Generating the Be´zier points of a &bgr;-spline curve
Computer Aided Geometric Design
On the choice of parameters in shape-preserving quadratic spline interpolation
Journal of Computational and Applied Mathematics
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Guest Editor's Introduction CAGD's Top Ten: What to Watch
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
An approach of designing and controlling free-form surfaces by using NURBS boundary Gregory patches
Computer Aided Geometric Design - Special issue: in memory of John Gregory
Weighted rational cubic spline interpolation and its application
Journal of Computational and Applied Mathematics
The Mathematical Basis of the UNISURF CAD System
The Mathematical Basis of the UNISURF CAD System
IEEE Computer Graphics and Applications
Universal parametrization and interpolation on cubic surfaces
Computer Aided Geometric Design
A new bivariate rational interpolation based on function values
Information Sciences—Informatics and Computer Science: An International Journal
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Technical section: Convexity control of a bivariate rational interpolating spline surfaces
Computers and Graphics
Rational Biquartic Interpolating Surface Based on Function Values
Edutainment '08 Proceedings of the 3rd international conference on Technologies for E-Learning and Digital Entertainment
Local control of interpolating rational cubic spline curves
Computer-Aided Design
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
Hi-index | 0.09 |
A bivariate rational interpolation method with parameters was created in an earlier work which was based on function values only. This paper will deal with the bounded property and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be; this is called the bounded property of the interpolation. Also, the approximation expressions of the interpolation are derived; they do not depend on the parameters. More important is that the value of the interpolating function at any point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting suitable parameters, so the interpolation surface may be modified for the given interpolation data when needed in practical design. In the special case, the ''Central Point-Mean Value'' control is studied, and an example is given to show the control.