An Optimal Hidden-Surface Algorithm and Its Parallelization

Analytic Visibility on the GPU

“…The computational geometry community showed continued interest in analytic visibility, and in recent years Dévai gave an easier‐to‐implement optimal sequential algorithm and an optimal parallel algorithm that runs in Θ(log n ) using n 2 / logn processors in the CREW PRAM model (Concurrent Read Exclusive Write Parallel Random Access Machine) [Dév11]. However, such optimal algorithms use intricate data structures and are highly non‐trivial to implement on actual GPU hardware.…”

“…Our method performs the visibility computation independently for each edge, which yields an embarrassingly parallel workload. Building on a method of Dévai [Dév11], we present a new edge‐triangle intersection method that allows replacing the theoretical ‘black hole’ treatment of Dévai with a novel, implementation‐friendly boundary completion stage. Both algorithms and the additional hidden line elimination stage are presented in the next sections.…”

“…Hidden line elimination is a standard technique in line rendering and was first introduced by Appel [App67]. We adapt a recent result of Dévai [Dév11] on the optimal runtime of parallel hidden surface algorithms for our method. We use a scan‐based approach which walks along the line of a given edge e and determines for each intersection point if it is an endpoint of a visible segment of e .…”