Frame: refine critical lens regions

tests/test_frame.c

@@ -164,9 +164,10 @@ int main(void) {
    * shared diagonal probe must produce one stable midpoint and conforming
    * children only after its endpoint has been installed. */
   FrameLensMesh adaptive_mesh = {0};
-  const RefinementConfig refine = {.max_level = 1,
+  RefinementConfig refine = {.max_level = 1,
                                    .angle_absolute_rad = 1e-4,
                                    .angle_relative = 1e-4,
+                                   .jacobian_minimum = 1e-3,
                                    .min_edge_pixels = 1.0,
                                    .min_area_pixels2 = 1.0};
   if (frame_lens_mesh_build_coarse(&adaptive_mesh, width, height, 100, 30.0))
@@ -192,6 +193,28 @@ int main(void) {
     goto done;
   }
   frame_lens_mesh_destroy(&adaptive_mesh);
+  /* A zero discrete Jacobian is an independent fold/critical-band trigger:
+   * the probe below agrees exactly with linear endpoint interpolation, so the
+   * direction-error criterion cannot request this split. */
+  if (frame_lens_mesh_build_coarse(&adaptive_mesh, width, height, 100, 30.0))
+    goto done;
+  for (size_t i = 0; i < adaptive_mesh.vertex_count; ++i) {
+    adaptive_mesh.vertices[i].traced = 1;
+    adaptive_mesh.vertices[i].status = RAY_ENDPOINT_ESCAPED;
+    adaptive_mesh.vertices[i].n_infinity[0] = 1.0;
+  }
+  const RayEndpoint flat_probe = {.n_infinity = {1.0, 0.0, 0.0},
+                                  .frequency_ratio = 1.0,
+                                  .status = RAY_ENDPOINT_ESCAPED};
+  if (frame_lens_mesh_prepare_generation(&adaptive_mesh, &refine) != 1 ||
+      frame_lens_mesh_install_sample(&adaptive_mesh, 0, &flat_probe) ||
+      frame_lens_mesh_finish_generation(&adaptive_mesh, &refine) != 1 ||
+      adaptive_mesh.vertex_count != 5 || adaptive_mesh.triangle_count != 4) {
+    fputs("adaptive discrete-Jacobian split regression failed\n", stderr);
+    frame_lens_mesh_destroy(&adaptive_mesh);
+    goto done;
+  }
+  frame_lens_mesh_destroy(&adaptive_mesh);
   result = 0;
 done:
   frame_lens_mesh_destroy(&mesh);

tests/test_schwarzschild.c

@@ -64,6 +64,7 @@ int main(void) {
   const RefinementConfig refinement = {.max_level = 1,
                                        .angle_absolute_rad = 1e-5,
                                        .angle_relative = 1e-5,
+                                       .jacobian_minimum = 1e-3,
                                        .min_edge_pixels = 1.0,
                                        .min_area_pixels2 = 1.0};
   if (frame_lens_mesh_build_coarse(&mesh, 48, 48, 24, 40.0) ||