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A Convexity-Preserving Grid Refinement Algorithm for Interpolation of Bivariate Functions
January 1987 (vol. 7 no. 1)
pp. 57-62
John Roulier, University of Connecticut
This article presents an algorithms to refine bevariate grid data that is convex (and monotonic) along the grid lines so that the refined data exhibits the same convexity (and monotonicity). The algorithm is based on some observations about univariate data and an algorithm for shape-preserving quadratic splines for such data. It can be used as is or with standard surface-path techniques.

1. R.E.Carlson and F.N.Fritsch, "Monotone Piecewise Bicubic Interpolation," SIAM J. Numerical Analysis Vol. 22, No. 2, pp. 386-400 Apr. 1985
2. R.K.Beatson and Z.Ziegler, "Monotonicity Preserving Surface Interpolation," SIAM J. Numerical Analysis Vol. 22, No. 2, pp. 401-411 Apr. 1985
3. S.L.Dodd, D.F.McAllister, and J.A.Roulier, "Shape-Preserving Spline Interpolation for Specifying Bivariate Functions on Grids," IEEE CG&A Vol. 3, No. 6, pp. 70-79 Sept. 1983
4. D.E.McAllister and J.A.Roulier, "An Algorithm for Computing a Shape Preserving Osculatory Quadratic Spline," ACM Trans. Mathematical Software Vol. 7, No. 3, pp. 331-347 Sept. 1981

Citation:
John Roulier, "A Convexity-Preserving Grid Refinement Algorithm for Interpolation of Bivariate Functions," IEEE Computer Graphics and Applications, vol. 7, no. 1, pp. 57-62, Jan. 1987, doi:10.1109/MCG.1987.277027
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