diff --git a/mk/reference_images.mk b/mk/reference_images.mk
index 9aa408d..40f26d3 100644
--- a/mk/reference_images.mk
+++ b/mk/reference_images.mk
@@ -13,7 +13,4 @@ test-reference-images: $(FLOATDIFF_SCRIPT) $(REFERENCE_DIR)/minkowski_ra1_dec1_6
 	python3 $(FLOATDIFF_SCRIPT) $(REFERENCE_DIR)/minkowski_ra1_dec1_640x360_HDR.fits $(REFERENCE_TMP_DIR)/minkowski_ra1_dec1_640x360_HDR.fits
 	$(MAKE) SPACETIME=schwarzschild ENABLE_HDR=1 backend
 	OMP_NUM_THREADS=16 $(BUILD_DIR)/schwarzschild_sky --catalog assets/sky_grid_5deg.csv --output $(REFERENCE_TMP_DIR)/schwarzschild_ra1_dec1_fov60_640x360.png --hdr-output --width 640 --height 360 --fov-deg 60 --look-ra-deg 1 --look-dec-deg 1 --exposure 0.1 --observer-radius 30 --observer-velocity 0 0 0 --psf-fwhm-pixels 2.7 --psf-moffat-beta 4.5 --max-magnification 1e300 --max-cache-psf-flux 1 --psf-relative-tail 1e-8 --psf-min-y 0 --coarse-cell-pixels 16 --refine-max-level 0 --refine-angle-abs-deg 0.001 --refine-angle-rel 0.1 --refine-jacobian-min 1e-3 --refine-min-edge-pixels 0.5 --refine-min-area-pixels2 0.25 --catalog-load-workers 4
-	# The general metric-based tetrad changes four float32 samples by one ULP
-	# versus the legacy analytic static tetrad. Keep the original fixture and
-	# allow at most float32 relative rounding (2^-23), with zero abs tolerance.
-	python3 $(FLOATDIFF_SCRIPT) $(REFERENCE_DIR)/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits $(REFERENCE_TMP_DIR)/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits --rel-tolerance 1.1920928955078125e-7
+	python3 $(FLOATDIFF_SCRIPT) $(REFERENCE_DIR)/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits $(REFERENCE_TMP_DIR)/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits
diff --git a/nr_spacetime_movie_renderer_design.md b/nr_spacetime_movie_renderer_design.md
index 9cfffe5..135fc90 100644
--- a/nr_spacetime_movie_renderer_design.md
+++ b/nr_spacetime_movie_renderer_design.md
@@ -250,6 +250,21 @@ typedef struct {
 
 # 8. 局部 adaptive refinement
 
+局部 inverse map 的球面面积权重必须满足凸组合约束。当前实现以无符号
+子面积除以总面积得到权重，在插值位置和频移前检查权重和有限、为正，且
+`abs(sum(weights) - 1) <= 1e-8`；不满足时只跳过当前恒星在当前 triangle
+中的像。通过检查后，将权重除以其总和，消除小的归一化误差。整 tile
+包含的 catalog 快速路径也必须执行这项检查。
+
+这是反演有效性保护，不是 refinement 阈值：细长 source triangle 的带容差
+边测试可能误接纳外部点，无符号子面积之和便大于总面积，直接插值会把像
+放到 image triangle 外。不能先归一化明显无效的权重来掩盖误接纳。
+固定的无量纲容差 `1e-8` 依据 Schwarzschild 3840×2160、45° FOV、R=100、
+coarse cell=32、level=4、J=0.2 网格上的诊断选定：正对中心及偏离
+0.00161°、方位为 1°/44°/23° 的单星测试中，严格包含样本的 double
+权重和误差不超过约 `2.5e-13`，正对中心的越界样本最小误差约 `5.9e-4`。
+这不保证临界曲线附近的离散映射已经收敛，也不保证数值亮环无缺口。
+
 每个 triangle 只关心自身局部映射。
 
 不需要先把整个像平面映射到天球、再全局分类“第几阶像”。
diff --git a/src/frame.c b/src/frame.c
index 1612d71..56901e1 100644
--- a/src/frame.c
+++ b/src/frame.c
@@ -930,6 +930,17 @@ static int spherical_barycentric_weights(const double point[3], const double a[3
   weights[0] = spherical_area(point, b, c) / area;
   weights[1] = spherical_area(point, c, a) / area;
   weights[2] = spherical_area(point, a, b) / area;
+  /* A thin source triangle can admit an exterior point through the tolerant
+   * edge test. Unsigned subareas then do not partition the total area, and
+   * interpolating with their ratios can move an image outside its triangle.
+   * Reject that case before normalizing roundoff in valid convex weights.
+   * The 1e-8 bound is dimensionless; see the inverse-map design notes. */
+  const double weight_sum = weights[0] + weights[1] + weights[2];
+  if (!isfinite(weight_sum) || weight_sum <= 0.0 ||
+      fabs(weight_sum - 1.0) > 1e-8)
+    return -1;
+  for (int i = 0; i < 3; ++i)
+    weights[i] /= weight_sum;
   return 0;
 }
 
@@ -1055,7 +1066,7 @@ static int splat_catalog_tile(const Star *stars, size_t count,
                                         context->vertex[0]->n_infinity,
                                         context->vertex[1]->n_infinity,
                                         context->vertex[2]->n_infinity, weights))
-        return -1;
+        continue;
     }
     if (!owns_source_boundary(context->triangle, weights))
       continue;
diff --git a/tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits b/tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits
index 678196a..064bfd2 100644
Binary files a/tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits and b/tests/data/psf_event_sink_reference/minkowski_ra1_dec1_640x360_HDR.fits differ
diff --git a/tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits b/tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits
index 0aca09c..8b12615 100644
Binary files a/tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits and b/tests/data/psf_event_sink_reference/schwarzschild_ra1_dec1_fov60_640x360_HDR.fits differ
diff --git a/tests/test_frame.c b/tests/test_frame.c
index e472bd0..ccd08b3 100644
--- a/tests/test_frame.c
+++ b/tests/test_frame.c
@@ -330,6 +330,50 @@ int main(void) {
     goto done;
   }
   frame_lens_mesh_destroy(&fine_mesh);
+  /* Schwarzschild level-4/J=0.2 ring triangle: the old edge tolerance accepts
+   * (1,0,0) although it is outside, producing unsigned weights summing to
+   * 1.09608. Keep a genuine interior source after it to check that rejecting
+   * one source does not discard subsequent stars. Exercise both parities. */
+  const double thin_directions[3][3] = {
+      {0.99999998891116071, 0.00013431364716360775, 6.4323579270168807e-05},
+      {0.99999997228355786, -0.00021216644782556991, -0.00010206998544149922},
+      {0.9999927016945267, -0.0034455730513416835, -0.001650631403158936}};
+  LensVertex thin_vertices[3] = {
+      {.image_x = 40, .image_y = 40, .status = RAY_ENDPOINT_ESCAPED},
+      {.image_x = 48, .image_y = 40, .status = RAY_ENDPOINT_ESCAPED},
+      {.image_x = 40, .image_y = 48, .status = RAY_ENDPOINT_ESCAPED}};
+  LensTriangle thin_triangle = {.vertex = {0, 1, 2}};
+  FrameLensMesh thin_mesh = {.vertices = thin_vertices, .vertex_count = 3,
+                            .triangles = &thin_triangle, .triangle_count = 1};
+  Star thin_stars[2] = {
+      {.direction = {1, 0, 0}, .temperature_K = 7000, .amplitude = 1},
+      {.temperature_K = 7000, .amplitude = 1}};
+  for (int i = 0; i < 3; ++i) {
+    memcpy(thin_vertices[i].n_infinity, thin_directions[i],
+           sizeof thin_directions[i]);
+    memcpy(thin_vertices[i].camera_direction, thin_directions[i],
+           sizeof thin_directions[i]);
+    for (int axis = 0; axis < 3; ++axis)
+      thin_stars[1].direction[axis] += thin_directions[i][axis];
+  }
+  const double thin_norm = hypot(hypot(thin_stars[1].direction[0],
+                                      thin_stars[1].direction[1]),
+                                thin_stars[1].direction[2]);
+  for (int axis = 0; axis < 3; ++axis)
+    thin_stars[1].direction[axis] /= thin_norm;
+  StarCatalog thin_catalog = {.stars = thin_stars, .count = 2};
+  for (int parity = 0; parity < 2; ++parity) {
+    thin_triangle.vertex[1] = parity ? 2 : 1;
+    thin_triangle.vertex[2] = parity ? 1 : 2;
+    memset(hdr, 0, (size_t)width * height * 3 * sizeof *hdr);
+    if (frame_splat_catalog(&thin_mesh, &thin_catalog, hdr, width, height,
+                            test_exposure, &psf, NULL, 1.0, 1.0,
+                            psf_relative_tail, 0.0, 0, 1, NULL, NULL, NULL) != 1 ||
+        hdr[3 * (43 * width + 43)] <= 0.0) {
+      fputs("thin source-triangle inverse-map regression failed\n", stderr);
+      goto done;
+    }
+  }
   /* Refinement probes are temporary until their generation is complete.  A
    * shared diagonal probe must produce one stable midpoint and conforming
    * children only after its endpoint has been installed. */