cupyx.scipy.interpolate.CloughTocher2DInterpolator#

class cupyx.scipy.interpolate.CloughTocher2DInterpolator(points, values, fill_value=nan, tol=1e-06, maxiter=400, rescale=False)[source]#

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

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

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 GDel2D [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()