Generation of an Implicit Surface Based on the Delaunay Tetrahedralization

本研究的目的是产生一个可以快速可视化的隐式函数。为此，隐式曲面由Delaunay四面体化生成的重构结果代替。此外，传统的隐式函数的特性被附加到重建结果。本程序的研究成果如下：首先，提出了一种删除Delaunay四面体化重构结果中冗余曲面的方法。在该方法中，冗余曲面的识别是通过使用一个简化的生成的隐式函数。此外，通过简化生成的隐函数，将可视化过程与隐函数生成过程完全分离，并将常规隐函数的特征附加到Delaunay四面体化生成的结果中。此外，为了从没有法线的点数据获得重构结果，已经开发了用于估计点法线的方法。实验结果表明，利用估计的点法线，对无法线的点数据进行Delaunay四面体化，得到了预期的结果。

The purpose of this study is generation of an implicit function that can be fast visualized. To this end, the implicit surface is replaced by a reconstructed result generated by the Delaunay tetrahedralization. In addition, the characteristics of conventional implicit functions are appended to the reconstructed result. Study results of this program are as follows : first, a method for erasing redundant surfaces of a reconstructed result generated by the Delaunay tetrahedralization has been developed. In this method, the redundant surfaces are recognized by using a simplified generated implicit function. In addition, by using the simplified generated implicit function, procedures of visualization and those of generating an implicit function are completely separated, and the characteristics of conventional implicit functions are appended to the result generated by the Delaunay tetrahedralization. Moreover, in order to obtain a reconstructed result from the point data without normals, a method for estimation of point normals has been developed. Experiments illustrate that, by using the estimated point normals, some expected results generated by the Delaunay tetrahedralization are obtained from the point data without normals.