Topic
Piecewise
About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.
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TL;DR: A new third-order Energy Stable Weighted Essentially Non-Oscillatory (ESWENO) finite difference scheme for scalar and vector hyperbolic equations with piecewise continuous initial conditions is developed and is proven to be linearly stable in the energy norm for both continuous and discontinuous solutions.
117 citations
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TL;DR: The basic theory of rational motions is summarized and a linear control structure for piecewise rational motions suitable for geometry processing is introduced and algorithms for the calculation of the surface which is swept out by a moving polyhedron are provided.
Abstract: Using rational motions it is possible to apply many fundamental B-spline techniques to the design of motions. The present paper summarizes the basic theory of rational motions and introduces a linear control structure for piecewise rational motions suitable for geometry processing. Moreover it provides algorithms for the calculation of the surface which is swept out by a moving polyhedron and examines interpolation techniques. The methods presented in this paper can be applied to various problems in computer animation as well as in robotics.
117 citations
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TL;DR: In this paper, a Galerkin finite element method that uses piecewise bilinear on a simple piecewise equidistant mesh is applied to a linear convection-dominated convectiondiffusion problem in two dimensions.
117 citations
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09 Jun 1997TL;DR: This survey presents several techniques for solving variants of the following scattered data interpolation problem: given a finite set of N points in R3, find a surface that interpolates the given set of points.
Abstract: This survey presents several techniques for solving variants of the following scattered data interpolation problem: given a finite set of N points in R3, find a surface that interpolates the given set of points. Problems of this variety arise in numerous areas of applications such as geometric modeling and scientific visualization. A large class of solutions exists for these problems and many excellent surveys exist as well.The focus of this survey is on presenting techniques that are relatively recent. Some discussion of two popular variants of the scattered data interpolation problem -- trivariate (or volumetric) case and surface-on-surface -- is also included.Solutions are classified into one of the five categories: piecewise polynomial or rational parametric solutions, algebraic solutions, radial basis function methods, Shepard's methods and subdivision surfaces. Discussion on parametric solutions includes global interpolation by a single polynomial, interpolants based on data dependent triangulations, piecewise linear solutions such as alpha-shapes, and interpolants on irregular mesh.Algebraic interpolants based on cubic A-patches are described. Interpolants based on radial basis functions include Hardy's multiquadrics, inverse multiquadrics and thin plate splines. Techniques for blending local solutions and natural neighbor interpolants are described as variations of Shepard's methods. Subdivision techniques include Catmull-Clark subdivision technique and its variants and extensions. A brief discussion on surface interrogation techniques and visualization techniques is also included.
117 citations
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18 Jun 2018TL;DR: A hybrid l1-l0 decomposition model is proposed that achieves visually compelling results with little halo artifacts, outperforming the state-of-the-art tone mapping algorithms in both subjective and objective evaluations.
Abstract: Tone mapping aims to reproduce a standard dynamic range image from a high dynamic range image with visual information preserved. State-of-the-art tone mapping algorithms mostly decompose an image into a base layer and a detail layer, and process them accordingly. These methods may have problems of halo artifacts and over-enhancement, due to the lack of proper priors imposed on the two layers. In this paper, we propose a hybrid l1-l0 decomposition model to address these problems. Specifically, an l1 sparsity term is imposed on the base layer to model its piecewise smoothness property. An l0 sparsity term is imposed on the detail layer as a structural prior, which leads to piecewise constant effect. We further propose a multiscale tone mapping scheme based on our layer decomposition model. Experiments show that our tone mapping algorithm achieves visually compelling results with little halo artifacts, outperforming the state-of-the-art tone mapping algorithms in both subjective and objective evaluations.
117 citations