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?
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Bilinear interpolation between the corners of a quadrilateral gives the coordinates
This forms a system of two quadratic equations in the unknowns
u
,v
. IfP
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 formfrom which we eliminate
v
bywhich is quadratic univariate. Compute the roots and keep the one in the domain. From
u
you getv
.