Splines do the job.

secondary_mesh_planning.py

@@ -5,6 +5,8 @@ import textwrap
 import math
 from pathlib import Path
 import webbrowser
+import scipy
+import numpy as np
 
 import click
 
@@ -257,26 +259,46 @@ def cli(out_svg, out_txt, mesh_thickness, offset, mesh_space, mesh_width, start,
     points = [(0, 0, 0)]
 
     radii.append(radii[-1] + 20)
-    rt = 10
-    dx = rt - offset
-    n = 0
-    e = 30
+    h = 18
     with open(out_txt, 'w') as f:
-        for i in range(steps):
-            rp, rt = rt, (radii[i] + radii[i+1])/2
+        for i, r in enumerate(radii):
+            sign_i = (i%2)*2 - 1
+            offset_i = 0 if i%2 == 0 else offset
+            a = math.pi/3 if i == 0 else -sign_i * math.pi/2
 
-            for j in range(e):
-                k = i + j/e
-                a = k**0.85 * math.pi # - k/steps * math.pi * 0.3
-                r = rp + (rt-rp)*j/e
-                x = dx + offset - math.cos(a)*r
-                y = math.sin(a)*r
-                points.append((x, y))
+            x = offset_i + math.cos(a)*r
+            y =            math.sin(a)*r
+            z = sign_i*h/2
+            points.append((x, y, z))
 
-                z = (math.cos(a/2 + 0.3*math.pi)**4) * 18
-                f.write(f'[{x}, {y}, {z}],')
-                n += 1
-    print(f'wrote {n} points')
+            a = -sign_i * math.pi/2
+            a -= math.pi/4
+            r += 15
+            x = offset_i + math.cos(a)*r
+            y =            math.sin(a)*r
+            z = sign_i*h/2
+            points.append((x, y, z))
+
+            if i == len(radii)-1:
+                break
+
+            a -= math.pi/2
+            x = offset_i + math.cos(a)*r
+            y =            math.sin(a)*r
+            z = -sign_i*h/2
+            points.append((x, y, z))
+
+        lens_cum = np.zeros(len(points))
+        total = 0
+        for i, (p1, p2) in enumerate(zip(points[:-1], points[1:])):
+            total += math.dist(p1, p2)
+            lens_cum[i+1] = total
+        lens_cum /= lens_cum[-1]
+        print(lens_cum)
+
+        points = scipy.interpolate.make_interp_spline(lens_cum, points)(np.linspace(0, 1, 500))
+        f.write(', '.join(f'[{x:.3f},{y:.3f},{z:.3f}]' for x, y, z in points))
+    print(f'wrote {len(points)} points')
 
     tags.append(Tag('path', fill='none', stroke='magenta', stroke_width='0.5mm', stroke_linecap='round', stroke_linejoin='round',
                     d='M ' + ' L '.join(f'{x:.3f},{y:.3f}' for x, y, z in points)))