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原标题:Bilinear interpolation on quadrilateral
I am interpolating data from the vertices of a quadrilateral to any random point inside the quadrilateral. I implement this by first doing a coordinate transformation which reshapes the quadrilateral to a unit square and then using bilinear interpolation. Does any of the python libraries already have an implementation to do this?
最佳回答
Based on this answer, scipy.interpolate.bisplrep does the job for me.
问题回答
Bilinear interpolation between the corners of a quadrilateral gives the coordinates P = (P00 (1-u) + P10 u) (1-v) + (P01 (1-u) + P11 u) v = P00 + (P10-P00) u + (P01-P00) v + (P11-P10-P01+P00) uv. This forms a system of two quadratic equations in the unknowns u, v. If P is inside the quadrilateral, u, v ε [0, 1]. If we take the dot and cross products with P11-P10-P01+P0, the system takes the form A + B u + C v + D uv = 0 a + b u + c v = 0 from which we eliminate v by c (A + B u) - (C + D u) (a + b u) = -b D u² + (B c - b C - a D) u + (A c - a C) = 0 which is quadratic univariate. Compute the roots and keep the one in the domain. From u you get v.




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