Piecewise Polynomial Monotonic Interpolation of 2D Gridded Data
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A method for interpolating monotone increasing 2D scalar data with a monotone piecewise cubic C1-continuous surface is presented. Monotonicity is a sufficient condition for a function to be free of critical points inside its domain. The standard axial monotonicity for tensor-product surfaces is however too restrictive. We therefore introduce a more relaxed monotonicity constraint. We derive sufficient conditions on the partial derivatives of the interpolating function to ensure its monotonicity. We then develop two algorithms to effectively construct a monotone C1 surface composed of cubic triangular Bézier surfaces interpolating a monotone gridded data set. Our method enables to interpolate given topological data such as minima, maxima and saddle points at the corners of a rectangular domain without adding spurious extrema inside the function domain. Numerical examples are given to illustrate the performance of the algorithm.
KeywordsLocal Extremum Monotonicity Constraint Regular Vertex Grid Vertex Hermite Data
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