期刊
AIMS MATHEMATICS
卷 6, 期 2, 页码 1677-1694出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2021099
关键词
bicubic B-spline surfaces; sixth order PDE; PDE surfaces
资金
- National Natural Science Foundation of China [12071057, 11671068]
This paper presents a method for generating bicubic B-spline surfaces from sixth order PDEs, allowing for flexible and effective surface design based on different boundary conditions. Representative examples demonstrate the method's effectiveness in surface modeling.
As the solutions of partial differential equations (PDEs), PDE surfaces provide an effective way for physical-based surface design in surface modeling. The bicubic B-spline surface is a useful tool for surface modeling in computer aided geometric design (CAGD). In this paper, we present a method for generating bicubic B-spline surfaces with the uniform knots and the quasi-uniform knots from the sixth order PDEs. From the given boundary condition, based on the cubic B-spline basis representation and the PDE mask, the resulting bicubic B-spline surface can be generated uniquely. The boundary condition is more flexible and can be applied for curvature-continuous surface design, surface blending and hole filling. Some representative examples show the effectiveness of the presented method.
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