Interactive Exploration of the Temporal $α$-Shape

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.