Function periodicApproximate

cadquery/occ_impl/nurbs.py:1521–1577

Approximate a periodic curve.

(
    data: Array,
    us: Optional[Array] = None,
    knots: int | Array = 50,
    order: int = 3,
    penalty: int = 4,
    lam: float = 0,
)

@multidispatch
def periodicApproximate(
    data: Array,
    us: Optional[Array] = None,
    knots: int | Array = 50,
    order: int = 3,
    penalty: int = 4,
    lam: float = 0,
) -> Curve:
    """
    Approximate a periodic curve.
    """

    npts = data.shape[0]

    # parameterize the points if needed
    if us is None:
        us = linspace(0, 1, npts, endpoint=False)

    # construct the knot vector
    if isinstance(knots, int):
        knots_ = linspace(0, 1, knots)
    else:
        knots_ = np.array(knots)

    # construct the design matrix
    C = periodicDesignMatrix(us, order, knots_).csc()
    CtC = C.T @ C

    # add the penalty if requested
    if lam:
        up = linspace(0, 1, order * npts, endpoint=False)

        assert penalty <= order + 2

        # discrete + exact derivatives
        if penalty > order:
            Pexact = periodicDerMatrix(up, order, order - 1, knots_)[-1].csc()
            Pdiscrete = periodicDiscretePenalty(up, penalty - order).csc()

            P = Pdiscrete @ Pexact

        # only exact derivatives
        else:
            P = periodicDerMatrix(up, order, penalty, knots_)[-1].csc()

        CtC += lam * P.T @ P

    # factorize
    D, L, P = ldl(CtC, True)

    # invert
    pts = ldl_solve(C.T @ data, D, L, P).toarray()

    # convert to an edge
    rv = Curve(pts, knots_, order, periodic=True)

    return rv