Compute moment of inertia for concave and boundary meshes. Resolve #338.

- Mesh inertias can now be computed exactly for well-formed (no holes) non-convex meshes.
- To activate this feature, set `<compiler exactmeshinertia="true">` (defaults to `false`). This default may change in the future.
- Added `<geom shellinertia="true/false">` (defaults to `false`). When true, geom inertia is computed assuming all the mass is concentrated on the surface, and `density` is interpreted as surface density (mass/area). Currently only mesh geoms are supported.

PiperOrigin-RevId: 464368395
Change-Id: I17afd99b9b221c9d24ae951f6e63d5c61ff89820

test/user/testdata/cube_cup.obj

@@ -0,0 +1,83 @@
+v -0.050000 0.050000 0.100000
+v -0.050000 0.050000 0.000000
+v -0.050000 -0.050000 0.000000
+v -0.050000 -0.050000 0.100000
+v -0.050000 -0.050000 0.100000
+v -0.050000 -0.050000 0.000000
+v 0.050000 -0.050000 0.000000
+v 0.050000 -0.050000 0.100000
+v 0.050000 -0.050000 0.100000
+v 0.050000 -0.050000 0.000000
+v 0.050000 0.050000 0.000000
+v 0.050000 0.050000 0.100000
+v 0.050000 0.050000 0.100000
+v 0.050000 0.050000 0.000000
+v -0.050000 0.050000 0.000000
+v -0.050000 0.050000 0.100000
+v 0.050000 0.050000 0.000000
+v 0.050000 -0.050000 0.000000
+v -0.050000 -0.050000 0.000000
+v -0.050000 0.050000 0.000000
+v -0.050000 0.050000 0.100000
+v -0.050000 -0.050000 0.100000
+v -0.040000 -0.040000 0.100000
+v 0.050000 -0.050000 0.100000
+v 0.040000 -0.040000 0.100000
+v 0.050000 0.050000 0.100000
+v 0.040000 0.040000 0.100000
+v -0.040000 0.040000 0.100000
+v 0.040000 -0.040000 0.100000
+v 0.040000 -0.040000 0.010000
+v -0.040000 -0.040000 0.010000
+v -0.040000 -0.040000 0.100000
+v 0.040000 0.040000 0.100000
+v 0.040000 0.040000 0.010000
+v 0.040000 -0.040000 0.010000
+v 0.040000 -0.040000 0.100000
+v -0.040000 0.040000 0.100000
+v -0.040000 0.040000 0.010000
+v 0.040000 0.040000 0.010000
+v 0.040000 0.040000 0.100000
+v -0.040000 -0.040000 0.100000
+v -0.040000 -0.040000 0.010000
+v -0.040000 0.040000 0.010000
+v -0.040000 0.040000 0.100000
+v -0.040000 0.040000 0.010000
+v -0.040000 -0.040000 0.010000
+v 0.040000 -0.040000 0.010000
+v 0.040000 0.040000 0.010000
+vn -1.0000 0.0000 0.0000
+vn 0.0000 -1.0000 0.0000
+vn 1.0000 0.0000 0.0000
+vn 0.0000 1.0000 0.0000
+vn 0.0000 0.0000 -1.0000
+vn 0.0000 0.0000 1.0000
+s 1
+f 1//1 2//1 3//1
+f 3//1 4//1 1//1
+f 5//2 6//2 7//2
+f 7//2 8//2 5//2
+f 9//3 10//3 11//3
+f 11//3 12//3 9//3
+f 13//4 14//4 15//4
+f 15//4 16//4 13//4
+f 17//5 18//5 19//5
+f 19//5 20//5 17//5
+f 21//6 22//6 23//6
+f 22//6 24//6 25//6
+f 24//6 26//6 27//6
+f 26//6 21//6 28//6
+f 25//6 23//6 22//6
+f 28//6 27//6 26//6
+f 27//6 25//6 24//6
+f 23//6 28//6 21//6
+f 29//4 30//4 31//4
+f 31//4 32//4 29//4
+f 33//1 34//1 35//1
+f 35//1 36//1 33//1
+f 37//2 38//2 39//2
+f 39//2 40//2 37//2
+f 41//3 42//3 43//3
+f 43//3 44//3 41//3
+f 45//6 46//6 47//6
+f 47//6 48//6 45//6

test/user/testdata/inertia_concave.xml

@@ -0,0 +1,27 @@
+<mujoco>
+  <compiler exactmeshinertia="true"/>
+  <asset>
+    <mesh file="cube_cup.obj" scale="10 10 10"/>
+    <mesh file="cube_cup_quad.obj" scale="10 10 10"/>
+    <mesh file="cube_cup_hi.obj" scale="10 10 10"/>
+  </asset>
+  <worldbody>
+    <light directional="true" diffuse=".6 .6 .6" specular="0.2 0.2 0.2" pos="0 0 4" dir="0 0 -1"/>
+    <body pos="-1.5 0 1">
+      <geom type="mesh" mesh="cube_cup" density="1"/>
+    </body>
+    <body pos="0 0 1">
+      <geom type="mesh" mesh="cube_cup_quad" density="1"/>
+    </body>
+    <body pos="1.5 0 1">
+      <geom type="mesh" mesh="cube_cup_hi" density="1"/>
+    </body>
+    <body pos="3 0 1">
+      <geom type="box" pos="0 0 0.05" size=".5 .5 .05" density="1"/>
+      <geom type="box" pos="-.45 0 .55" size=".05 .5 .45" density="1"/>
+      <geom type="box" pos=" .45 0 .55" size=".05 .5 .45" density="1"/>
+      <geom type="box" pos="0 -.45 .55" size=".4 .05 .45" density="1"/>
+      <geom type="box" pos="0 .45 .55" size=".4 .05 .45" density="1"/>
+    </body>
+  </worldbody>
+</mujoco>

test/user/testdata/inertia_convex.xml

@@ -0,0 +1,23 @@
+<mujoco>
+  <asset>
+    <mesh file="cube.obj"/>
+    <mesh name="inline_cube"
+        vertex="
+          -.5 -.5 -.5
+          .5 -.5 -.5
+          .5  .5 -.5
+          -.5  .5 -.5
+          -.5 -.5  .5
+          .5 -.5  .5
+          .5  .5  .5
+          -.5  .5  .5"/>
+  </asset>
+  <worldbody>
+    <body>
+      <geom type="mesh" mesh="cube" density="1"/>
+    </body>
+    <body>
+      <geom type="mesh" mesh="inline_cube" density="1"/>
+    </body>
+  </worldbody>
+</mujoco>

test/user/testdata/inertia_shell.xml

@@ -0,0 +1,11 @@
+<mujoco>
+  <compiler exactmeshinertia="true"/>
+  <asset>
+    <mesh file="cube.obj" name="hollow_cube"/>
+  </asset>
+  <worldbody>
+    <body>
+      <geom type="mesh" mesh="hollow_cube" density="1" shellinertia="true"/>
+    </body>
+  </worldbody>
+</mujoco>