发表机构
Brigham Young University; Coreform Inc（杨百翰大学; Coreform公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究提出算法构建组合映射拓扑数据结构，用于表示满足相容性的层次样条Bézier网格，其拓扑信息可使样条下游应用计算时间最多缩短一个数量级。
AI 中文摘要
层次样条是多尺度自适应等几何分析格式的重要组成部分，其Bézier网格是自身定义及多种关键层次样条算法（如自适应细化、Bézier提取）的核心部分。与Bézier网格关联的拓扑数据（如邻接信息）可提升这些算法及样条下游应用的性能，但典型层次样条格式不计算该拓扑数据，仅存储元素列表。本研究提出算法构建高性能拓扑数据结构——组合映射，用于表示立方体复形上层次样条的Bézier网格，要求细化层级的Bézier网格满足相容性，涵盖层次B样条、截断层次B样条及其他层次样条格式的子集。我们展示了这些层次组合映射构建算法的性能特征及一个用例，结果表明拓扑信息可使样条下游应用的计算时间最多缩短一个数量级。
英文摘要
Hierarchical splines are an important part of multiscale and adaptive isogeometric analysis formulations. The Bézier meshes of these splines are an essential part of their definition and of several important hierarchical spline algorithms, such as adaptive refinement and Bézier extraction. Topological data associated with the Bézier mesh-such as adjacency information-can be used to improve the performance of many of these algorithms as well as downstream applications of the splines, but typical hierarchical spline formulations do not compute the topological data, storing instead just a list of elements. In this work we present algorithms to build a performant topological data structure, namely the combinatorial map, to represent Bézier meshes of hierarchical splines over cubical cell complexes where the refinement levels have conforming Bézier meshes. This includes hierarchical and truncated hierarchical B-splines, as well as subsets of other hierarchical spline formulations. We show the performance characteristics of the construction algorithms of these hierarchical combinatorial maps, as well as an example use case, showing that the topological information can provide up to an order of magnitude reduction in computation time in downstream applications of the splines.
