/// @see Shape::ComputeMass
public override void ComputeMass(out MassData massData, float Density) {
massData = new MassData();
massData.mass = Density * (float)Math.PI * m_radius * m_radius;
massData.center = m_p;
// inertia about the local origin
massData.I = massData.mass * (0.5f * m_radius * m_radius + Utilities.Dot(m_p, m_p));
}
/// @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.
Utilities.Assert(m_count >= 3);
Vec2 center = new Vec2(0.0f, 0.0f);
float area = 0.0f;
float I = 0.0f;
// s is the reference point for forming triangles.
// It's location doesn't change the result (except for rounding error).
Vec2 s = new Vec2(0.0f, 0.0f);
// This code would put the reference point inside the polygon.
for (int i = 0; i < m_count; ++i)
{
s += m_vertices[i];
}
s *= 1.0f / m_count;
const float k_inv3 = 1.0f / 3.0f;
for (int i = 0; i < m_count; ++i)
{
// Triangle vertices.
Vec2 e1 = m_vertices[i] - s;
Vec2 e2 = i + 1 < m_count ? m_vertices[i+1] - s : m_vertices[0] - s;
float D = Utilities.Cross(e1, e2);
float triangleArea = 0.5f * D;
area += triangleArea;
// Area weighted centroid
center += triangleArea * k_inv3 * (e1 + e2);
float ex1 = e1.X, ey1 = e1.Y;
float ex2 = e2.X, ey2 = e2.Y;
float intx2 = ex1*ex1 + ex2*ex1 + ex2*ex2;
float inty2 = ey1*ey1 + ey2*ey1 + ey2*ey2;
I += (0.25f * k_inv3 * D) * (intx2 + inty2);
}
// Total mass
massData.mass = Density * area;
// Center of mass
Utilities.Assert(area > Single.Epsilon);
center *= 1.0f / area;
massData.center = center + s;
// Inertia tensor relative to the local origin (point s).
massData.I = Density * I;
// Shift to center of mass then to original body origin.
massData.I += massData.mass * (Utilities.Dot(massData.center, massData.center) - Utilities.Dot(center, center));
}
/// @see Shape::ComputeMass
public override void ComputeMass(out MassData massData, float Density) {
throw new NotImplementedException();
//massData.mass = 0.0f;
//massData.center = 0.5f * (m_vertex1 + m_vertex2);
//massData.I = 0.0f;
}
/// Chains have zero mass.
/// @see Shape::ComputeMass
public override void ComputeMass(out MassData massData, float Density){
massData = new MassData();
massData.mass = 0.0f;
massData.center.SetZero();
massData.I = 0.0f;
}
/// Set the mass properties to override the mass properties of the fixtures.
/// Note that this changes the center of mass position.
/// Note that creating or destroying fixtures can also alter the mass.
/// This function has no effect if the body isn't dynamic.
/// @param massData the mass properties.
public void SetMassData(MassData data){
Utilities.Assert(m_world.IsLocked() == false);
if (m_world.IsLocked() == true) {
return;
}
if (m_type != BodyType._dynamicBody) {
return;
}
m_invMass = 0.0f;
m_I = 0.0f;
m_invI = 0.0f;
m_mass = data.mass;
if (m_mass <= 0.0f) {
m_mass = 1.0f;
}
m_invMass = 1.0f / m_mass;
if (data.I > 0.0f && (m_flags & Body.BodyFlags.e_fixedRotationFlag) == 0) {
m_I = data.I - m_mass * Utilities.Dot(data.center, data.center);
Utilities.Assert(m_I > 0.0f);
m_invI = 1.0f / m_I;
}
// Move center of mass.
Vec2 oldCenter = m_sweep.c;
m_sweep.localCenter = data.center;
m_sweep.c0 = m_sweep.c = Utilities.Mul(m_xf, m_sweep.localCenter);
// Update center of mass velocity.
m_linearVelocity += Utilities.Cross(m_angularVelocity, m_sweep.c - oldCenter);
}
/// Get the mass data of the body.
/// @return a struct containing the mass, inertia and center of the body.
public MassData GetMassData() {
MassData data = new MassData();
data.mass = m_mass;
data.I = m_I + m_mass * Utilities.Dot(m_sweep.localCenter, m_sweep.localCenter);
data.center = m_sweep.localCenter;
return data;
}
/// Compute the mass properties of this shape using its dimensions and Density. /// The inertia tensor is computed about the local origin. /// @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);
/// Get the mass data for this fixture. The mass data is based on the Density and
/// the shape. The rotational inertia is about the shape's origin. This operation
/// may be expensive.
public void GetMassData(out MassData massData){
m_shape.ComputeMass(out massData, m_Density);
}
/// Compute the mass properties of this shape using its dimensions and Density. /// The inertia tensor is computed about the local origin. /// @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);
/// Get the mass data for this fixture. The mass data is based on the density and
/// the Shape. The rotational inertia is about the Shape's origin.
public void GetMassData(out MassData massData)
{
_shape.ComputeMass(out massData, _density);
}
