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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120 citations
Book•
01 Jan 1994
TL;DR: The results and presentations of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993 as discussed by the authors, represent directions for future research and development in many areas of application.
Abstract: This volume documents the results and presentations, related to aspects of geometric design, of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application. From the table of contents: - Object Oriented Spline Software - An Introduction to Pade Approximations - Zonoidal Surfaces - Projective Blossoms and Derivatives - Piecewise Polynomial Approximation of Spheres - A Geometrical Approach to Interpolation on Quadric Surfaces
120 citations
Posted Content•
TL;DR: In this article, the authors presented versions of the proofs of two classic theorems of combinatorial topology, namely, the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves.
Abstract: Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This is used in the proof, modelled on that of Pachner, of the second theorem. This states that moves from only a finite collection are needed to relate two triangulations of a piecewise linear manifold.
120 citations
TL;DR: The simplified results, which rely heavily on a careful dissection and improved understanding of the tangent cone of the feasible region of the program, bypass the combinatorial characterization that is intrinsic to B-stationarity.
Abstract: With the aid of some novel complementarity constraint qualifications, we derive some simplified primal-dual characterizations of a B-stationary point for a mathematical program with complementarity constraints (MPEC). The approach is based on a locally equivalent piecewise formulation of such a program near a feasible point. The simplified results, which rely heavily on a careful dissection and improved understanding of the tangent cone of the feasible region of the program, bypass the combinatorial characterization that is intrinsic to B-stationarity.
120 citations
TL;DR: Two algorithms are presented, one point-based and one element-based, that extract separation and attachment lines using eigenvalue analysis of a locally linear function, which shows that both algorithms detect open separation lines-a type of separation that is not captured by conventional vector field topology algorithms.
Abstract: Separation and attachment lines are topologically significant curves that exist on 2D surfaces in 3D vector fields. Two algorithms are presented, one point-based and one element-based, that extract separation and attachment lines using eigenvalue analysis of a locally linear function. Unlike prior techniques based on piecewise numerical integration, these algorithms use robust analytical tests that can be applied independently to any point in a vector field. The feature extraction is fully automatic and suited to the analysis of large-scale numerical simulations. The strengths and weaknesses of the two algorithms are evaluated using analytic vector fields and also results from computational fluid dynamics (CFD) simulations. We show that both algorithms detect open separation lines-a type of separation that is not captured by conventional vector field topology algorithms.
119 citations