added test_IMCtorus to test for concave shapes

tests/test_integralmeancurvature.py

@@ -38,6 +38,19 @@ def test_IMCbox(self):
             ref = 4 * extent.sum() * g.np.pi / 2 * 0.5
             assert g.np.isclose(IMC, ref, rtol=tol)
 
+    def test_IMCtorus(self):
+        # how close do we need to be - relative tolerance
+        tol = 1e-2
+        r = 1.1
+        for aspect_ratio in [1.1, 2.1, 4.0, 10.0]:
+            R = r * aspect_ratio
+            m = g.trimesh.creation.torus(
+                major_radius=R, minor_radius=r, major_sections=100, minor_sections=100
+            )
+            IMC = m.integral_mean_curvature
+            ref = 2 * (g.np.pi**2) * R
+            assert g.np.isclose(IMC, ref, rtol=tol)
+
 
 if __name__ == "__main__":
     g.trimesh.util.attach_to_log()

trimesh/base.py

@@ -1437,7 +1437,7 @@ def face_adjacency_angles(self) -> NDArray[float64]:
         # find the angle between the pairs of vectors
         angles = geometry.vector_angle(pairs)
         return angles
-    
+
     @cache_decorator
     def face_adjacency_angles_with_sign(self) -> NDArray[float64]:
         """

trimesh/geometry.py

@@ -146,6 +146,7 @@ def vector_angle(pairs):
 
     return angles
 
+
 def vector_angle_with_sign(mesh):
     """
     Find the signed angles between between adjacent face normals in a mesh.