Improve error message for bad geometry in .obj file.

geometry/BUILD.bazel

@@ -777,6 +777,9 @@ filegroup(
     name = "test_obj_files",
     testonly = 1,
     srcs = [
+        "test/bad_geometryA.obj",
+        "test/bad_geometryB.obj",
+        "test/bad_geometry_corrected.obj",
         "test/convex.obj",
         "test/cube_corners.obj",
         "test/cube_with_hole.obj",

geometry/test/bad_geometryA.obj

@@ -0,0 +1,25 @@
+# File: bad_geometryA.obj
+# The geometry in this file produces invalid mass and inertia properties
+# due to the winding (order of the vertices) in some of the faces.
+# Related files: bad_geometryB.obj and bad_geometry_corrected.obj
+# ----------------------------------------------------------------------
+
+g test
+
+# 6 vertices.
+v 0.0  0.0   0.5
+v 0.0  0.0  -0.5
+v 0.0  1.0   0.5
+v 0.0  1.0  -0.5
+v 1.0  0.0   0.5
+v 1.0  0.0  -0.5
+
+# 8 faces.
+f 1 3 5
+f 2 4 6
+f 1 2 3
+f 2 3 4
+f 3 4 5
+f 4 5 6
+f 5 6 1
+f 6 1 2

geometry/test/bad_geometryB.obj

@@ -0,0 +1,25 @@
+# File: bad_geometryB.obj
+# The geometry in this file produces invalid mass and inertia properties
+# due to the winding (order of the vertices) in some of the faces.
+# Related files: bad_geometryA.obj and bad_geometry_corrected.obj
+# -----------------------------------------------------------------------
+
+g test
+
+# 6 vertices.
+v 0.0  0.0   0.5
+v 0.0  0.0  -0.5
+v 0.0  1.0   0.5
+v 0.0  1.0  -0.5
+v 1.0  0.0   0.5
+v 1.0  0.0  -0.5
+
+# 8 faces.
+f 1 3 5
+f 6 4 2
+f 1 2 3
+f 4 3 2
+f 3 4 5
+f 6 5 4
+f 5 6 1
+f 2 1 6

geometry/test/bad_geometry_corrected.obj

@@ -0,0 +1,25 @@
+# File: bad_geometry_corrected.obj
+# The geometry in this file produces valid mass and inertia properties
+# as contrasted with the invalid mass and inertia properties produced
+# by the related files bad_geometryA.obj and bad_geometryB.obj.
+# -----------------------------------------------------------------------
+
+g test
+
+# 6 vertices.
+v 0.0  0.0   0.5
+v 0.0  0.0  -0.5
+v 0.0  1.0   0.5
+v 0.0  1.0  -0.5
+v 1.0  0.0   0.5
+v 1.0  0.0  -0.5
+
+# 8 faces.
+f 1 5 3
+f 2 4 6
+f 1 3 2
+f 2 3 4
+f 3 5 4
+f 4 5 6
+f 5 1 6
+f 6 1 2

multibody/tree/geometry_spatial_inertia.cc

@@ -2,6 +2,7 @@
 
 #include <algorithm>
 #include <filesystem>
+#include <limits>
 #include <memory>
 #include <string>
 
@@ -127,7 +128,19 @@ SpatialInertia<double> CalcSpatialInertia(
     accum_com += (p + q + r) * tet_vol_times_six;
   }
 
+  // Volume should be inherently positive.
   const double volume = vol_times_six / 6.0;
+  constexpr double kEpsilon = std::numeric_limits<double>::epsilon();
+  if (volume <= kEpsilon) {
+    const std::string error_message = fmt::format(
+        "{}(): The calculated volume of a triangle surface mesh is {} whereas "
+        "a reasonable positive value was expected. The mesh may have bad "
+        "geometry, e.g., the winding (order of the vertices) of some faces do "
+        "not produce outward normals.", __func__, volume);
+    throw std::logic_error(error_message);
+    // Note: In a Wavefront .obj file, each face's vertices should be stored
+    // in a counter-clockwise order by default.
+  }
   const double mass = density * volume;
   const Vector3d p_GoGcm = accum_com / (vol_times_six * 4);
   // We can compute I = C.trace * 1₃ - C. Two key points:

multibody/tree/test/geometry_spatial_inertia_test.cc

@@ -161,6 +161,29 @@ GTEST_TEST(GeometrySpatialInertiaTest, Convex) {
       /* tolerance = */ 1e-1));
 }
 
+// Check exception messages when CalcSpatialInertia(Shape) is called on a file
+// with bad geometry (e.g. not watertight or bad outward normals, or ...).
+GTEST_TEST(GeometrySpatialInertiaTest, ExceptionOnBadGeometry) {
+  std::string geometry_file_path = FindResourceOrThrow(
+      "drake/geometry/test/bad_geometryA.obj");
+  const geometry::Mesh bad_geometryA_obj(geometry_file_path, 1.0);
+  DRAKE_EXPECT_THROWS_MESSAGE(CalcSpatialInertia(bad_geometryA_obj, kDensity),
+      ".*volume of a triangle surface mesh is.* whereas a reasonable "
+      "positive value was expected. The mesh may have bad geometry.*");
+
+  geometry_file_path = FindResourceOrThrow(
+      "drake/geometry/test/bad_geometryB.obj");
+  const geometry::Mesh bad_geometryB_obj(geometry_file_path, 1.0);
+  DRAKE_EXPECT_THROWS_MESSAGE(CalcSpatialInertia(bad_geometryB_obj, kDensity),
+      ".*volume of a triangle surface mesh is.* whereas a reasonable "
+      "positive value was expected. The mesh may have bad geometry.*");
+
+  geometry_file_path = FindResourceOrThrow(
+      "drake/geometry/test/bad_geometry_corrected.obj");
+  const geometry::Mesh ok_geometry_obj(geometry_file_path, 1.0);
+  EXPECT_NO_THROW(CalcSpatialInertia(ok_geometry_obj, kDensity));
+}
+
 // Exercises the common code paths for Mesh and Convex (i.e., "MeshTypes").
 template <typename MeshType>
 class MeshTypeSpatialInertaTest : public testing::Test {};