fast_fibonacci(from + 1),
         fn = floor(f1 * 6.28312 / point_distance), 
         $fn = fn + 4 - (fn % 4),
         circle_pts = circle_path(radius = f1, n = $fn / 4 + 1),
-        a_step = 360 / $fn,
+        len_pts = len(circle_pts),
-        arc_points_angles = [
+        a_step = 360 / $fn * rt_dir,
-            for(i = [0:len(circle_pts) - 1])
+        arc_points_angles = (rt_dir == 1 ? [
+            for(i = [0:len_pts - 1])
                 // to 3D points because of rotate_p
                 [[circle_pts[i][0], circle_pts[i][1], 0], a_step * i] 
-        ],
+        ] : [
+            for(i = [0:len_pts - 1]) let(idx = len_pts - i - 1)
+                // to 3D points because of rotate_p
+                [[circle_pts[idx][0], circle_pts[idx][1], 0], a_step * i] 
+        ]),
         offset = f2 - f1
     ) _remove_same_pts(
         arc_points_angles, 
         [
-            for(pt_a = _golden_spiral(from + 1, to, point_distance)) 
+            for(pt_a = _golden_spiral(from + 1, to, point_distance, rt_dir)) 
-                [rotate_p(pt_a[0], [0, 0, 90]) + [0, -offset, 0], pt_a[1] + 90]
+                [ 
+                    rotate_p(pt_a[0], [0, 0, 90 * rt_dir]) + 
+                    (rt_dir == 1 ? [0, -offset, 0] : [-offset, 0, 0]), 
+                    pt_a[1] + 90 * rt_dir
+                ]
         ] 
     ); 
 
-function _golden_spiral(from, to, point_distance) = 
+function _golden_spiral(from, to, point_distance, rt_dir) = 
     from <= to ? 
-        _golden_spiral_from_ls_or_eql_to(from, to, point_distance) : [];
+        _golden_spiral_from_ls_or_eql_to(from, to, point_distance, rt_dir) : [];
 
-function golden_spiral(from, to, point_distance) =    
+function golden_spiral(from, to, point_distance, rt_dir = "CT_CLK") =    
     [
-        for(pt_a = _golden_spiral(from, to, point_distance)) 
+        for(pt_a = _golden_spiral(from, to, point_distance, (rt_dir == "CT_CLK" ? 1 : -1))) 
             [[pt_a[0][0], pt_a[0][1]], pt_a[1]]  // to 2D points
     ];