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基于GNURBS的多边洞曲面填充算法

N-sided Hole Filling Algorithm based on GNURBS

  • 摘要: 多边洞曲面填充是计算机辅助几何设计中的基础问题, 广泛应用于顶点过渡、复杂倒角等算法中. 本文提出了一种基于广义非均匀有理B样条(GNURBS)的多边洞曲面填充算法. 对于任意给定的四边形网格和节点信息,GNURBS可以给出全局G1连续的基函数生成方法,得到一个全局G1连续的曲面. 本文提出的多边洞曲面填充算法主要包含两个步骤,首先将多边洞区域剖分为全四边形网格, 并定义该网格对应的GNURBS基函数, 再由边界连续约束和能量优化方法确定GNURBS表示的控制点的位置和权值. 由于新算法与非均匀有理B样条(NURBS)完全兼容, 从而可以直接应用于计算机辅助设计(CAD)软件, 可以无损失的在CAD软件包之间传递. 对不同边数的多边洞进行算法测试,并将结果和CATIA填充曲面进行对比, 新型算法可以构建更加光滑自然的多边洞填充曲面, 且曲面质量优于CATIA的算法结果.

     

    Abstract: N-sided hole filling algorithm is an foundation problem in computer-aided geometric design, which is widely used in vertex transition and complex chamfering. This paper proposes a n-sided hole filling algorithm based on generalized non-uniform rational B-splines (GNURBS). Given a quadrilateral mesh with knot intervals, GNURBS can define a set of basis functions with globally G1 continuous. The new algorithm includes two main steps. Firstly, the n-sided hole is divides into a complete quadrilateral mesh, which can be used to define corresponding GNURBS basis functions, and then the position and weight of control points are computed according to the boundary continuity constraints and energy optimization methods. The new algorithm is compatible with non-uniform rational B-splines (NURBS), which can be directly applied to computer-aided design (CAD) software, and can be seamlessly transferred between CAD software packages without any loss. The algorithm was tested for different number of edges and the results were compared with CATIA filled surfaces. The experimental results show that the new algorithm can construct smoother and more natural n-sided hole filling surfaces, with better surface quality than the algorithm results of CATIA.

     

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