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complementary_constraint_matrix

complementary_constraint_matrix(V, T, J, dt=None)

Computes the complementarity constraint matrix C = J D M Where J is the rig jacobian, D is the momentum leaking matrix and M is the mass matrix. The momentum leaking matrix is computed via surface diffusion using the timestep dt, which is set to 1/l^2 by default.

Parameters:

Name Type Description Default
V (n, 3) float numpy array

Mesh vertices

 required
T (t, 4) int numpy array

Mesh tets

 required
J (3n, 12m) float numpy array

Rig jacobian matrix

 required
dt float

Timestep used for momentum leaking matrix, (default=1/l^2)

 None

Returns:

Name Type Description
C (12m, 3n) float numpy array

Complementarity constraint matrix
Source code in src\fast_cody\complementary_constraint_matrix.py 
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def complementary_constraint_matrix(V, T, J, dt=None):
    """ Computes the complementarity constraint matrix
        ```
        C = J D M
        ```
        Where J is the rig jacobian, D is the momentum leaking matrix and M is the mass matrix.
        The momentum leaking matrix is computed via surface diffusion using the timestep dt, which is set to 1/l^2 by default.

    Parameters
    ----------
    V : (n, 3) float numpy array
        Mesh vertices
    T : (t, 4) int numpy array
        Mesh tets
    J : (3n, 12m) float numpy array
        Rig jacobian matrix
    dt : float
        Timestep used for momentum leaking matrix, (default=1/l^2)

    Returns
    --------
    C : (12m, 3n) float numpy array
        Complementarity constraint matrix

    """
    M = igl.massmatrix(V, T)
    Me = sp.sparse.kron(sp.sparse.identity(3), M)
    D = fc.momentum_leaking_matrix(V, T, dt=dt)

    C =  (Me @ D @ J).T


    return C