非均匀Doo-Sabin细分曲面的尖锐特征构造

Sharp feature construction of non-uniform doo-sabin subdivision surface

为进一步增强细分技术的特征造型能力,从修改细分规则的角度提出非均匀Doo-Sabin细分曲面的尖锐特征构造方法。根据基于非均匀Doo-Sabin细分方法的曲线插值理论,分析推导了控制网格中特征面细分的几何规则,并对细分极限曲面在特征附近的连续性进行了分析。在节点距大于零、所有面片边数及所有顶点价均小于11的情况下,细分极限曲面具有分片G1连续性。该方法既可以表示具有各种尖锐特征的任意拓扑复杂曲面,所构造的边界、折痕可以为一般二次NURBS曲线,同时还可以借助加权细分精确构造球面、柱面等一些常用二次曲面。

To further promote the modeling ability of subdivision technology,a method for constructing sharp features of non-uniform Doo-Sabin subdivision surfaces was presented from the perspective of modifying subdivision rules.According to the curve interpolation theory based on non-uniform Doo-Sabin subdivision scheme,the subdivision geometric rules in the feature faces were derived and the continuities near the features were analyzed.If all knot spacings were greater than zero,the subdivision limit surface was of piecewise G1 smoothness when the edges of each face and the degree of each vertex were both less than eleven.The complicated surfaces of arbitrary topologies with various sharp features could be well represented,and the constructed boundaries and creases might be any generic quadric NURBS curves.In addition,some quadric surfaces such as spheres and cylinders could also be accurately represented with the weighted subdivision.