Function periodicDerMatrix

cadquery/occ_impl/nurbs.py:1132–1185

Create a sparse periodic design matrix and corresponding derivative matrices.

(u: Array, order: int, dorder: int, knots: Array)

@njit
def periodicDerMatrix(u: Array, order: int, dorder: int, knots: Array) -> list[COO]:
    """
    Create a sparse periodic design matrix and corresponding derivative matrices.
    """

    # extend the knots
    knots_ext = np.concat(
        (knots[-order:-1] - knots[-1], knots, knots[-1] + knots[1:order])
    )

    # number of parameter values
    nu = len(u)

    # number of basis functions
    nb = len(knots) - 1

    # chunk size
    n = order + 1

    # temp chunk storage
    temp = np.zeros((dorder + 1, n))

    # initialize the empty matrix
    rv = []

    for _ in range(dorder + 1):
        rv.append(
            COO(
                i=np.empty(n * nu, dtype=np.int64),
                j=np.empty(n * nu, dtype=np.int64),
                v=np.empty(n * nu),
                shape=(nu, len(knots) - 1),
            )
        )

    # loop over parameter values
    for i in range(nu):
        ui = u[i]

        # find the supporting span
        span = nbFindSpan(ui, order, knots, 0, nb) + order - 1

        # evaluate non-zero functions
        nbBasisDer(span, ui, order, dorder, knots_ext, temp)

        # update the matrices
        for di in range(dorder + 1):
            rv[di].i[i * n : (i + 1) * n] = i
            rv[di].j[i * n : (i + 1) * n] = (
                span - order + 1 + np.arange(n)
            ) % nb  # NB: this is due to periodicity
            rv[di].v[i * n : (i + 1) * n] = temp[di, :]

    return rv


@njit