public static double CalculateMassInertia(Shape shape, out JVector centerOfMass,
out JMatrix inertia)
{
double mass = 0.0f;
centerOfMass = JVector.Zero; inertia = JMatrix.Zero;
if (shape is Multishape) throw new ArgumentException("Can't calculate inertia of multishapes.", "shape");
// build a triangle hull around the shape
List<JVector> hullTriangles = new List<JVector>();
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;
JMatrix C = new JMatrix(a, b, b, b, a, b, b, b, a);
for (int i = 0; i < hullTriangles.Count; i += 3)
{
JVector column0 = hullTriangles[i + 0];
JVector column1 = hullTriangles[i + 1];
JVector column2 = hullTriangles[i + 2];
JMatrix A = new JMatrix(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
JMatrix tetrahedronInertia = JMatrix.Multiply(A * C * JMatrix.Transpose(A), detA);
JVector 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 = JMatrix.Multiply(JMatrix.Identity, inertia.Trace()) - inertia;
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
JMatrix t = new JMatrix(
-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));
JMatrix.Add(ref inertia, ref t, out inertia);
return mass;
}
/// <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 float CalculateMassInertia(Shape shape, out JVector centerOfMass, out JMatrix inertia)
public static float CalculateMassInertia(Shape shape, out Vector3 centerOfMass,
out Matrix3x3 inertia)
{
float mass = 0.0f;
centerOfMass = Vector3.zero; inertia = Matrix3x3.Zero;
if (shape is Multishape)
{
throw new ArgumentException("Can't calculate inertia of multishapes.", "shape");
}
// build a triangle hull around the shape
List <Vector3> hullTriangles = new List <Vector3>();
shape.MakeHull(ref hullTriangles, 3);
// create inertia of tetrahedron with vertices at
// (0,0,0) (1,0,0) (0,1,0) (0,0,1)
float a = 1.0f / 60.0f, b = 1.0f / 120.0f;
Matrix3x3 C = new Matrix3x3(a, b, b, b, a, b, b, b, a);
for (int i = 0; i < hullTriangles.Count; i += 3)
{
Vector3 column0 = hullTriangles[i + 0];
Vector3 column1 = hullTriangles[i + 1];
Vector3 column2 = hullTriangles[i + 2];
Matrix3x3 A = new Matrix3x3(column0.x, column1.x, column2.x,
column0.y, column1.y, column2.y,
column0.z, column1.z, column2.z);
float detA = A.Determinant();
// now transform this canonical tetrahedron to the target tetrahedron
// inertia by a linear transformation A
Matrix3x3 tetrahedronInertia = Matrix3x3.Multiply(A * C * Matrix3x3.Transpose(A), detA);
Vector3 tetrahedronCOM = (1.0f / 4.0f) * (hullTriangles[i + 0] + hullTriangles[i + 1] + hullTriangles[i + 2]);
float tetrahedronMass = (1.0f / 6.0f) * detA;
inertia += tetrahedronInertia;
centerOfMass += tetrahedronMass * tetrahedronCOM;
mass += tetrahedronMass;
}
inertia = Matrix3x3.Multiply(Matrix3x3.Identity, inertia.Trace()) - inertia;
centerOfMass = centerOfMass * (1.0f / mass);
float x = centerOfMass.x;
float y = centerOfMass.y;
float z = centerOfMass.z;
// now translate the inertia by the center of mass
Matrix3x3 t = new Matrix3x3(
-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));
Matrix3x3.Add(ref inertia, ref t, out inertia);
return(mass);
}
/// <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 float CalculateMassInertia(Shape shape, out JVector centerOfMass, out JMatrix inertia)
public static float CalculateMassInertia(Shape shape, out JVector centerOfMass,
out JMatrix inertia)
{
float mass = 0.0f;
centerOfMass = JVector.Zero; inertia = JMatrix.Zero;
if (shape is Multishape)
{
throw new ArgumentException("Can't calculate inertia of multishapes.", "shape");
}
// build a triangle hull around the shape
List <JVector> hullTriangles = new List <JVector>();
shape.MakeHull(ref hullTriangles, 3);
// create inertia of tetrahedron with vertices at
// (0,0,0) (1,0,0) (0,1,0) (0,0,1)
float a = 1.0f / 60.0f, b = 1.0f / 120.0f;
JMatrix C = new JMatrix(a, b, b, b, a, b, b, b, a);
for (int i = 0; i < hullTriangles.Count; i += 3)
{
JVector column0 = hullTriangles[i + 0];
JVector column1 = hullTriangles[i + 1];
JVector column2 = hullTriangles[i + 2];
JMatrix A = new JMatrix(column0.X, column1.X, column2.X,
column0.Y, column1.Y, column2.Y,
column0.Z, column1.Z, column2.Z);
float detA = A.Determinant();
// now transform this canonical tetrahedron to the target tetrahedron
// inertia by a linear transformation A
JMatrix tetrahedronInertia = JMatrix.Multiply(A * C * JMatrix.Transpose(A), detA);
JVector tetrahedronCOM = (1.0f / 4.0f) * (hullTriangles[i + 0] + hullTriangles[i + 1] + hullTriangles[i + 2]);
float tetrahedronMass = (1.0f / 6.0f) * detA;
inertia += tetrahedronInertia;
centerOfMass += tetrahedronMass * tetrahedronCOM;
mass += tetrahedronMass;
}
inertia = JMatrix.Multiply(JMatrix.Identity, inertia.Trace()) - inertia;
centerOfMass = centerOfMass * (1.0f / mass);
float x = centerOfMass.X;
float y = centerOfMass.Y;
float z = centerOfMass.Z;
// now translate the inertia by the center of mass
JMatrix t = new JMatrix(
-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));
JMatrix.Add(ref inertia, ref t, out inertia);
return(mass);
}
