基于广义基曲面参数化的N边域曲面重构

N-sieded Surface Reconstruction Based on Generalized Base Surfaces Parametrization

研究了由散乱数据点集重构N边域曲面的方法。已有方法大都使用单张B样条曲面进行拟合,或由用户手工描绘曲面片的边界曲线网格。与之不同,为便于数字处理,采用广义基曲面参数化方法可以在建立曲面片网格同时进行散乱数据的参数化,全过程无需人工干预。另外,推导了在曲面拟合算法中控制顶点约束的确定方法以满足给定的边界条件。通过仿真,研究了曲面片网格的光顺以在N边域曲面内部达到G^1连续,并以实例证明了文中算法的有效性。

In this paper,we propose a method for reconstructing B - spline surface from a set of scattered 3D points of n - sided boundary.Unlike previous work which considers primarily the problem of fitting a single B - spline patch or draw a network of B - spline patches manually,the solution named generalized base surfaces parameterization by the author is a scheme for automatically constructing both a network of patches and a parameterization of the data points over these patches.In addition,formulas for determining constrained vertexes in surface fitting are deduced, which can be used to meet boundary condition.Finally,we study the smoothing of the patch network in order to satisfy G1 continuity of N - sided surface,and demonstrate the efficiency of the method by an example.