Abstract
Abstract Based on the relationship between probability operators and curve/surface modeling, a new kind of surface modeling method is introduced in this paper. According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are defined over a triangular domain. The main properties of the basis functions are studied, which guarantee that the basis functions are suitable for surface modeling. Then, the corresponding triangular surface patch called a triangular Meyer-König-Zeller surface patch is constructed. We prove that the new surface patch has the important properties of surface modeling, such as affine invariance, convex hull property and so on. Finally, based on given control vertices, whose number is finite, a truncated triangular Meyer-König-Zeller surface and a redistributed triangular Meyer-König-Zeller surface are constructed and studied.
Highlights
In computer aided geometric design (CAGD), representing a parametric curve or surface with shape preserving is important
According to a kind of bivariate Meyer-König-Zeller operator, we study the corresponding basis functions called triangular Meyer-König-Zeller basis functions which are de ned over a triangular domain
We prove that the new surface patch has the important properties of surface modeling, such as a ne invariance, convex hull property and so on
Summary
In computer aided geometric design (CAGD), representing a parametric curve or surface with shape preserving is important. We will introduce a method that constructs a kind of surface called a triangular Meyer-KönigZeller surface by triangular Meyer-König-Zeller basis functions Pn,k,l(μ). From the properties of triangular Meyer-König-Zeller basis functions, we can derive the geometric properties of a triangular Meyer-König-Zeller surface as follows: (1) A ne Invariance (2) Convex Hull Property (3) Interpolative control vertex V , (4) Non-Degenerate (5) The boundary curves are rational Bézier curves in terms of the Bernstein basis functions of negative degree
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