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通过代奇点调整计算平滑和可整合的交叉场
IEEE transactions on visualization and computer graphics
|June 25, 2024
概括
我们介绍了一种用于在表面上产生光滑,可整合的交叉场的新方法. 我们的方法自动确定奇点配置,确保无表面参数化和网格化的整合性.
科学领域:
- 计算几何学的计算几何学
- 计算机图形 计算机图形
- 应用数学 应用数学 应用数学
背景情况:
- 在计算机图形和几何处理中的各种应用中,光滑和可整合的交叉场是至关重要的.
- 计算交叉场的现有方法通常依赖于复杂的优化或整数编程技术.
- 确保整合性仍然存在挑战,特别是在多个连接领域.
研究的目的:
- 开发一种新的自动方法,用于计算2D和3D表面上的光滑和可整合的交叉场.
- 通过提供更强大,更易于使用的解决方案来解决现有方法的局限性.
- 为了实现诸如无合规参数化和无T连接的四角化等应用.
主要方法:
- 将迪里克莱特能量最小化以计算初始平滑交叉场.
- 代调整奇点 (位置,合并,分裂) 来确定它们的配置.
- 构建一个向量场来指导奇点优化以保证可整合性,特别是在多个连接域.
主要成果:
- 一种完全自动的方法,用于计算可控制的奇点配置的平滑交叉场.
- 在简单连接的领域保证了整合性,并在多个连接的领域实现它的一种方法.
- 该方法避免了专门的数值解析器,并且非常适合需要精确边界对齐的光滑模型.
结论:
- 拟议的方法在计算可整合的交叉场方面取得了重大进展.
- 它为现有的基于优化和整数编程方法提供了更直接和自动的替代方案.
- 该技术促进了高质量的表面参数化和网格化,并且将发布源代码.
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