7-spheres-3d

diff --git a/model.py b/model.py
@@ -29,27 +29,42 @@ class Model:
 
     def write_obj(self, path: str):
         with open(path, "w") as f:
+            vs = set()       # vertices
+            eff_vis = list() # effective indixes
+
             f.write("# vertices\n")
 
-            # TODO: omit repeated points
+            vi = 0 # OBJ indices start at 1
             for x1, x2, x3 in self.vertices():
-                f.write(f"v {x1:.3f} {x2:.3f} {x3:.3f}\n")
+                v = f"{x1:.3f} {x2:.3f} {x3:.3f}"
+                eff_vis.append(vi)
+
+                if v not in vs:
+                    vs.add(v)
+                    vi += 1
+
+                    f.write(f"v {v}\n")
 
             f.write("\n# faces\n")
 
-            v_i = 1 # OBJ indices start at 1
+            v_i = 0
+            fs = set() # faces
             for patch in self.patches:
                 _, cols, rows = patch.shape
 
                 for theta_i in range(rows - 1):
                     for xi_i in range(cols - 1):
-                        v1 = v_i + xi_i + theta_i * cols
-                        v2 = v_i + xi_i + (theta_i + 1) * cols
-                        v3 = v_i + (xi_i + 1) + theta_i * cols
-                        v4 = v_i + (xi_i + 1) + (theta_i + 1) * cols
-
-                        f.write(f"f {v1} {v2} {v3}\n")
-                        f.write(f"f {v2} {v4} {v3}\n")
+                        v1 = eff_vis[v_i + xi_i + theta_i * cols]
+                        v2 = eff_vis[v_i + xi_i + (theta_i + 1) * cols]
+                        v3 = eff_vis[v_i + (xi_i + 1) + theta_i * cols]
+                        v4 = eff_vis[v_i + (xi_i + 1) + (theta_i + 1) * cols]
+
+                        if (v1, v2, v3) not in fs:
+                            fs.add((v1, v2, v3))
+                            f.write(f"f {v1} {v2} {v3}\n")
+                        if (v2, v4, v3) not in fs:
+                            fs.add((v1, v2, v3))
+                            f.write(f"f {v2} {v4} {v3}\n")
 
                 v_i += rows * cols
 
@@ -109,7 +124,7 @@ def brieskorn_surface(z0: complex, n: int,
                       patches: Iterator[Tuple[int, int]] = None,
                       eps: float = EPS, xi_max: float = XI_MAX) -> Model:
     """
-    Returns the model of the Brieskorn surface z1^3 + z2^(6 n - 1) = -z0^2
+    Returns the model of the Brieskorn surface z0^2 + z1^3 + z2^(6 n - 1) = 0
     """
     if not (1 <= n <= 11):
         raise ValueError(f"\"n\" should be in between 1 and 11: n = {n}")
@@ -141,26 +156,28 @@ def brieskorn_surface(z0: complex, n: int,
 
 def main():
     print("==> creating Brieskorn model for n = 1")
-    for k1 in range(3):
-        for k2 in range(5):
-            z0 = 1/2
-
-            eps = 0.1
-            if k2 == 4: eps = 0.008
-
-            print(f"=>  creating patch ({k1}, {k2:2})...", end=" ", flush=True)
-            m = brieskorn_surface(z0, 1, patches = [(k1, k2)], eps=eps)
-            print("done!")
-
-            print("=>  rendering model to OBJ...", end=" ", flush=True)
-            m.write_obj(f"models/brieskorn1/{k1}.{k2}.obj")
-            print("done!")
-
-    # print("=> creating Brieskorn model for n = 6...", end=" ", flush=True)
-    # m = brieskorn_surface(6, eps=0.05)
-    # print("done!")
-    # print("=> rendering model to OBJ...", end=" ", flush=True)
-    # m.write_obj("models/brieskorn6.obj")
-    # print("done!")
+
+    z0 = 1/2
+    eps = 0.1
+    print(f"=>  creating patches (k1, 3), with resulution ϵ = {eps}...",
+          end=" ", flush=True)
+    m = brieskorn_surface(z0, 1,
+                          patches = ((k1, 3) for k1 in range(3)), eps=eps)
+    print("done!")
+
+    print("=>  rendering model to OBJ...", end=" ", flush=True)
+    m.write_obj(f"models/brieskorn1/brieskorn1.1.obj")
+    print("done!")
+
+    eps = 0.008
+    print(f"=>  creating patches (k1,  4) with resulution ϵ = {eps}...",
+          end=" ", flush=True)
+    m = brieskorn_surface(z0, 1,
+                          patches = ((k1, 4) for k1 in range(3)), eps=eps)
+    print("done!")
+
+    print("=>  rendering model to OBJ...", end=" ", flush=True)
+    m.write_obj(f"models/brieskorn1/brieskorn1.2.obj")
+    print("done!")
 
 if __name__ == "__main__": main()