BLENDING POLYHEDRA WITH NURBS

DOI：

 作者 单位 王学福 清华大学计算机系,北京,100084 孙家广 清华大学计算机系,北京,100084 秦开怀 清华大学计算机系,北京,100084

本文应用ＮＵＲＢＳ曲面磨光多面体，产生了处处Ｃ′连续的过渡曲面．多面体的磨光分为边的磨光和顶点的磨光两种情形，边的磨光相对较容易，而顶点的磨光则很困难．本文所采用的应用ＮＵＲＢＳ曲面磨光多面体的顶点和边的方法，不仅可以统一实现二者的磨光操作，而且方法简单且统一，产生了Ｃ′连续的过渡面．较之以前的方法，首先，利用ＮＵＲＢＳ曲面可以精确地描述对边磨光所用的柱面（等半径或非等半径），其次，在对顶点的磨光中，同以往的方法不同，将与该顶点相邻的边的过渡曲面相互分离，并首次引入了“补面”的概念，使得对该点所产生的过渡曲面处处Ｃ′连续．本算法首先构造用以磨光多面体顶点和边的ＮＵＲＢＳ曲面的边界曲线网络图产生边界曲线的控制点及其权值（ＮＵＲＢＳ表示），然后依据连续性准则，产生ＮＵＲＢＳ曲面的控制信息．

An approach of blending edges and venices of a polyhedron with NURBS surfaces that are C' continuous along their common boundaries is presented in this paper. In general, the edge blending is a bit easier, but the vertex blending is more difficult. The approach presented in this paper can unify the transaction of these two cases. Compared with other method presented, first, NURBS surface can represent the edge blending surface (constant radius blending or variable radius blending) precisely; second, In blending the vertex, they depart the blending surfaces of its adjacent edges, so they don't need to meet with each other, then "supplementary surfaces" are generated to make C' transitions between them. They generate the blending surfaces by constructing boundary curve networks with C' continuity, then according to the continuity rule, generating the NURBS surfaces.
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