refactor out a tri_circle_packing

src/experimental/_impl/_circle_packing_triangle.scad

@@ -1,44 +0,0 @@
-use <triangle/tri_incenter.scad>;
-
-function r(sin, leng_cv, pre_R) = sin * (leng_cv - pre_R) / (1 + sin);
-
-function circle_packing_triangle(t, density, min_r) =
-    let(
-        center = tri_incenter(t),
-        s1 = t[1] - t[0],
-        s2 = t[2] - t[1],
-        s3 = t[0] - t[2],
-        leng_s1 = norm(s1),
-        leng_s2 = norm(s2),
-        leng_s3 = norm(s3),
-        R = abs(cross(s1, s2)) / (leng_s1 + leng_s2 + leng_s3),
-        ca = center - t[0],
-        leng_ca = norm(ca),
-        unit_ca = ca / leng_ca,
-        sina = R / leng_ca,
-        cb = center - t[1],
-        leng_cb = norm(cb),
-        unit_cb = cb / leng_cb,
-        sinb = R / leng_cb,
-        cc = center - t[2],
-        leng_cc = norm(cc),
-        unit_cc = cc / leng_cc,
-        sinc = R / leng_cc,
-        _small_circles = function(density, pre_Ra = R, pre_Rb = R, pre_Rc = R) 
-            density <= 0 ? [] :
-            let(
-                ra = r(sina, leng_ca, pre_Ra),
-                Ra = pre_Ra + ra,
-                rb = r(sinb, leng_cb, pre_Rb),
-                Rb = pre_Rb + rb,
-                rc = r(sinc, leng_cc, pre_Rc),
-                Rc = pre_Rc + rc
-            )
-            [
-                if(ra > min_r) [center - unit_ca * Ra, ra], 
-                if(rb > min_r) [center - unit_cb * Rb, rb], 
-                if(rc > min_r) [center - unit_cc * Rc, rc], 
-                each _small_circles(density - 1, ra + Ra, rb + Rb, rc + Rc)]
-    )
-    [[center, R], each _small_circles(density - 1)];    
-    

src/experimental/circle_packing.scad

@@ -1,20 +1,20 @@
-use <triangle/tri_delaunay.scad>;
+use <experimental/tri_circle_packing.scad>;
 
-use <_impl/_circle_packing_triangle.scad>;
+use <triangle/tri_delaunay.scad>;
 
 function circle_packing(points, density = 1, min_r = 1) =
     [
         for(t = tri_delaunay(points, ret = "TRI_SHAPES"))
-        each circle_packing_triangle(t, density, min_r)
+        each tri_circle_packing(t, density, min_r)
     ];
 
 
 $fn = 24;
-density = 4;
+density = 3;
 min_r = 1;
 points = [for(i = [0:100]) rands(-100, 100, 2)]; 
 
 for(c = circle_packing(points, density, min_r)) {
     translate(c[0])
         sphere(c[1]);
-}
+}

src/experimental/circle_packing3.scad

@@ -1,7 +1,8 @@
 use <experimental/tri_subdivide.scad>;
+use <experimental/tri_circle_packing.scad>;
+
 use <triangle/tri_delaunay.scad>;
 
-use <_impl/_circle_packing_triangle.scad>;
 
 function circle_packing3(points, density = 1, min_r = 1) =
     [
@@ -12,7 +13,7 @@ function circle_packing3(points, density = 1, min_r = 1) =
 function circle_packing_triangle3(t, density, min_r) =
     [
         for(st = tri_subdivide(t, density))
-        each circle_packing_triangle(st, density, min_r)
+        each tri_circle_packing(st, density, min_r)
     ];
     
 $fn = 24;

src/experimental/tri_circle_packing.scad

@@ -0,0 +1,79 @@
+use <triangle/tri_incenter.scad>;
+use <ptf/ptf_rotate.scad>;
+
+function r(sin, leng_cv, pre_R) = sin * (leng_cv - pre_R) / (1 + sin);
+
+// the 3rd circle
+function c3_r(r1, r2) = (r1 * r2) / (r1 + r2 + 2 * sqrt(r1 * r2));
+function c3_a(r1, r2, r3) = 
+    let(
+        a = r3 + r1,
+        b = r3 + r2,
+        c = r1 + r2
+    )
+    acos((b ^ 2 + c ^ 2 - a ^ 2) / (2 * b * c));
+
+function tri_circle_packing(t, density, min_r) =
+    let(
+        center = tri_incenter(t),
+        s1 = t[1] - t[0],
+        s2 = t[2] - t[1],
+        s3 = t[0] - t[2],
+        leng_s1 = norm(s1),
+        leng_s2 = norm(s2),
+        leng_s3 = norm(s3),
+        R = abs(cross(s1, s2)) / (leng_s1 + leng_s2 + leng_s3),
+        ca = center - t[0],
+        leng_ca = norm(ca),
+        unit_ca = ca / leng_ca,
+        sina = R / leng_ca,
+        cb = center - t[1],
+        leng_cb = norm(cb),
+        unit_cb = cb / leng_cb,
+        sinb = R / leng_cb,
+        cc = center - t[2],
+        leng_cc = norm(cc),
+        unit_cc = cc / leng_cc,
+        sinc = R / leng_cc,
+        _small_circles = function(density, pre_leng_a = R, pre_leng_b = R, pre_leng_c = R, pre_ra = R, pre_rb = R, pre_rc = R) 
+            density <= 0 ? [] :
+            let(
+                ra = r(sina, leng_ca, pre_leng_a),
+                Ra = pre_leng_a + ra,
+                ct_a = center - unit_ca * Ra,
+
+                rb = r(sinb, leng_cb, pre_leng_b),
+                Rb = pre_leng_b + rb,
+                ct_b = center - unit_cb * Rb,
+
+                rc = r(sinc, leng_cc, pre_leng_c),
+                Rc = pre_leng_c + rc,
+                ct_c = center - unit_cc * Rc,
+
+                r3a = c3_r(pre_ra, ra),
+                alpha3a = c3_a(pre_ra, ra, r3a),
+                vta = unit_ca * (r3a + ra),
+                ct1a = ct_a + ptf_rotate(vta, alpha3a),
+                ct2a = ct_a + ptf_rotate(vta, -alpha3a),
+
+                r3b = c3_r(pre_rb, rb),
+                alpha3b = c3_a(pre_rb, rb, r3b),
+                vtb = unit_cb * (r3b + rb),
+                ct1b = ct_b + ptf_rotate(vtb, alpha3b),
+                ct2b = ct_b + ptf_rotate(vtb, -alpha3b),
+
+                r3c = c3_r(pre_rc, rc),
+                alpha3c = c3_a(pre_rc, rc, r3c),
+                vtc = unit_cc * (r3c + rc),
+                ct1c = ct_c + ptf_rotate(vtc, alpha3c),
+                ct2c = ct_c + ptf_rotate(vtc, -alpha3c)                  
+            )
+            [
+                if(ra > min_r) each [[ct_a, ra], if(r3a > min_r) each [[ct1a, r3a], [ct2a, r3a]]], 
+                if(rb > min_r) each [[ct_b, rb], if(r3b > min_r) each [[ct1b, r3b], [ct2b, r3b]]], 
+                if(rc > min_r) each [[ct_c, rc], if(r3c > min_r) each [[ct1c, r3c], [ct2c, r3c]]], 
+                each _small_circles(density - 1, ra + Ra, rb + Rb, rc + Rc, ra, rb, rc)
+            ]
+    )
+    [[center, R], each _small_circles(density - 1)];    
+