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examples/spiral_polygons/spiral_polygons.scad

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+use <shape_circle.scad>;
+use <hull_polyline2d.scad>;
+use <util/sum.scad>;
+
+beginning_radius = 10;
+line_width = 2;
+fn = 3;
+number_of_polygons = 10;
+height = 2;
+
+linear_extrude(height)
+    spiral_polygons(beginning_radius, line_width, fn, number_of_polygons);
+
+module spiral_polygons(beginning_radius, line_width, fn, n) {
+    theta = 180 / fn;
+	
+	y = beginning_radius - beginning_radius * cos(theta);
+	dr = y / cos(theta);
+	pw = pow((beginning_radius + dr) * sin(theta), 2);
+	
+	function a(ri, ro, i) = acos((pow(ro, 2) + pow(ri, 2) - pw * pow(0.985, i)) / (2 * ro * ri));
+	
+	module drawPolygon(r) {
+	    pts = shape_circle(radius = r, $fn = fn);
+	    hull_polyline2d(concat(pts, [pts[0]]), width = line_width, $fn = 12);
+	}
+	
+	rs = [for(i = [0: n - 1]) beginning_radius + i * dr];
+	as = [for(i = [1: n - 1]) a(rs[i - 1], rs[i], i) / 2];
+	
+	rotate(-as[0])
+	    drawPolygon(beginning_radius);
+
+	for(i = [1:n - 1]) {
+	    rotate(sum([for(j = [0:i - 1]) as[j]]))
+	        drawPolygon(rs[i]);	
+	}
+}

examples/spiral_polygons/stick_tower.scad

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+use <line3d.scad>;
+
+/* [Basic] */
+
+stick_leng = 80;
+stick_diameter = 5;
+inner_square_leng = 60;
+leng_diff = 1.75;
+min_leng = 13;
+stick_fn = 24;
+
+/* [Advanced] */
+
+cap_style = "CAP_CIRCLE"; // [CAP_BUTT, CAP_CIRCLE, CAP_SPHERE]
+angle_offset = 5;
+layer_offset = 1.2;
+
+module stick_square(inner_square_leng, stick_leng, stick_diameter, cap_style) {
+    diff_leng = stick_leng - inner_square_leng;
+    half_inner_square_leng = inner_square_leng / 2;
+    half_stick_leng = stick_leng / 2;
+    
+    module stick() {
+        line3d(
+            [0, -half_stick_leng, 0], 
+            [0, half_stick_leng, 0], 
+            stick_diameter,
+            cap_style,
+            cap_style
+        );
+    }
+
+    module sticks() {
+        translate([-half_inner_square_leng, 0, 0])
+            stick();
+        translate([half_inner_square_leng, 0, 0])
+            stick();
+    }
+
+    sticks();
+    translate([0, 0, stick_diameter]) 
+    rotate(90) 
+        sticks();
+}
+    
+module spiral_stack(orig_leng, orig_height, current_leng, leng_diff, min_leng, angle_offset, pre_height = 0, i = 0) {
+    if(current_leng > min_leng) {
+        angle = atan2(leng_diff, current_leng - leng_diff);
+        
+        factor = current_leng / orig_leng;
+        
+        translate([0, 0, pre_height]) 
+        scale(factor) 
+            children();
+         
+        next_square_leng = sqrt(pow(leng_diff, 2) + pow(current_leng - leng_diff, 2));
+        
+        height = factor * orig_height + pre_height;
+        
+        rotate(angle + angle_offset)
+            spiral_stack(
+                orig_leng, 
+                orig_height, 
+                next_square_leng, 
+                leng_diff, 
+                min_leng,
+                angle_offset,                
+                height,
+                i + 1
+            ) children();
+    } 
+}
+
+height = stick_diameter * layer_offset;
+$fn = stick_fn;
+
+spiral_stack(inner_square_leng, stick_diameter * 2, inner_square_leng, leng_diff, min_leng, angle_offset)
+    stick_square(
+        inner_square_leng, 
+        stick_leng, 
+        height, 
+        cap_style
+    );