An interesting subcomplex of the Delaunay triangulation are $\alpha$-shapes, which give a more detailed representation of the shape of point sets than the convex hull. We extend an algorithm which computes all Delaunay simplices over all time windows to also compute the temporal $\alpha$-shape, which is a description of all $\alpha$-shapes over all time windows and all values of $\alpha$, in output-sensitive linear time. We present an interactive demo application based on a fast query data structure. Experimental results show that our algorithm is practical and can be used on real-world data sets.

翻译：德劳内三角剖分的一个有趣子复形是$α$形状，它比凸包能更详细地表示点集的形状。我们将一种计算所有时间窗口内所有德劳内单纯形的算法进行扩展，使其能够以输出敏感的线性时间计算时间$α$形状——即在所有时间窗口和所有$α$值下对全部$α$形状的描述。我们基于快速查询数据结构开发了一款交互式演示应用。实验结果表明，该算法具有实用性，可应用于真实世界数据集。