/// <summary>
/// Calculates the inertia of the shape relative to the center of mass.
/// </summary>
/// <param name="shape"></param>
/// <param name="centerOfMass"></param>
/// <param name="inertia">Returns the inertia relative to the center of mass, not to the origin</param>
/// <returns></returns>
#region public static double CalculateMassInertia(Shape shape, out Vector3D centerOfMass, out MatrixD inertia)
public static double CalculateMassInertia(Shape shape, out Vector3D centerOfMass,
out MatrixD inertia)
{
double mass = 0.0f;
centerOfMass = Vector3D.Zero; inertia = MatrixD.Zero;
//if (shape is Multishape) throw new ArgumentException("Can't calculate inertia of multishapes.", "shape");
// build a triangle hull around the shape
List <Vector3D> hullTriangles = new List <Vector3D>();
shape.MakeHull(ref hullTriangles, 3);
// create inertia of tetrahedron with vertices at
// (0,0,0) (1,0,0) (0,1,0) (0,0,1)
double a = 1.0f / 60.0f, b = 1.0f / 120.0f;
MatrixD C = new MatrixD(a, b, b, b, a, b, b, b, a);
for (int i = 0; i < hullTriangles.Count; i += 3)
{
Vector3D column0 = hullTriangles[i + 0];
Vector3D column1 = hullTriangles[i + 1];
Vector3D column2 = hullTriangles[i + 2];
MatrixD A = new MatrixD(column0.X, column1.X, column2.X,
column0.Y, column1.Y, column2.Y,
column0.Z, column1.Z, column2.Z);
double detA = A.Determinant();
// now transform this canonical tetrahedron to the target tetrahedron
// inertia by a linear transformation A
MatrixD tetrahedronInertia = MatrixD.Multiply(A * C * MatrixD.Transpose(A), detA);
Vector3D tetrahedronCOM = (1.0f / 4.0f) * (hullTriangles[i + 0] + hullTriangles[i + 1] + hullTriangles[i + 2]);
double tetrahedronMass = (1.0f / 6.0f) * detA;
inertia += tetrahedronInertia;
centerOfMass += tetrahedronMass * tetrahedronCOM;
mass += tetrahedronMass;
}
inertia = MatrixD.Multiply(MatrixD.Identity, Trace(inertia.M11, inertia.M22, inertia.M33)) - inertia; //test was inertia.Trace()
centerOfMass = centerOfMass * (1.0f / mass);
double x = centerOfMass.X;
double y = centerOfMass.Y;
double z = centerOfMass.Z;
// now translate the inertia by the center of mass
MatrixD t = new MatrixD(
-mass * (y * y + z * z), mass * x * y, mass * x * z,
mass * y * x, -mass * (z * z + x * x), mass * y * z,
mass * z * x, mass * z * y, -mass * (x * x + y * y));
MatrixD.Add(ref inertia, ref t, out inertia);
return(mass);
}