A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
The Mathematical Basis of the UNISURF CAD System
The Mathematical Basis of the UNISURF CAD System
The symmetric analogue of the polynomial power basis
ACM Transactions on Graphics (TOG)
Construction of triangular DP surface and its application
Journal of Computational and Applied Mathematics
Conversion and evaluation for two types of parametric surfaces constructed by NTP bases
Computers & Mathematics with Applications
A new bivariate basis representation for Bézier-based triangular patches with quadratic complexity
Computers & Mathematics with Applications
A class of quartic rational polynomial triangular patch
Proceedings of the 12th ACM SIGGRAPH International Conference on Virtual-Reality Continuum and Its Applications in Industry
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The use of Bernstein polynomials as the basis functions in Bézier's UNISURF is well known. These basis functions possess the shape-preserving properties that are required in designing free form curves and surfaces. These curves and surfaces are computed efficiently using the de Casteljau Algorithm. Ball uses a similar approach in defining cubic curves and bicubic surfaces in his CONSURF program. The basis functions employed are slightly different from the Bernstein polynomials. However, they also possess the same shape-preserving properties. A generalization of these cubic basis functions of Ball, such that higher order curves and surfaces can be defined and a recursive algorithm for generating the generalized curve are presented. The algorithm could be extended to generate a generalized surface in much the same way that the de Casteljau Algorithm could be used to generate a Bézier surface.