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.

A low computational cost method is proposed for detecting actuator/sensor faults. Typical model-based fault detection (FD) units for multiple sensor faults require a bank of estimators [i.e., conventional Kalman estimators or artificial intelligence (AI)-based ones]. The proposed FD scheme uses an AI approach for developing of a low computational power FD unit abbreviated as iFD. In contrast to the bank-of-estimators approach, the proposed iFD unit employs a single estimator for multiple actuator/sensor FD. The efficacy of the proposed FD scheme is illustrated through a rigorous analysis of the results for a number of sensor fault scenarios on an electromagnetic suspension system.