Merge pull request #104 from gabrielebndn/topic/inertias

[geometric_shape] Fix radius, CoM and inertia computation + Python unit tests

.gitignore

 build*
 Xcode/*
+*~
+*.pyc
+

include/hpp/fcl/collision_object.h

@@ -125,10 +125,10 @@ public:
   FCL_REAL threshold_free;
 
   /// @brief compute center of mass
-  virtual Vec3f computeCOM() const { return Vec3f(); }
+  virtual Vec3f computeCOM() const { return Vec3f::Zero(); }
 
   /// @brief compute the inertia matrix, related to the origin
-  virtual Matrix3f computeMomentofInertia() const { return Matrix3f(); }
+  virtual Matrix3f computeMomentofInertia() const { return Matrix3f::Constant(NAN); }
 
   /// @brief compute the volume
   virtual FCL_REAL computeVolume() const { return 0; }

include/hpp/fcl/shape/geometric_shapes.h

@@ -143,7 +143,7 @@ public:
 
   FCL_REAL computeVolume() const
   {
-    return 4 * boost::math::constants::pi<FCL_REAL>() * radius * radius / 3;
+    return 4 * boost::math::constants::pi<FCL_REAL>() * radius * radius * radius / 3;
   }
 };
 
@@ -178,7 +178,9 @@ public:
     FCL_REAL v_cyl = radius * radius * (halfLength * 2) * boost::math::constants::pi<FCL_REAL>();
     FCL_REAL v_sph = radius * radius * radius * boost::math::constants::pi<FCL_REAL>() * 4 / 3.0;
     
-    FCL_REAL ix = v_cyl * halfLength * halfLength / 3. + 0.25 * v_cyl * radius + 0.4 * v_sph * radius * radius + v_sph * halfLength * halfLength;
+    FCL_REAL h2 = halfLength * halfLength;
+    FCL_REAL r2 = radius * radius;
+    FCL_REAL ix = v_cyl * (h2 / 3. + r2 / 4.) + v_sph * (0.4 * r2 + h2 + 0.75 * radius * halfLength);
     FCL_REAL iz = (0.5 * v_cyl + 0.4 * v_sph) * radius * radius;
 
     return (Matrix3f() << ix, 0, 0,
@@ -214,7 +216,6 @@ public:
     return boost::math::constants::pi<FCL_REAL>() * radius * radius * (halfLength * 2) / 3;
   }
 
-  /// \todo verify this formula as it seems different from https://en.wikipedia.org/wiki/List_of_moments_of_inertia#List_of_3D_inertia_tensors
   Matrix3f computeMomentofInertia() const
   {
     FCL_REAL V = computeVolume();

test/python_unit/geometric_shapes.py

 import unittest
+from test_case import TestCase
 import hppfcl
 hppfcl.switchToNumpyMatrix()
 import numpy as np
 
-class TestGeometricShapes(unittest.TestCase):
+class TestGeometricShapes(TestCase):
 
     def test_capsule(self):
         capsule = hppfcl.Capsule(1.,2.)
@@ -17,6 +18,28 @@ class TestGeometricShapes(unittest.TestCase):
         capsule.halfLength = 4.
         self.assertEqual(capsule.radius,3.)
         self.assertEqual(capsule.halfLength,4.)
+        com = capsule.computeCOM()
+        self.assertApprox(com, np.zeros(3))
+        V = capsule.computeVolume()
+        V_cylinder = capsule.radius * capsule.radius * np.pi * 2. * capsule.halfLength
+        V_sphere = 4. * np.pi/3 * capsule.radius**3
+        V_ref = V_cylinder + V_sphere
+        self.assertApprox(V, V_ref)
+        I0 = capsule.computeMomentofInertia()
+        Iz_cylinder = V_cylinder * capsule.radius**2 / 2.
+        Iz_sphere = 0.4 * V_sphere * capsule.radius * capsule.radius
+        Iz_ref = Iz_cylinder + Iz_sphere
+        Ix_cylinder = V_cylinder*(3 * capsule.radius**2 + 4 * capsule.halfLength**2)/12.
+        V_hemi = 0.5 * V_sphere                                          # volume of hemisphere
+        I0x_hemi = 0.5 * Iz_sphere                                       # inertia of hemisphere w.r.t. origin
+        com_hemi = 3. * capsule.radius / 8.                              # CoM of hemisphere w.r.t. origin
+        Icx_hemi = I0x_hemi - V_hemi * com_hemi * com_hemi               # inertia of hemisphere w.r.t. CoM
+        Ix_hemi = Icx_hemi + V_hemi * (capsule.halfLength + com_hemi)**2 # inertia of hemisphere w.r.t. tip of cylinder
+        Ix_ref = Ix_cylinder + 2*Ix_hemi                                 # total inertia of capsule
+        I0_ref = np.diag([Ix_ref,Ix_ref,Iz_ref])
+        self.assertApprox(I0, I0_ref)
+        Ic = capsule.computeMomentofInertiaRelatedToCOM()
+        self.assertApprox(Ic, I0_ref)
 
     def test_box1(self):
         box = hppfcl.Box(np.matrix([1.,2.,3.]).T)
@@ -27,6 +50,22 @@ class TestGeometricShapes(unittest.TestCase):
         self.assertTrue(np.array_equal(box.halfSide,np.matrix([.5,1.,1.5]).T))
         box.halfSide = np.matrix([4.,5.,6.]).T
         self.assertTrue(np.array_equal(box.halfSide,np.matrix([4.,5.,6.]).T))
+        com = box.computeCOM()
+        self.assertApprox(com, np.zeros(3))
+        V = box.computeVolume()
+        x = float(2*box.halfSide[0])
+        y = float(2*box.halfSide[1])
+        z = float(2*box.halfSide[2])
+        V_ref = x * y * z
+        self.assertApprox(V, V_ref)
+        I0 = box.computeMomentofInertia()
+        Ix = V_ref * (y*y + z*z) / 12.
+        Iy = V_ref * (x*x + z*z) / 12.
+        Iz = V_ref * (y*y + x*x) / 12.
+        I0_ref = np.diag([Ix,Iy,Iz])
+        self.assertApprox(I0, I0_ref)
+        Ic = box.computeMomentofInertiaRelatedToCOM()
+        self.assertApprox(Ic, I0_ref) 
 
     def test_box2(self):
         box = hppfcl.Box(1.,2.,3)
@@ -37,22 +76,26 @@ class TestGeometricShapes(unittest.TestCase):
         self.assertEqual(box.halfSide[0],0.5)
         self.assertEqual(box.halfSide[1],1.0)
         self.assertEqual(box.halfSide[2],1.5)
-        box.halfSide[0] = 4.
-        box.halfSide[0] = 5.
-        box.halfSide[0] = 6.
-#         self.assertEqual(box.halfSide[0],4.)
-#         self.assertEqual(box.halfSide[1],5.)
-#         self.assertEqual(box.halfSide[2],6.)
-
+ 
     def test_sphere(self):
         sphere = hppfcl.Sphere(1.)
         self.assertIsInstance(sphere, hppfcl.Sphere)
         self.assertIsInstance(sphere, hppfcl.ShapeBase)
         self.assertIsInstance(sphere, hppfcl.CollisionGeometry)
         self.assertEqual(sphere.getNodeType(), hppfcl.NODE_TYPE.GEOM_SPHERE)
-        self.assertEqual(sphere.radius,1.)
+        self.assertEqual(sphere.radius, 1.)
         sphere.radius = 2.
-        self.assertEqual(sphere.radius,2.)
+        self.assertEqual(sphere.radius, 2.)
+        com = sphere.computeCOM()
+        self.assertApprox(com, np.zeros(3))
+        V = sphere.computeVolume()
+        V_ref = 4. * np.pi/3 * sphere.radius**3
+        self.assertApprox(V, V_ref)
+        I0 = sphere.computeMomentofInertia()
+        I0_ref = 0.4 * V_ref * sphere.radius * sphere.radius * np.identity(3)
+        self.assertApprox(I0, I0_ref)
+        Ic = sphere.computeMomentofInertiaRelatedToCOM()
+        self.assertApprox(Ic, I0_ref)
 
     def test_cylinder(self):
         cylinder = hppfcl.Cylinder(1.,2.)
@@ -62,6 +105,22 @@ class TestGeometricShapes(unittest.TestCase):
         self.assertEqual(cylinder.getNodeType(), hppfcl.NODE_TYPE.GEOM_CYLINDER)
         self.assertEqual(cylinder.radius,1.)
         self.assertEqual(cylinder.halfLength,1.)
+        cylinder.radius = 3.
+        cylinder.halfLength = 4.
+        self.assertEqual(cylinder.radius,3.)
+        self.assertEqual(cylinder.halfLength,4.)
+        com = cylinder.computeCOM()
+        self.assertApprox(com, np.zeros(3))
+        V = cylinder.computeVolume()
+        V_ref = cylinder.radius * cylinder.radius * np.pi * 2. * cylinder.halfLength
+        self.assertApprox(V, V_ref)
+        I0 = cylinder.computeMomentofInertia()
+        Ix_ref = V_ref*(3 * cylinder.radius**2 + 4 * cylinder.halfLength**2)/12.
+        Iz_ref = V_ref * cylinder.radius**2 / 2.
+        I0_ref = np.diag([Ix_ref,Ix_ref,Iz_ref])
+        self.assertApprox(I0, I0_ref)
+        Ic = cylinder.computeMomentofInertiaRelatedToCOM()
+        self.assertApprox(Ic, I0_ref)
 
     def test_cone(self):
         cone = hppfcl.Cone(1.,2.)
@@ -75,6 +134,20 @@ class TestGeometricShapes(unittest.TestCase):
         cone.halfLength = 4.
         self.assertEqual(cone.radius,3.)
         self.assertEqual(cone.halfLength,4.)
+        com = cone.computeCOM()
+        self.assertApprox(com, np.matrix([0.,0.,-0.5 * cone.halfLength]).T)
+        V = cone.computeVolume()
+        V_ref = np.pi * cone.radius**2 * 2. * cone.halfLength / 3.
+        self.assertApprox(V, V_ref)
+        I0 = cone.computeMomentofInertia()
+        Ix_ref = V_ref * (3./20. * cone.radius**2 + 0.4 * cone.halfLength**2)
+        Iz_ref = 0.3 * V_ref * cone.radius**2
+        I0_ref = np.diag([Ix_ref,Ix_ref,Iz_ref])
+        self.assertApprox(I0, I0_ref)
+        Ic = cone.computeMomentofInertiaRelatedToCOM()
+        Icx_ref = V_ref * 3./20. * (cone.radius**2 + cone.halfLength**2)
+        Ic_ref = np.diag([Icx_ref,Icx_ref,Iz_ref])
+        self.assertApprox(Ic, Ic_ref)
 
 if __name__ == '__main__':
-    unittest.main()
\ No newline at end of file
+    unittest.main()

test/python_unit/test_case.py

+import unittest
+import numpy as np
+
+class TestCase(unittest.TestCase):
+    def assertApprox(self, a, b, epsilon=1e-6):
+        return self.assertTrue(np.allclose(a, b, epsilon), "%s !~= %s" % (a, b))
+