/// @see Shape.ComputeMass
public override void ComputeMass(out MassData massData, float density)
{
massData.mass = density * Settings.b2_pi * _radius * _radius;
massData.center = _p;
// inertia about the local origin
massData.i = massData.mass * (0.5f * _radius * _radius + Vector2.Dot(_p, _p));
}
/// Compute the mass properties of this shape using its dimensions and density.
/// The inertia tensor is computed about the local origin, not the centroid.
/// @param massData returns the mass data for this shape.
public void ComputeMass(out MassData massData)
{
_shape.ComputeMass(out massData, _density);
}
/// @see Shape.ComputeMass
public override void ComputeMass(out MassData massData, float density)
{
// Polygon mass, centroid, and inertia.
// Let rho be the polygon density in mass per unit area.
// Then:
// mass = rho * int(dA)
// centroid.X = (1/mass) * rho * int(x * dA)
// centroid.Y = (1/mass) * rho * int(y * dA)
// I = rho * int((x*x + y*y) * dA)
//
// We can compute these integrals by summing all the integrals
// for each triangle of the polygon. To evaluate the integral
// for a single triangle, we make a change of variables to
// the (u,v) coordinates of the triangle:
// x = x0 + e1x * u + e2x * v
// y = y0 + e1y * u + e2y * v
// where 0 <= u && 0 <= v && u + v <= 1.
//
// We integrate u from [0,1-v] and then v from [0,1].
// We also need to use the Jacobian of the transformation:
// D = cross(e1, e2)
//
// Simplification: triangle centroid = (1/3) * (p1 + p2 + p3)
//
// The rest of the derivation is handled by computer algebra.
Debug.Assert(_vertexCount >= 3);
Vector2 center = new Vector2(0.0f, 0.0f);
float area = 0.0f;
float I = 0.0f;
// pRef is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
Vector2 pRef = new Vector2(0.0f, 0.0f);
#if false
// This code would put the reference point inside the polygon.
for (int i = 0; i < _vertexCount; ++i)
{
pRef += _vertices[i];
}
pRef *= 1.0f / count;
#endif
float k_inv3 = 1.0f / 3.0f;
for (int i = 0; i < _vertexCount; ++i)
{
// Triangle vertices.
Vector2 p1 = pRef;
Vector2 p2 = _vertices[i];
Vector2 p3 = i + 1 < _vertexCount ? _vertices[i+1] : _vertices[0];
Vector2 e1 = p2 - p1;
Vector2 e2 = p3 - p1;
float D = MathUtils.Cross(e1, e2);
float triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (p1 + p2 + p3);
float px = p1.X, py = p1.Y;
float ex1 = e1.X, ey1 = e1.Y;
float ex2 = e2.X, ey2 = e2.Y;
float intx2 = k_inv3 * (0.25f * (ex1*ex1 + ex2*ex1 + ex2*ex2) + (px*ex1 + px*ex2)) + 0.5f*px*px;
float inty2 = k_inv3 * (0.25f * (ey1*ey1 + ey2*ey1 + ey2*ey2) + (py*ey1 + py*ey2)) + 0.5f*py*py;
I += D * (intx2 + inty2);
}
// Total mass
massData.mass = density * area;
// Center of mass
Debug.Assert(area > Settings.b2_FLT_EPSILON);
center *= 1.0f / area;
massData.center = center;
// Inertia tensor relative to the local origin.
massData.i = density * I;
}
/// Set the mass properties. Note that this changes the center of mass position.
/// If you are not sure how to compute mass properties, use SetMassFromShapes.
/// The inertia tensor is assumed to be relative to the center of mass.
/// You can make the body static by using a zero mass.
/// @param massData the mass properties.
public void SetMassData(MassData massData)
{
Debug.Assert(_world.IsLocked == false);
if (_world.IsLocked == true)
{
return;
}
_invMass = 0.0f;
_I = 0.0f;
_invI = 0.0f;
_mass = massData.mass;
if (_mass > 0.0f)
{
_invMass = 1.0f / _mass;
}
_I = massData.i;
if (_I > 0.0f && (_flags & BodyFlags.FixedRotation) == BodyFlags.None)
{
_invI = 1.0f / _I;
}
// Move center of mass.
_sweep.localCenter = massData.center;
_sweep.c0 = _sweep.c = MathUtils.Multiply(ref _xf, _sweep.localCenter);
BodyType oldType = _type;
if (_invMass == 0.0f && _invI == 0.0f)
{
_type = BodyType.Static;
}
else
{
_type = BodyType.Dynamic;
}
// If the body type changed, we need to flag contacts for filtering.
if (oldType != _type)
{
for (ContactEdge ce = _contactList; ce != null; ce = ce.Next)
{
ce.Contact.FlagForFiltering();
}
}
}
/// Compute the mass properties of this shape using its dimensions and density. /// The inertia tensor is computed about the local origin, not the centroid. /// @param massData returns the mass data for this shape. /// @param density the density in kilograms per meter squared. public abstract void ComputeMass(out MassData massData, float density);
