Related papers: Fast and Accurate Intersections on a Sphere
Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art…
Abstract. The Set Intersection Problem (SIP) is the problem of finding a point in the intersection of convex sets. This problem is typically solved by the method of alternating projections. To accelerate the convergence, the idea of using…
The application of error-free transformation (EFT) is recently being developed to solve ill-conditioned problems. It can reduce the number of arithmetic operations required, compared with multiple precision arithmetic, and also be applied…
Information transfer between triangle meshes is of great importance in computer graphics and geometry processing. To facilitate this process, a smooth and accurate map is typically required between the two meshes. While such maps can…
The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…
Fast Fourier Transform (FFT) is an efficient algorithm to compute the Discrete Fourier Transform (DFT) and its inverse. In this paper, we pay special attention to the description of complex-data FFT. We analyze two common descriptions of…
Object orientation provides a flexible framework for the implementation of the convolution of arbitrary distributions of real-valued random variables. We discuss an algorithm which is based on the discrete Fourier transformation (DFT) and…
Autonomous driving demands accurate perception and safe decision-making. To achieve this, automated vehicles are now equipped with multiple sensors (e.g., camera, Lidar, etc.), enabling them to exploit complementary environmental context by…
Strong multiple scattering of the probe in scanning transmission electron microscopy (STEM) means image simulations are usually required for quantitative interpretation and analysis of elemental maps produced by electron energy-loss…
We construct a new quantum algorithm for the graph collision problem; that is, the problem of deciding whether the set of marked vertices contains a pair of adjacent vertices in a known graph G. The query complexity of our algorithm is…
The problem of finding a point in the intersection of closed sets can be solved by the method of alternating projections and its variants. It was shown in earlier papers that for convex sets, the strategy of using quadratic programming (QP)…
Many real-world physics and engineering problems arise in geometrically complex domains discretized by meshes for numerical simulations. The nodes of these potentially irregular meshes naturally form point clouds whose limited tractability…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of…
In this paper we propose and test the validity of simple and easy-to-implement algorithms within the immersed boundary framework geared towards large scale simulations involving thousands of deformable bodies in highly turbulent flows.…
Calculations of the Fourier transform of a constant quantity over an area or volume defined by polygons (connected vertices) are often useful in modeling wave scattering, or in fourier-space filtering of real-space vector-based volumes and…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class,…
This paper presents a state-of-the-art approach in object detection for being applied in future SLAM problems. Although, many SLAM methods are proposed to create suitable autonomy for mobile robots namely ground vehicles, they still face…
This paper presents a state-of-the-art filter that reduces the complexity in object detection, tracking and mapping applications. Existing edge detection and tracking methods are proposed to create suitable autonomy for mobile robots,…