Generating the Be´zier points of a &bgr;-spline curve
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
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
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
Positivity-preserving interpolation of positive data by rational cubics
Journal of Computational and Applied Mathematics
Point control of the interpolating curve with a rational cubic spline
Journal of Visual Communication and Image Representation
Local control of interpolating rational cubic spline curves
Computer-Aided Design
Data visualization using rational spline interpolation
Journal of Computational and Applied Mathematics
A bivariate rational interpolation based on scattered data on parallel lines
Journal of Visual Communication and Image Representation
Geometric constraints on quadratic Bézier curves using minimal length and energy
Journal of Computational and Applied Mathematics
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A weighted blending rational interpolator, a kind of smooth interpolator, is constructed using the rational cubic spline with linear denominator and the standard Hermite interpolator. In order to meet the needs of practical design, a new method of value control is employed to control the shape of curves, and the optimal solution for the value control equation with minimal strain energy is derived. The advantage of the method is that it can be applied to modify the local shape of an interpolating curve by selecting suitable parameters and weight coefficients simply. Also when the weight coefficient is in [0,1], the error estimation formula of this interpolator is obtained.