Improve NURBS and SSX intersection handling:

- Add `show_wires` property for better rendering control.
- Extend `_try_deflated_hard_case` with recursion support for tangential cases.
- Refactor `_leaf_boundary_test_and_march` and `_bez_ssx_recursive` with enhanced boundary logic and overlap deduplication.
- Standardize parameter naming for clarity (`atol` over `spt`).

Author: sth-v

examples/ssx/common_helpers.py

@@ -44,6 +44,7 @@ class WiresMaterial(CurveMaterial):
 class SurfaceMaterial:
 
     color:tuple[float,float,float,float]=field(default=(0.5, 0.5, 0.9, 0.05))
+    show_wires:bool=field(default=True)
     wires_material: WiresMaterial = field(
         default_factory=lambda: WiresMaterial((1.0, 1.0, 1.0, 1.0), show_control_net=False, u_count=1, v_count=1)
     )
@@ -98,7 +99,7 @@ def save_pkl(s1,s2,result,fp=None)->Path:
         fp=inspect.getfile(_find_root_frame(inspect.currentframe()))
     pth=Path(fp).with_suffix('.pkl')
     with open(pth, 'wb') as f:
-        pickle.dump(((s1, s2), [r.curve_xyz for r in result[0]], [r.curve_st for r in result[0]], [r.curve_uv for r in result[0]]), f)
+        pickle.dump(((s1, s2), [r.curve_xyz for r in result[0]], [r.curve_st for r in result[0]], [r.curve_uv for r in result[0]], [p.xyz for p in result[1]]), f)
     return pth
 
 
@@ -126,9 +127,9 @@ def draw_ssx(
     if viewer is None:
         viewer = Viewer(camera=OrbitCamera(target=bb.centroid(), distance=np.linalg.norm(bb.diag())*2, near=1.0))
 
-    viewer.add_nurbs_surface(s1, color=surf1_material.wires_material.color, surface_color=surf1_material.color, u_count=surf1_material.wires_material.u_count, v_count=surf1_material.wires_material.v_count)
+    viewer.add_nurbs_surface(s1, color=surf1_material.wires_material.color, surface_color=surf1_material.color, u_count=surf1_material.wires_material.u_count, v_count=surf1_material.wires_material.v_count,show_edges=surf1_material.show_wires,show_isocurves=surf1_material.show_wires,)
     viewer.add_nurbs_surface(
-        s2,color=surf2_material.wires_material.color,surface_color=surf2_material.color,u_count=surf2_material.wires_material.u_count,v_count=surf2_material.wires_material.v_count
+        s2,color=surf2_material.wires_material.color,surface_color=surf2_material.color,u_count=surf2_material.wires_material.u_count,v_count=surf2_material.wires_material.v_count,show_edges=surf1_material.show_wires,show_isocurves=surf1_material.show_wires,
 
     )
 

examples/ssx/nurbs_nurbs_intersection_8.py

@@ -44,7 +44,7 @@
 
 
 import logging
-from examples.ssx.common_helpers import parse_args, save_pkl, draw_ssx, VIEWER_INSTALLED, CurveMaterial, ControlNetMaterial, PointMaterial
+from examples.ssx.common_helpers import parse_args, save_pkl, draw_ssx, VIEWER_INSTALLED, CurveMaterial, ControlNetMaterial, PointMaterial,surface_material
 args = parse_args()
 logging.basicConfig(level=getattr(logging, args.loglevel, logging.INFO))
 from mmcore.numeric.intersection.ssx import nurbs_ssx
@@ -63,12 +63,13 @@
 RENDER = args.viewer and VIEWER_INSTALLED
 
 if RENDER:
+    surface_material.show_wires = False
     inter_curves_mat = CurveMaterial(
         (0.0, 1.0, 0.5, 1.0),
         show_control_net=args.show_inter_cpts,
         control_net_material=ControlNetMaterial((0.0, 1.0, 0.5, 0.7), control_point_material=PointMaterial((0.0, 1.0, 0.5, 0.4), size=8)),
     )
 
-    viewer = draw_ssx(s1, s2, result, intersection_curves_material=inter_curves_mat)
+    viewer = draw_ssx(s1, s2, result, surf1_material=surface_material,surf2_material=surface_material,intersection_curves_material=inter_curves_mat)
 
     viewer.run()

mmcore/extras/renderer/renderer3d.py

@@ -710,14 +710,15 @@ def _add_nurbs_curve(self, curve: NURBSCurveTuple, color=(1.0, 1.0, 1.0, 1.0),*a
         return tuple(self.add(to_homogeneous_1d(bezier.control_points, bezier.weights), rational=True, color=color,*args,**kwargs)        for bezier in beziers)
     def add_nurbs_curve(self, curve: NURBSCurveTuple, color=(1.0, 1.0, 1.0, 1.0),*args,**kwargs):
         return self._add_nurbs_curve(curve, color, *args, **kwargs)
-    def add_nurbs_surface(self, surface:NURBSSurfaceTuple, color=(1.0, 1.0, 1.0, 1.0),surface_color=(0.5, 0.5, 0.9, 0.05),u_count=1,v_count=1,*args,**kwargs):
+    def add_nurbs_surface(self, surface:NURBSSurfaceTuple, color=(1.0, 1.0, 1.0, 1.0),surface_color=(0.5, 0.5, 0.9, 0.05),u_count=1,v_count=1,show_edges:bool=True,show_isocurves:bool=True,*args,**kwargs):
         shade = kwargs.pop("shade", True)
         surface_color = surface_color
 
         surface_tol = kwargs.pop("surface_tol", 0.01)
+        meshes=[]
         if shade:
 
-            self._add_surface_mesh(surface, color=surface_color, tol=surface_tol)
+            meshes.append(self._add_surface_mesh(surface, color=surface_color, tol=surface_tol))
         (u0,u1),(v0,v1) = surface.interval()
         umid,vmid=(u1-u0)*0.5+u0, (v1-v0)*0.5+v0
         us=np.linspace(u0,u1,u_count+2)[1:][:-1]
@@ -727,13 +728,16 @@ def add_nurbs_surface(self, surface:NURBSSurfaceTuple, color=(1.0, 1.0, 1.0, 1.0
         color[2]*0.5,
         color[3])
         isolines=[]
-
-        for crv in  [extract_isocurve(surface, u,'u') for u in us]+[extract_isocurve(surface, v,'v') for v in vs]:
-            isolines.append(self._add_nurbs_curve(crv,iso_color,*args,**kwargs))
+        if show_isocurves:
+            for crv in  [extract_isocurve(surface, u,'u') for u in us]+[extract_isocurve(surface, v,'v') for v in vs]:
+                isolines.append(self._add_nurbs_curve(crv,iso_color,*args,**kwargs))
         bnds=[]
-        for bnd in extract_surface_boundaries(surface):
-            bnds.append(self._add_nurbs_curve(bnd,color,*args,**kwargs))
-        return tuple(bnds)+tuple(isolines)
+        if show_edges:
+            for bnd in extract_surface_boundaries(surface):
+
+                    bnds.append(self._add_nurbs_curve(bnd,color,*args,**kwargs))
+        return tuple(meshes)+tuple(bnds)+tuple(isolines)
+
 
     def _upload_matrices(self, P_row: np.ndarray, V_row: np.ndarray, M_row: np.ndarray):
         """

mmcore/numeric/bern.py

@@ -1196,7 +1196,7 @@ def bernstein_cutout_box_nd(control_grid: np.ndarray,
     Notes
     -----
     • Per axis k we split into up to three slabs: L=[0,a_k], M=[a_k,b_k], H=[b_k,1], with matrices
-      T^L_k, T^M_k, T^H_k computed once from de Casteljau (matrix form).
+      T^L_k, T^M_k, T^H_k computed once from de Casteljau (matrix form).
     • We enumerate the Cartesian product of available slabs across axes and exclude the all‑'M' box.
     • Each sub‑patch is produced by a single `einsum` that applies all T_k at once.
     """

mmcore/numeric/intersection/_deflate.py

@@ -1024,14 +1024,16 @@ def analyse_deflated_system(
         lo, hi = Bf[axis]
         if curve_mode != "krawczyk":
             gamma_rows = choose_gamma_3eq(sys, xw)
-            curve_4d = trace_gamma(
+            curve_4d, curve_h_steps = trace_gamma(
                 sys, gamma_rows, xw, Bf,
                 h0=curve_trace_h0,
                 h_min=curve_trace_h_min,
                 h_max=curve_trace_h_max,
                 max_steps=curve_trace_max_steps,
                 tol=curve_trace_tol,
             )
+            out["trace_points"] = curve_4d
+            out["trace_h_steps"] = curve_h_steps
             samples = []
             for xm in curve_4d:
                 fn = float(np.linalg.norm(sys.delta_point(xm)))
@@ -1343,12 +1345,13 @@ def newton_corrector_arclen(x_pred, t_pred, x_init=None, max_iter=12):
 
     def trace_one_direction(sign):
         pts = [x0.copy()]
+        h_steps = [0.0]  # step size used to reach each point (0 for initial)
         h = h0
 
         J0 = sys.jac_rows_point(x0, gamma_rows)
         t = nullspace_direction(J0)
         if t is None:
-            return pts
+            return pts, h_steps
         t *= sign
 
         for _ in range(max_steps):
@@ -1367,6 +1370,7 @@ def trace_one_direction(sign):
                                                      axis_near, bound_near, B, tol=tol)
                 if ok and inside(x_end):
                     pts.append(x_end)
+                    h_steps.append(h)
                 break
 
             # Predict
@@ -1384,6 +1388,7 @@ def trace_one_direction(sign):
                                                          axis_hit, bound_hit, B, tol=tol)
                     if ok and inside(x_end) and np.linalg.norm(sys.delta_point(x_end)) < 1e-7:
                         pts.append(x_end)
+                        h_steps.append(h)
                         solved = True
                         break
                 if solved:
@@ -1417,6 +1422,7 @@ def trace_one_direction(sign):
                 continue
 
             pts.append(x_new)
+            h_steps.append(h)
 
             # Update tangent
             Jn = sys.jac_rows_point(x_new, gamma_rows)
@@ -1429,12 +1435,15 @@ def trace_one_direction(sign):
 
             h = min(h_max, h * 1.2)
 
-        return pts
+        return pts, h_steps
 
-    fwd = trace_one_direction(+1)
-    bwd = trace_one_direction(-1)
-    bwd = bwd[::-1]
-    return bwd[:-1] + fwd
+    fwd_pts, fwd_h = trace_one_direction(+1)
+    bwd_pts, bwd_h = trace_one_direction(-1)
+    bwd_pts = bwd_pts[::-1]
+    bwd_h = bwd_h[::-1]
+    points = bwd_pts[:-1] + fwd_pts
+    h_steps = bwd_h[:-1] + fwd_h
+    return points, h_steps
 
 
 if __name__ == "__main__":