more fixes

butterfly_catastrophe.py

@@ -20,11 +20,11 @@ import os
 A_FIXED = -3.0      # butterfly unfolding parameter (must be negative)
 
 # ── Tuning ──────────────────────────────────────────────────────────────────
-GRID      = 50      # control-space resolution — increase to 80–100 for print
+GRID      = 80      # control-space resolution — increase to 100–120 for print
 C_RANGE   = (-2.0, 7.0)   # range of control parameter c
 D_RANGE   = (-6.0, 6.0)   # range of control parameter d
 X_RANGE   = 2.5            # half-width of root search window
-MAX_EDGE_DZ = 0.6          # max z-jump per quad edge (filters branch mismatches)
+MAX_MATCH_DZ = 0.8         # max z-gap for inter-row branch matching
 
 # ── 1. Root finding ──────────────────────────────────────────────────────────
 
@@ -58,53 +58,127 @@ def find_roots(c, d, n_starts=80):
                 roots.append(x)
     return sorted(roots)
 
-# ── 2. Build mesh ────────────────────────────────────────────────────────────
+# ── 2. Branch tracking ───────────────────────────────────────────────────────
+
+def track_branches(roots_along_axis):
+    """
+    Track branches along one axis (fixed d, varying c) using greedy
+    nearest-neighbour matching.  Returns a list of tracks; each track is a
+    list of length GRID where entry i is the root value at column i, or None
+    when the branch does not exist there.
+
+    Sorting-index matching (branch 0 always = branch 0) breaks at folds
+    because two adjacent branches coalesce, shifting every higher index by
+    one.  Nearest-neighbour tracking follows each physical sheet through the
+    fold correctly: the two merging branches each get None past the fold, and
+    the surviving sheet keeps its track unbroken.
+    """
+    n = len(roots_along_axis)
+    if n == 0:
+        return []
+
+    tracks = [[r] for r in roots_along_axis[0]]
+
+    for i in range(1, n):
+        curr = roots_along_axis[i]
+
+        prev_live = [(ti, t[-1]) for ti, t in enumerate(tracks)
+                     if t[-1] is not None]
+        prev_matched, curr_matched = set(), set()
+        matches = {}  # track_idx → curr_root_idx
+
+        cands = sorted(
+            [(abs(pv - curr[ci]), ti, ci)
+             for ti, pv in prev_live
+             for ci in range(len(curr))],
+            key=lambda x: x[0]
+        )
+        for _, ti, ci in cands:
+            if ti not in prev_matched and ci not in curr_matched:
+                matches[ti] = ci
+                prev_matched.add(ti)
+                curr_matched.add(ci)
+
+        for ti, t in enumerate(tracks):
+            t.append(curr[matches[ti]] if ti in matches else None)
+
+        # Branches that appear for the first time at this column
+        for ci in range(len(curr)):
+            if ci not in curr_matched:
+                tracks.append([None] * i + [curr[ci]])
+
+    return tracks
+
+# ── 3. Build mesh ────────────────────────────────────────────────────────────
 
 def build_mesh():
     c_vals = np.linspace(*C_RANGE, GRID)
     d_vals = np.linspace(*D_RANGE, GRID)
 
     print(f'  Computing roots on {GRID}×{GRID} grid…')
+    # roots_grid[i][j] = sorted roots at (c_vals[i], d_vals[j])
     roots_grid = [[find_roots(c, d) for d in d_vals] for c in c_vals]
 
+    # Track branches along each row (fixed d, varying c)
+    print('  Tracking branches…')
+    row_tracks = []
+    for j in range(GRID):
+        row = [roots_grid[i][j] for i in range(GRID)]
+        row_tracks.append(track_branches(row))
+    # row_tracks[j] = list of tracks; track[i] = root value at column i
+
     triangles = []
 
-    for i in range(GRID - 1):
+    for j in range(GRID - 1):
-        for j in range(GRID - 1):
+        d0, d1 = d_vals[j], d_vals[j+1]
+        tracks_j  = row_tracks[j]
+        tracks_j1 = row_tracks[j + 1]
+
+        for i in range(GRID - 1):
             c0, c1 = c_vals[i], c_vals[i+1]
-            d0, d1 = d_vals[j], d_vals[j+1]
 
-            r00 = roots_grid[i  ][j  ]
+            # Collect valid quad-edge segments for both rows at this column
-            r10 = roots_grid[i+1][j  ]
+            # A segment is valid when both endpoints of the edge exist
-            r11 = roots_grid[i+1][j+1]
+            segs_j  = [(t[i], t[i+1], k)
-            r01 = roots_grid[i  ][j+1]
+                       for k, t in enumerate(tracks_j)
+                       if t[i] is not None and t[i+1] is not None]
+            segs_j1 = [(t[i], t[i+1], k)
+                       for k, t in enumerate(tracks_j1)
+                       if t[i] is not None and t[i+1] is not None]
 
-            # Only draw branch k when ALL four corners have it.
+            if not segs_j or not segs_j1:
-            # The rs[-1] fallback used previously created false triangles at
+                continue
-            # fold edges by connecting unrelated branches — this is the main
-            # cause of the messy, self-intersecting geometry.
-            n = min(len(r00), len(r10), len(r11), len(r01))
 
-            for k in range(n):
+            # Greedy nearest-neighbour matching between the two row-bands.
-                p0 = (c0, d0, r00[k])
+            # Each j1-segment is claimed by at most one j-segment so we never
-                p1 = (c1, d0, r10[k])
+            # emit overlapping quads.
-                p2 = (c1, d1, r11[k])
+            j1_used = set()
-                p3 = (c0, d1, r01[k])
+            # Sort j-segments by midpoint so iteration order is deterministic
+            for x00, x10, _ in sorted(segs_j, key=lambda s: (s[0] + s[1]) / 2):
+                best_k1 = best_x01 = best_x11 = None
+                best_dist = MAX_MATCH_DZ
+                for x01, x11, k1 in segs_j1:
+                    if k1 in j1_used:
+                        continue
+                    dist = max(abs(x00 - x01), abs(x10 - x11))
+                    if dist < best_dist:
+                        best_dist, best_k1 = dist, k1
+                        best_x01, best_x11 = x01, x11
 
-                # Reject quads where any edge has a large z-jump.  A large
+                if best_k1 is None:
-                # jump indicates a branch-index mismatch near a fold line
-                # (sorted order is preserved within a branch but can
-                # "swap" across folds where adjacent branches coalesce).
-                if any(abs(a[2] - b[2]) > MAX_EDGE_DZ
-                       for a, b in [(p0,p1),(p1,p2),(p2,p3),(p3,p0)]):
                     continue
+                j1_used.add(best_k1)
 
-                triangles.append((p0, p1, p2))
+                p00 = (c0, d0, x00)
-                triangles.append((p0, p2, p3))
+                p10 = (c1, d0, x10)
+                p11 = (c1, d1, best_x11)
+                p01 = (c0, d1, best_x01)
+                triangles.append((p00, p10, p11))
+                triangles.append((p00, p11, p01))
 
     return triangles
 
-# ── 3. Flat base ─────────────────────────────────────────────────────────────
+# ── 4. Flat base ─────────────────────────────────────────────────────────────
 
 def add_base(triangles, z_base=-2.8):
     c0, c1 = C_RANGE
@@ -127,7 +201,7 @@ def add_base(triangles, z_base=-2.8):
         ]
     return triangles
 
-# ── 4. ASCII STL output ───────────────────────────────────────────────────────
+# ── 5. ASCII STL output ───────────────────────────────────────────────────────
 
 def normal(v0, v1, v2):
     a = np.subtract(v1, v0)
@@ -153,7 +227,7 @@ def write_ascii_stl(triangles, filename):
     print(f'  Triangles : {len(triangles):,}')
     print(f'  File size : {size_kb:.0f} KB  →  {filename}')
 
-# ── 5. Main ───────────────────────────────────────────────────────────────────
+# ── 6. Main ───────────────────────────────────────────────────────────────────
 
 if __name__ == '__main__':
     print(f'Building butterfly catastrophe mesh (grid={GRID})…')