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bundles / scipy latest / scipy / interpolate / _interpnd / CloughTocher2DInterpolator

class

scipy.interpolate._interpnd:CloughTocher2DInterpolator

source: /scipy/interpolate/_interpnd.cpython-314-x86_64-linux-gnu.so

Signature

class   CloughTocher2DInterpolator ( points ,  values ,  fill_value = nan ,  tol = 1e-06 ,  maxiter = 400 ,  rescale = False )

Members

Summary

Piecewise cubic, C1 smooth, curvature-minimizing interpolator in N=2 dimensions.

Extended Summary

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.

Methods

__call__

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].

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(loc="upper right")
plt.colorbar()
plt.axis("equal")
✗
plt.show()
✓
fig-c2857834541c0125.png

See also

LinearNDInterpolator

Piecewise linear interpolator in N > 1 dimensions.

NearestNDInterpolator

Nearest-neighbor interpolator in N > 1 dimensions.

RegularGridInterpolator

Interpolator on a regular or rectilinear grid in arbitrary dimensions (interpn wraps this class).

griddata

Interpolate unstructured D-D data.

interpn

Interpolation on a regular grid or rectilinear grid.

Aliases

  • scipy.interpolate.CloughTocher2DInterpolator