Classe « CloughTocher2DInterpolator »

Informations générales

Héritage

builtins.object
    NDInterpolatorBase
        CloughTocher2DInterpolator

Définition

class CloughTocher2DInterpolator(NDInterpolatorBase):

help(CloughTocher2DInterpolator)

CloughTocher2DInterpolator(points, values, tol=1e-6).

    Piecewise cubic, C1 smooth, curvature-minimizing interpolator in 2D.

    .. versionadded:: 0.9

    Methods
    -------
    __call__

    Parameters
    ----------
    points : ndarray of floats, shape (npoints, ndims); or Delaunay
        2-D array of data point coordinates, or a precomputed Delaunay triangulation.
    values : ndarray of float or complex, shape (npoints, ...)
        N-D array of data values at `points`. The length of `values` along the
        first axis must be equal to the length of `points`. Unlike some
        interpolators, the interpolation axis cannot be changed.
    fill_value : float, optional
        Value used to fill in for requested points outside of the
        convex hull of the input points.  If not provided, then
        the default is ``nan``.
    tol : float, optional
        Absolute/relative tolerance for gradient estimation.
    maxiter : int, optional
        Maximum number of iterations in gradient estimation.
    rescale : bool, optional
        Rescale points to unit cube before performing interpolation.
        This is useful if some of the input dimensions have
        incommensurable units and differ by many orders of magnitude.

    Notes
    -----
    The interpolant is constructed by triangulating the input data
    with Qhull [1]_, and constructing a piecewise cubic
    interpolating Bezier polynomial on each triangle, using a
    Clough-Tocher scheme [CT]_.  The interpolant is guaranteed to be
    continuously differentiable.

    The gradients of the interpolant are chosen so that the curvature
    of the interpolating surface is approximatively minimized. The
    gradients necessary for this are estimated using the global
    algorithm described in [Nielson83]_ and [Renka84]_.

    .. note:: For data on a regular grid use `interpn` instead.

    Examples
    --------
    We can interpolate values on a 2D plane:

    >>> from scipy.interpolate import CloughTocher2DInterpolator
    >>> import numpy as np
    >>> import matplotlib.pyplot as plt
    >>> rng = np.random.default_rng()
    >>> x = rng.random(10) - 0.5
    >>> y = rng.random(10) - 0.5
    >>> z = np.hypot(x, y)
    >>> X = np.linspace(min(x), max(x))
    >>> Y = np.linspace(min(y), max(y))
    >>> X, Y = np.meshgrid(X, Y)  # 2D grid for interpolation
    >>> interp = CloughTocher2DInterpolator(list(zip(x, y)), z)
    >>> Z = interp(X, Y)
    >>> plt.pcolormesh(X, Y, Z, shading='auto')
    >>> plt.plot(x, y, "ok", label="input point")
    >>> plt.legend()
    >>> plt.colorbar()
    >>> plt.axis("equal")
    >>> plt.show()

    See also
    --------
    griddata :
        Interpolate unstructured D-D data.
    LinearNDInterpolator :
        Piecewise linear interpolator in N > 1 dimensions.
    NearestNDInterpolator :
        Nearest-neighbor interpolator in N > 1 dimensions.
    interpn : Interpolation on a regular grid or rectilinear grid.
    RegularGridInterpolator : Interpolator on a regular or rectilinear grid
                              in arbitrary dimensions (`interpn` wraps this
                              class).

    References
    ----------
    .. [1] http://www.qhull.org/

    .. [CT] See, for example,
       P. Alfeld,
       ''A trivariate Clough-Tocher scheme for tetrahedral data''.
       Computer Aided Geometric Design, 1, 169 (1984);
       G. Farin,
       ''Triangular Bernstein-Bezier patches''.
       Computer Aided Geometric Design, 3, 83 (1986).

    .. [Nielson83] G. Nielson,
       ''A method for interpolating scattered data based upon a minimum norm
       network''.
       Math. Comp., 40, 253 (1983).

    .. [Renka84] R. J. Renka and A. K. Cline.
       ''A Triangle-based C1 interpolation method.'',
       Rocky Mountain J. Math., 14, 223 (1984).