python - 有谁知道如何在 Python 中执行双三次样条插值？

Question

双三次样条插值是三次样条的扩展，用于在二维规则网格上进行插值。插值后的曲面比双线性插值得到的对应曲面更光滑。

有没有人已经有相应的函数来启用这样的插值？

这是代码的开头:

def bicubicspline_interpolation(x, y, points):
'''Interpolate (x,y) from values associated with four points.

The four points are a list of four triplets:  (x, y, value).
The four points can be in any order.  They should form a rectangle.

    >>> bilinear_interpolation(12, 5.5,
    ...                        [(10, 4, 100),
    ...                         (20, 4, 200),
    ...                         (10, 6, 150),
    ...                         (20, 6, 300)])
    165.0

'''
# See formula at:  http://en.wikipedia.org/wiki/Bicubic_interpolationon

points = sorted(points)               # order points by x, then by y
(x1, y1, q11), (_x1, y2, q12), (x2, _y1, q21), (_x2, _y2, q22) = points

if x1 != _x1 or x2 != _x2 or y1 != _y1 or y2 != _y2:
    raise ValueError('points do not form a rectangle')
if not x1 <= x <= x2 or not y1 <= y <= y2:
    raise ValueError('(x, y) not within the rectangle')



value = 

return value

有什么帮助吗？

谢谢!

一个

Answer 1

正如@Will 指出的，scipy 有一些插值函数。查看 griddata，因为它具有三次插值。我只是想出了一个小例子。

import numpy as np
from scipy.interpolate import griddata
import matplotlib.pyplot as plt

def func( x, y ):
    return np.sin(x*12.0)*np.sin(y*20.0)

points = np.random.rand(1000, 2)
values = func(points[:,0], points[:,1])

grid_x, grid_y = np.mgrid[0:1:100j, 0:1:200j]
grid_z = griddata(points, values, (grid_x, grid_y), method='cubic')

plt.imshow(grid_z.T, extent=(0,1,0,1), origin='lower')
plt.scatter(points[:,0], points[:,1], c='k')

plt.show()