How to perform bilinear interpolation in Python

Here’s a reusable function you can use. It includes doctests and data validation:

def bilinear_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/Bilinear_interpolation

    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')

    return (q11 * (x2 - x) * (y2 - y) +
            q21 * (x - x1) * (y2 - y) +
            q12 * (x2 - x) * (y - y1) +
            q22 * (x - x1) * (y - y1)
           ) / ((x2 - x1) * (y2 - y1) + 0.0)

You can run test code by adding:

if __name__ == '__main__':
    import doctest
    doctest.testmod()

Running the interpolation on your dataset produces:

>>> n = [(54.5, 17.041667, 31.993),
         (54.5, 17.083333, 31.911),
         (54.458333, 17.041667, 31.945),
         (54.458333, 17.083333, 31.866),
    ]
>>> bilinear_interpolation(54.4786674627, 17.0470721369, n)
31.95798688313631