Replace volume_polyhedron with signed volume approach for non-convex support

- volume_polyhedron only works for convex meshes (as per its documentation)
- Implemented signed volume of tetrahedra approach which works for both convex and non-convex meshes
- Removed volume_polyhedron import, added dot_vectors import
- Updated CHANGELOG.md to document the new volume() method
- All tests pass with same accuracy

Co-authored-by: Licini <17893605+Licini@users.noreply.github.com>

Author: Copilot

CHANGELOG.md

@@ -11,6 +11,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 * Added `compas_rhino.install_with_pip` with corresponding command line utility `install_in_rhino`.
 * Added support for `.stp` file extension in addition to `.step` for `RhinoBrep.from_step()` and `RhinoBrep.to_step()` methods.
+* Added `volume()` method to `compas.datastructures.Mesh` for computing the volume of closed meshes using signed volume of triangles.
 
 ### Changed
 

src/compas/datastructures/mesh/mesh.py

@@ -42,6 +42,7 @@
 from compas.geometry import distance_line_line
 from compas.geometry import distance_point_plane
 from compas.geometry import distance_point_point
+from compas.geometry import dot_vectors
 from compas.geometry import length_vector
 from compas.geometry import midpoint_line
 from compas.geometry import normal_polygon
@@ -52,7 +53,6 @@
 from compas.geometry import sum_vectors
 from compas.geometry import transform_points
 from compas.geometry import vector_average
-from compas.geometry import volume_polyhedron
 from compas.itertools import linspace
 from compas.itertools import pairwise
 from compas.itertools import window
@@ -3920,12 +3920,33 @@ def volume(self):
         # Unify cycles to ensure consistent face orientation
         mesh_copy.unify_cycles()
 
-        # Get vertices and faces from the unified copy
-        # Make a copy of vertices list since volume_polyhedron modifies it in place
-        vertices, faces = mesh_copy.to_vertices_and_faces()
-        vertices = [v[:] for v in vertices]  # Deep copy of vertex coordinates
+        volume = 0.0
+        for fkey in mesh_copy.faces():
+            vertices = mesh_copy.face_vertices(fkey)
+            # Get coordinates for all vertices of the face
+            coords = [mesh_copy.vertex_coordinates(v) for v in vertices]
 
-        return abs(volume_polyhedron((vertices, faces)))
+            # Triangulate the face if it has more than 3 vertices
+            if len(coords) == 3:
+                triangles = [coords]
+            else:
+                # Use simple fan triangulation from first vertex
+                triangles = []
+                for i in range(1, len(coords) - 1):
+                    triangles.append([coords[0], coords[i], coords[i + 1]])
+
+            # Calculate signed volume contribution from each triangle
+            for triangle in triangles:
+                # Signed volume of tetrahedron formed by triangle and origin
+                # V = (1/6) * (a · (b × c)) where a, b, c are the vertices
+                a, b, c = triangle
+                # Calculate cross product of b and c
+                bc = cross_vectors(b, c)
+                # Calculate dot product with a
+                vol = dot_vectors(a, bc) / 6.0
+                volume += vol
+
+        return abs(volume)
 
     def centroid(self):
         """Calculate the mesh centroid.