Efficient evaluation of multivariate polynomials
Computer Aided Geometric Design
Shape preserving properties of the generalised Ball basis
Computer Aided Geometric Design
Fundamentals of computer aided geometric design
Fundamentals of computer aided geometric design
Efficient algorithms for Bézier curves
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Construction of triangular DP surface and its application
Journal of Computational and Applied Mathematics
Error analysis of efficient evaluation algorithms for tensor product surfaces
Journal of Computational and Applied Mathematics
Computer Aided Geometric Design
Conversion and evaluation for two types of parametric surfaces constructed by NTP bases
Computers & Mathematics with Applications
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Optimal Conditioning of Bernstein Collocation Matrices
SIAM Journal on Matrix Analysis and Applications
Multiple degree elevation and constrained multiple degree reduction for DP curves and surfaces
Computers & Mathematics with Applications
A new bivariate basis representation for Bézier-based triangular patches with quadratic complexity
Computers & Mathematics with Applications
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We consider a blending basis for which we obtain an algorithm for the evaluation of polynomial curves with linear time complexity and we prove that it is a normalized totally positive basis. Therefore, it simultaneously satisfies efficiency and shape preservation. We also provide the corner cutting algorithm for obtaining the Bézier polygon from the control polygon with respect this basis. Related bases with additional properties are also considered.