基于区域划分四边剖分的体参数化模型构建
Volume Parameterized Modeling Based on Region-Divided Quadrilateral Meshing

针对当前体参数化模型构建过程中需要进行模型分割的问题，本文提出一种基于区域划分的四边剖分算法。首先定义平面多亏格几何域，通过约束Delaunay三角化(Constrained Delaunay Triangulation, CDT)在给定几何域中生成背景网格，利用CDT网格中的相关信息来构建内外轮廓连接线，将平面多亏格轮几何域转化零亏格多子域集合，并将每个子域转化为凸多边形，然后对每个凸子域进行四边剖分，最后对所有非空全四边形子域进行Coons插值生成参数化曲面，并通过拉伸、扫描、旋转、放样等几何操作获得体参数化模型。结果表明该方法为CAD/CAE一体化提供了高鲁棒性的体参数化解决方案，可有效支撑复杂工程模型的等几何分析需求。
To address the model segmentation problem in current volumetric parameterization model construction, this paper proposes a quadrilateral decomposition algorithm based on regional partitioning. First, a planar multi-genus geometric domain is defined. A background mesh is generated within the given domain via Constrained Delaunay Triangulation (CDT). Utilizing information from the CDT mesh, connection lines between inner and outer contours are constructed to transform the planar multi-genus domain into a collection of zero-genus subdomains. Each subdomain is then converted into a convex polygon. Subsequently, quadrilateral decomposition is performed on each convex subdomain. Finally, Coons interpolation is applied to all non-empty fully quadrilateral subdomains to generate parameterized surfaces. Volumetric parameterization models are obtained through geometric operations such as extrusion, sweeping, rotation, and lofting. The results demonstrate that this method provides a highly robust volumetric parameterization solution for CAD/CAE integration, effectively supporting the isogeometric analysis requirements of complex engineering models.