On the choice of parameters in shape-preserving quadratic spline interpolation
Journal of Computational and Applied Mathematics
C1 Convexity-Preserving Interpolation of Scattered Data
SIAM Journal on Scientific Computing
Weighted rational cubic spline interpolation and its application
Journal of Computational and Applied Mathematics
Changes in Surface Convexity and Topology Caused by Distortions of Stereoscopic Visual Space
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
A new bivariate rational interpolation based on function values
Information Sciences—Informatics and Computer Science: An International Journal
Acquiring height data from a single image of a face using local shape indicators
Computer Vision and Image Understanding
Bounded Property and Point Control of a Bivariate Rational Interpolating Surface
Computers & Mathematics with Applications
Medical Image Zooming Algorithm Based on Bivariate Rational Interpolation
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
A New Algorithm for Image Resizing Based on Bivariate Rational Interpolation
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Local control of interpolating rational cubic spline curves
Computer-Aided Design
The conditions of convexity for Bernstein--Bézier surfaces over triangles
Computer Aided Geometric Design
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
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A bivariate rational interpolation surface based on function values has been constructed in the authors' earlier works. This paper deals with the convexity control of interpolating surfaces. The sufficient and necessary conditions for interpolating surfaces to be convex are derived. The convexity of the interpolating surface can be changed locally by selecting suitable parameters under the condition that the interpolation data are not changed. Examples are given to show how the parameters can be chosen and the shapes of the surfaces changed.