论文标题
一种简单的算法，用于高阶Delaunay Mosaics和Alpha形状
A Simple Algorithm for Higher-order Delaunay Mosaics and Alpha Shapes
论文作者
论文摘要
我们提出了一种简单的算法，用于计算在任何有限尺寸的欧几里得空间中起作用的高阶Delaunay马赛克。该算法从逐步构造的低阶马赛克中选择订单的顶点-K $ Mosaic，并使用算法将加权的一阶Delaunay Mosaics作为黑盒子来构建其顶点的订单-K $ Mosaic。除了这个黑色框之外，该算法仅使用组合操作，从而促进了易于实现。我们将此算法扩展到计算高阶$α$形状并提供开源实现。我们为随机点集的高阶Delaunay马赛克的性质提出了实验结果。
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-$k$ mosaic from incrementally constructed lower-order mosaics and uses an algorithm for weighted first-order Delaunay mosaics as a black-box to construct the order-$k$ mosaic from its vertices. Beyond this black-box, the algorithm uses only combinatorial operations, thus facilitating easy implementation. We extend this algorithm to compute higher-order $α$-shapes and provide open-source implementations. We present experimental results for properties of higher-order Delaunay mosaics of random point sets.
