7-spheres-3d

diff --git a/model.py b/model.py
@@ -105,13 +105,17 @@ def fermat_surface(n: int, eps: float = EPS, xi_max: float = XI_MAX) -> Model:
 
     return m
 
-def brieskorn_surface(n: int, patches: Iterator[Tuple[int, int]] = None,
+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) = 1
+    Returns the model of the Brieskorn surface z1^3 + z2^(6 n - 1) = -z0^2
     """
     if not (1 <= n <= 11):
-        raise ValueError(f"Parameter \"n\" should be in between 1 and 11: n = {n}")
+        raise ValueError(f"\"n\" should be in between 1 and 11: n = {n}")
+
+    if abs(z0) > 1:
+        raise ValueError(f"\"z0\" should have norm smaller than 1: z0 = {z0}")
 
     k0 = 6*n - 1
 
@@ -127,9 +131,9 @@ def brieskorn_surface(n: int, patches: Iterator[Tuple[int, int]] = None,
         if not (0 <= k1 < 3) or not (0 <= k2 < k0): continue
 
         u1 = (np.exp(xi + 1j * theta)+np.exp(-xi - 1j * theta))/2
-        z1 = s(k1, 3) * (u1**(2/3))
+        z1 = -(z0**(2/3)) * s(k1, 3) * (u1**(2/3))
         u2 = (np.exp(xi + 1j * theta)-np.exp(-xi - 1j * theta))/2j
-        z2 = s(k2, k0) * (u2**(2/k0))
+        z2 = -(z0**(2/k0)) * s(k2, k0) * (u2**(2/k0))
 
         m.append_patch(z1, z2)
 
@@ -139,11 +143,13 @@ 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 == 1: eps = 0.008
+            if k2 == 4: eps = 0.008
 
             print(f"=>  creating patch ({k1}, {k2:2})...", end=" ", flush=True)
-            m = brieskorn_surface(1, patches = [(k1, k2)], eps=eps)
+            m = brieskorn_surface(z0, 1, patches = [(k1, k2)], eps=eps)
             print("done!")
 
             print("=>  rendering model to OBJ...", end=" ", flush=True)