浙江大学学报（理学版）2025，Vol.52Issue(6)：719-727,765,10.DOI:10.3785/j.issn.1008-9497.2025.06.006
广义Bézier曲面的G1连续曲面逼近
G1 continuous surface approximation to generalized Bézier surfaces
摘要
Abstract
Generalized Bézier(GB)surface is a new N-sided surface.This kind of surfaces are generalizations of tensor product Bézier surfaces and have simple control meshes and good geometric properties as well.In order to apply GB surfaces in moden CAD/CAM systems,we present an algorithm for converting GB surfaces to G1 smoothly connected Bézier surfaces.Firstly,we subdivide the parameter domain of a GB surface into N quadrilateral subdomain based on N-splitting method.Then we construct a biquintic Bézier surface for each quadrilateral subdomain satisfying the conditions of G1 continuity on the boundaries.Finally,we optimize control points of the biquintic Bézier surfaces using the least square method with linear constraints.Particularly,the approximate surfaces interpolate the central point and boundaries of the GB surface.By applying this algorithm,a GB surface can be approximately converted into a macro-patch composed of N biquintic Bézier surfaces.The converted surfaces are standard surfaces in moden CAD/CAM system.Numerical examples show that the converted Bézier surfaces approximate the GB surfaces with high accuracy and preserve the geometric features of GB surfaces well.关键词
广义Bézier曲面/G1连续/曲面逼近/宏曲面片Key words
generalized Bézier surface/G1 continuity/surface approximation/macro-patch分类
信息技术与安全科学引用本文复制引用
杨耀源,杨勋年..广义Bézier曲面的G1连续曲面逼近[J].浙江大学学报（理学版）,2025,52(6):719-727,765,10.基金项目
国家自然科学基金资助项目(12171429). （12171429）
