CAD mass properties: volume / area / centre of mass / inertia

Port of snaporca c2821af783. New GeometryEngine::mass_properties over BRepGProp
(separate VolumeProperties/SurfaceProperties), bounds-checked
CadDocument::body_mass_properties, and a mass_properties MCP method. Query-only:
no CadFeature, no serialization, no version change. Analytic tests
(WithinRel/WithinAbs): cube 8000/2400/COM(0,0,10)/inertia 533333, cylinder
500pi/300pi, hollow = solid-500pi, invalid index -> valid=false.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01BVzKmX6Y1aEteit1HTXG4Q

src/libslic3r/CadDocument.cpp

@@ -1852,4 +1852,10 @@ bool CadDocument::export_step(const std::string& path,
     return true;
 }
 
+GeometryEngine::MassProps CadDocument::body_mass_properties(int body_index) const
+{
+    if (body_index < 0 || body_index >= int(bodies.size())) return {};
+    return GeometryEngine::mass_properties(bodies[body_index].shape);
+}
+
 } // namespace Slic3r

src/libslic3r/CadDocument.hpp

@@ -371,6 +371,8 @@ public:
                      const std::vector<Transform3d>& body_xforms,
                      std::string& err) const;
 
+    GeometryEngine::MassProps body_mass_properties(int body_index) const;
+
     // Undo/redo of the feature recipe (Onshape-style Ctrl+Z). The caller marks a
     // user-action boundary by calling checkpoint() BEFORE the mutation(s) for that
     // action (add/delete/move/replace, or a direct features edit). undo()/redo() then

src/libslic3r/GeometryEngine.cpp

@@ -465,6 +465,33 @@ GeometryEngine::surface_deviation(const TopoDS_Shape& candidate,
     return d;
 }
 
+GeometryEngine::MassProps GeometryEngine::mass_properties(const TopoDS_Shape& shape)
+{
+    MassProps p;
+    if (shape.IsNull()) return p;
+    try {
+        GProp_GProps vprops;
+        BRepGProp::VolumeProperties(shape, vprops);
+        double mass = vprops.Mass();
+        if (std::abs(mass) < 1e-30) return p;
+        p.volume        = std::abs(mass);
+        p.center_of_mass = Vec3d(vprops.CentreOfMass().X(), vprops.CentreOfMass().Y(), vprops.CentreOfMass().Z());
+        gp_Mat mat = vprops.MatrixOfInertia();
+        p.inertia = {{
+            mat(1,1), mat(1,2), mat(1,3),
+            mat(2,1), mat(2,2), mat(2,3),
+            mat(3,1), mat(3,2), mat(3,3),
+        }};
+        GProp_GProps sprops;
+        BRepGProp::SurfaceProperties(shape, sprops);
+        p.surface_area = sprops.Mass();
+        p.valid = true;
+    } catch (const Standard_Failure&) {
+        // leave valid = false
+    }
+    return p;
+}
+
 std::string GeometryEngine::primitive_name(PrimitiveType type)
 {
     switch (type) {

src/libslic3r/GeometryEngine.hpp

@@ -94,6 +94,15 @@ public:
                                      double merge_angle_deg,
                                      MeshBrepStats& stats);
 
+    struct MassProps {
+        double volume{0.0};
+        double surface_area{0.0};
+        Vec3d  center_of_mass{Vec3d::Zero()};
+        std::array<double, 9> inertia{};
+        bool   valid{false};
+    };
+    static MassProps mass_properties(const TopoDS_Shape& shape);
+
     struct Deviation { double max_mm{0}; double mean_mm{0}; double rms_mm{0}; int sample_count{0}; };
     static Deviation surface_deviation(const TopoDS_Shape& candidate,
                                        const TopoDS_Shape& reference,