A comprehensive survey on Delaunay Triangulation: applications, algorithms, and implementations over CPUs, GPUs, and FPGAs - Elshakhs, Yahia S.; Deliparaschos, Kyriakos M.; Charalambous, Themistoklis; Oliva, Gabriele; Zolotas, Argyrios (Institute of Electrical and Electronics Engineers (IEEE), 2024)
Delaunay triangulation is an effective way to build a triangulation of a cloud of points, i.e., a partitioning of the points into simplices (triangles in 2D, tetrahedra in 3D, and so on), such that no two simplices overlap and every point in the set is a vertex of at least one simplex. Such a triangulation has been shown to have several interesting properties in terms of the structure of the simplices it constructs (e.g., maximising the minimum angle of the triangles in the bi-dimensional case) and has several critical applications in the contexts of computer graphics, computational geometry, mobile robotics or indoor localisation, to name a few application domains. This review paper revolves around three main pillars: (I) algorithms, (II) implementations over central processing units (CPUs), graphics processing units (GPUs), and field programmable gate arrays (FPGAs), and (III) applications. Specifically, the paper provides a comprehensive review of the main state-of-the-art algorithmic approaches to compute the Delaunay Triangulation. Subsequently, it delivers a critical review of implementations of Delaunay triangulation over CPUs, GPUs, and FPGAs. Finally, the paper covers a broad and multi-disciplinary range of possible applications of this technique.
Keywords: Delaunay triangulation; applications of Delaunay triangulation; algorithmic approaches to Delaunay triangulation; CPU implementation of Delaunay triangulation; GPU implementation of Delaunay triangulation; FPGA implementation of Delaunay triangulation; Voronoi diagram; CPU; GPU; FPGA