Function designMatrix

cadquery/occ_impl/nurbs.py:951–996

Create a sparse (possibly periodic) design matrix.

(u: Array, order: int, knots: Array, periodic: bool = False)

@njit
def designMatrix(u: Array, order: int, knots: Array, periodic: bool = False) -> COO:
    """
    Create a sparse (possibly periodic) design matrix.
    """

    # extend the knots
    u_, knots_ext, minspan, maxspan, deltaspan = _preprocess(u, order, knots, periodic)

    # number of parameter values
    nu = len(u)

    # number of basis functions
    nb = maxspan

    # chunk size
    n = order + 1

    # temp chunk storage
    temp = np.zeros(n)

    # initialize the empty matrix
    rv = 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 - (not periodic) * order),
    )

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

        # find the supporting span
        span = nbFindSpan(ui, order, knots, minspan, maxspan) + deltaspan

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

        # update the matrix
        rv.i[i * n : (i + 1) * n] = i
        rv.j[i * n : (i + 1) * n] = (
            span - order + int(periodic) + np.arange(n)
        ) % nb  # NB: this is due to periodicity
        rv.v[i * n : (i + 1) * n] = temp

    return rv


@njit