We present a surface interpolation method for any dataset defined on a regular mesh. We used a second derivative fractal minimization by conjugate gradient. Because of the fractal approach, this algorithm is very fast to process millions of points in a few seconds. The interpolation is continuous, and the first derivative also. For examples in geosciences, the resulting dip of interpolation extends the dip of the input data. The algorithm also works if faults are given via broken lines. We present results from a synthetic and real examples taking into account fault network.


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