Nonnegativity of bivariate quadratic functions on a triangle
Computer Aided Geometric Design
Nonnegative quadratic Be´zier triangular patches
Computer Aided Geometric Design
Boundary-valued shape-preserving interpolating splines
ACM Transactions on Mathematical Software (TOMS)
Curve and surface construction using variable degree polynomial splines
Computer Aided Geometric Design
A Rational Spline for Visualizing Positive Data
IV '00 Proceedings of the International Conference on Information Visualisation
Data visualization using rational spline interpolation
Journal of Computational and Applied Mathematics
Positivity-preserving scattered data interpolation
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
C1 positive scattered data interpolation
Computers & Mathematics with Applications
Technical Section: A blending interpolator with value control and minimal strain energy
Computers and Graphics
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
Preserving convexity through rational cubic spline fractal interpolation function
Journal of Computational and Applied Mathematics
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This work is a contribution towards the graphical display of data when it is positive. The data are required to be represented in such a way that its visual display looks smooth and pleasant, its positive shape is preserved everywhere and the computation cost is economical. A C^1 piecewise rational cubic function, in its most general form, has been utilized for this objective. The method is implemented for the 1D data initially and then it is extended to an interpolating rational bicubic form for the data arranged over a rectangular grid. Simple sufficient conditions are developed on the free parameters in the description of the rational function to visualize the positive data in the form of positive curves and surfaces.