在色彩Delaunay马赛克的大小上
Ranita Biswas1, Sebastiano Cultrera di Montesano1, Ondřej Draganov1
1ISTA (Institute of Science and Technology Austria), Klosterneuburg, Austria.
概括
我们介绍了色彩Delaunay马赛克,这是一个新的结构,代表了更高维度的彩色点集. 它的尺寸取决于尺寸和颜色,随机颜色和广泛分布的点有特定的界限.
科学领域:
- 计算几何学计算几何学
- 几何组合学的几何组合学.
- 数据可视化数据可视化
背景情况:
- 对点集结构的研究是计算几何学的基础.
- 了解彩色点如何相互作用对于各种应用至关重要.
- 德劳内马赛克为分析点集中的空间关系提供了一个框架.
研究的目的:
- 介绍和定义d维空间中彩色点集的色彩Delaunay马赛克.
- 为了确定色彩Delaunay马赛克尺寸的界限.
- 探索点集合属性,色彩和马赛克大小之间的关系.
主要方法:
- 在R^{d+s}中构建一个色彩的Delaunay马赛克,用于R^{d+s}中的有色点集合A.
- 对于有限点集的随机染色的预期细胞数的导出.
- 对Delone集和Poisson点过程的马赛克大小的分析.
- 对R^2.2.中的分布良好的点集的马赛克大小的研究.
主要成果:
- 染色Delaunay马赛克有O(n^d/2) 细胞在等待随机染色.
- 对于Delone集和Poisson点过程,每个点的预期单元数是恒定的.
- 在R^2中,所有分布良好的点集合的色彩都会产生大小为O (n) 的马赛克.
结论:
- 染色Delaunay马赛克的尺寸对点集的性质及其色彩敏感.
- 彩色Delaunay马赛克为彩色点数据提供了一个可扩展的表示.
- 结果鼓励在各种领域应用色彩德劳内马赛克.
关键词:
染色的德劳内马赛克 德劳内马赛克染色点集是一种色彩点集.组合几何组合几何学德劳内 (Delaunay) 的马赛克德隆集是一套德隆集.波森点过程的过程.随机几何学的随机几何学.沃罗诺伊图表 沃罗诺伊图表更多相关视频
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