1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
|
# Copyright (c) 2017 Weitian LI <weitian@aaronly.me>
# MIT license
"""
Interpolation utilities.
"""
def bilinear(x, y, p11, p12, p21, p22):
"""
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.
p11 --+-- p12
| | |
+--(x,y)--+
| | |
p21 --+-- p22
Credit
------
[1] http://en.wikipedia.org/wiki/Bilinear_interpolation
[2] https://stackoverflow.com/a/8662355/4856091
"""
# Sort points by X then Y
points = sorted([p11, p12, p21, p22])
x1, y1, q11 = points[0]
_x1, y2, q12 = points[1]
x2, _y1, q21 = points[2]
_x2, _y2, q22 = points[3]
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")
a1 = (q11 * (x2 - x) * (y2 - y) + q21 * (x - x1) * (y2 - y) +
q12 * (x2 - x) * (y - y1) + q22 * (x - x1) * (y - y1))
a2 = (x2 - x1) * (y2 - y1)
q = a1 / a2
return q
|
