均匀T网格样条曲面的局部细分算法

Local Subdivision Algorithm for Uniform T-Grid Spline Surface

为解决T样条曲面造型中控制点插入的规范与半规范问题,提出基于均匀T网格样条曲面的局部细分算法。首先根据T样条曲面定义,将B样条曲面转换成均匀T网格样条曲面,然后在均匀T网格样条曲面中进行局部均匀控制点插入。为满足曲面局部特征细分要求,采用递进控制点插入形式:拥有局部特征的网格先进行全行(或全列)均匀控制点插入,之后进行局部列(局部行)均匀控制点插入,在此基础上,可以再次进行均匀控制点插入,以达到对网格的嵌套细分。该算法对初始网格控制点的混合函数进行矩阵转换,得到最终T网格上控制点的混合函数,实现最终曲面构造。与T样条曲面的局部细分相比,该方法简化了任意控制点插入的复杂度,与B样条曲面的局部细分相比,该方法减少了多余控制点。

To solve the standard and semi-standard problems of control point insertion in T-spline surface modeling,this paper proposes a local subdivision algorithm based on uniform T-grid spline surface.Firstwe convert the B-spline surface into a uniform T-grid spline surface based on the definition of the T-spline surface andthen perform the localuniform controlpoint insertion in a uniform T-grid spline surface.In order to meet the requirements for the local feature subdivision of theT-grid splinesurface,we adoptthe form of progressive control point insertion.The mesh for local feature subdivisionfirst performs uniform control point insertion in the full row(orfull column)and then in the local column(or local row).On this basis,the uniform control point insertion is performed again to achieve the purpose of mesh subdivision and subdivision again.The algorithm performs the matrix transformation of the blending functions of the initial grid control points to obtain the blending functions of the control points on the T-gridsurfaceand to generate the final T-gridsurface.Compared with the local subdivision of the T-grid spline surface,this algorithm simplifies the complexity of arbitrary control point insertion.Compared with the local subdivision of the T-grid spline surface,it simplifies the complexity of arbitrary control point insertion.Compared with the local subdivision of the B-spline surface,it reduces redundant control points and simplifies the T-spline surface.