added sphere_spiral

README.md

@@ -47,6 +47,7 @@ Some modules may depend on other modules. For example, the `polyline2d` module d
     - [bezier](https://openhome.cc/eGossip/OpenSCAD/lib-bezier.html)
     - [cylinder_spiral](https://openhome.cc/eGossip/OpenSCAD/lib-cylinder_spiral.html)
     - [archimedean_spiral](https://openhome.cc/eGossip/OpenSCAD/lib-archimedean_spiral.html)
+    - [sphere_spiral](https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral.html)
 
 - Other
     - [box_extrude](https://openhome.cc/eGossip/OpenSCAD/lib-box_extrude.html)

docs/lib-sphere_spiral.md

@@ -0,0 +1,71 @@
+# sphere_spiral
+
+Creates all points and angles on the path of a spiral around a sphere. It returns a vector of `[[x, y, z], [ax, ay, az]]`. `[x, y, z]` is actually obtained from rotating `[radius, 0, 0]` by `[ax, ay, az]`. It depends on the `rotate_p` function. Remember to include rotate_p.scad first.
+
+## Parameters
+
+- `radius` : The radius of the sphere.
+- `za_step` : The spiral rotates around the z axis. When the rotated angle increases `za_step`, a point will be calculated.
+- `z_circles` : The spiral rotates around the z axis. This parameter determines how many circles it will rotate from the top to the end. It defaults to 1.
+- `begin_angle` : The default value is 0 which means begins from the north pole of the sphere. See examples below.
+- `end_angle` : The default value is 0 which means begins from the sourth pole of the sphere. See examples below.
+
+## Examples
+    
+	include <rotate_p.scad>;
+	include <hull_polyline3d.scad>;
+	include <sphere_spiral.scad>;
+	
+	points_angles = sphere_spiral(
+	    radius = 40, 
+	    za_step = 10, 
+	    z_circles = 20, 
+	    begin_angle = 90, 
+	    end_angle = 90
+	);
+	
+	hull_polyline3d([for(pa = points_angles) pa[0]], 1);
+	
+	%sphere(40);
+
+![sphere_spiral](images/lib-sphere_spiral-1.JPG)
+
+![sphere_spiral](images/lib-sphere_spiral-2.JPG)
+
+![sphere_spiral](images/lib-sphere_spiral-3.JPG)
+
+	include <rotate_p.scad>;
+	include <sphere_spiral.scad>;
+
+	points_angles = sphere_spiral(
+	    radius = 40, 
+	    za_step = 20, 
+	    z_circles = 40, 
+	    begin_angle = 900
+	);
+	
+	for(pa = points_angles) {
+	    translate(pa[0]) rotate(pa[1])
+	        rotate([90, 0, 90]) linear_extrude(1) 
+	            text("A", valign = "center", halign = "center");
+	}
+	
+	%sphere(40);
+
+![sphere_spiral](images/lib-sphere_spiral-5.JPG)
+
+	include <rotate_p.scad>;
+	include <hull_polyline3d.scad>;
+	include <sphere_spiral.scad>;
+	
+	points_angles = sphere_spiral(
+	    radius = 40, 
+	    za_step = 5
+	);
+	
+	for(a = [0:30:360]) {
+	    rotate(a) 
+	        hull_polyline3d([for(pa = points_angles) pa[0]], 2);
+	}
+
+![sphere_spiral](images/lib-sphere_spiral-5.JPG)

src/sphere_spiral.scad

@@ -0,0 +1,21 @@
+/**
+* sphere_spiral.scad
+*
+* Creates all points and angles on the path of a spiral around a sphere. 
+* It returns a vector of [[x, y, z], [ax, ay, az]]. [x, y, z] is actually
+* obtained from rotating [radius, 0, 0] by [ax, ay, az].
+* It depends on the rotate_p function. Remember to include rotate_p.scad first.
+* 
+* @copyright Justin Lin, 2017
+* @license https://opensource.org/licenses/lgpl-3.0.html
+*
+* @see https://openhome.cc/eGossip/OpenSCAD/lib-sphere_spiral.html
+*
+**/ 
+
+function sphere_spiral(radius, za_step, z_circles = 1, begin_angle = 0, end_angle = 0) = 
+    [
+        for(a = [begin_angle:za_step:90 * z_circles - end_angle]) 
+            let(ra = [0, -90 + 2 * a / z_circles, a])
+            [rotate_p([radius, 0, 0], ra), ra]
+    ];