沃罗诺伊路径和风景的平均和预期扭曲
Herbert Edelsbrunner1, Anton Nikitenko1
1IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria.
概括
用网格近似曲线的周长扭曲平均是一致的. 这一发现适用于Voronoi路径,并将其概括为Voronoi scapes的更高维度.
科学领域:
- 计算几何学的计算几何学
- 几何测量理论 几何测量理论
- 数字几何数字几何学
背景情况:
- 与网格等离散元素相近的曲线引入了周边扭曲.
- 用一个正方形网格近似的圆的特定扭曲因子是一个已知的问题.
研究的目的:
- 为了确定周边扭曲因子是否平均恒定,对于各种曲线和网格类型.
- 为了将这一发现推广到更高的维度.
主要方法:
- 埃尔戈迪克理论被用来分析平均扭曲.
- 该研究考虑了使用Delaunay马赛克 (Voronoi路径) 的可调整曲线的近似值.
- 这些方法被扩展到所有维度.
主要成果:
- 周围扭曲因子被证明是平均恒定的,对于任何可纠正的曲线,通过非异国情调的德劳内马赛克 (沃罗诺伊路径) 进行近似.
- 这一结果被推广到更高的维度,引入了沃罗诺伊壁垒的概念.
结论:
- 平均周边扭曲在不同的可纠正曲线和特定类型的Delaunay三角形中是不变的.
- 沃罗诺伊路径及其扭曲性质的概念可以扩展到更高维度的空间,如沃罗诺伊壁垒.
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