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Local polyhedra and geometric graphs
 In Proc. 14th ACMSIAM Sympos. on Discrete Algorithms
, 2003
"... We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest ed ..."
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We introduce a new realistic input model for geometric graphs and nonconvex polyhedra. A geometric graph G is local if (1) the longest edge at every vertex v is only a constant factor longer than the distance from v to its Euclidean nearest neighbor and (2) the lengths of the longest and shortest edges differ by at most a polynomial factor. A polyhedron is local if all its faces are simplices and its edges form a local geometric graph. We show that any boolean combination of any two local polyhedra in IR d each with n vertices, can be computed in O(n log n) time, using a standard hierarchy of axisaligned bounding boxes. Using results of de Berg, we also show that any local polyhedron in IR d has a binary space partition tree of size O(n log d1 n). Finally, we describe efficient algorithms for computing Minkowski sums of local polyhedra in two and three dimensions.
An integration framework for simulations of solid rocket motors
 In 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference
, 2005
"... Simulation of solid rocket motors requires coupling physical models and software tools from multiple disciplines, and in turn demands advanced techniques to integrate independently developed physics solvers e ectively. In this paper, we overview some computer science components required for such int ..."
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Simulation of solid rocket motors requires coupling physical models and software tools from multiple disciplines, and in turn demands advanced techniques to integrate independently developed physics solvers e ectively. In this paper, we overview some computer science components required for such integration. We package these components into a software framework that provides system support of highlevel data management and performance monitoring, as well as computational services such as novel and robust algorithms for tracking Lagrangian surface meshes, parallel mesh optimization, and data transfer between nonmatching meshes. From these reusable framework components we construct domainspeci c building blocks to facilitate integration of parallel, multiphysics simulations from highlevel speci cations. Through examples, we demonstrate the exibility of our framework and its components. I.
Special Issue on Multiphysics simulations: Challenges and opportunities Contents
, 2013
"... 1.1 What constitutes multiphysics?................................................................................................................. 5 1.2 Prototype algebraic forms......................................................................................................................... ..."
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1.1 What constitutes multiphysics?................................................................................................................. 5 1.2 Prototype algebraic forms......................................................................................................................... 6
Local Polyhedra and Geometric Graphs*
"... Local Polyhedra and Geometric Graphs 1 1 Introduction Nonconvex polyhedra are ubiquitous in computer graphics, solid modeling, computer aided design and manufacturing, robotics, and other geometric application areas. Unlike nonconvex polygons or convex objects in space, for which many problems can b ..."
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Local Polyhedra and Geometric Graphs 1 1 Introduction Nonconvex polyhedra are ubiquitous in computer graphics, solid modeling, computer aided design and manufacturing, robotics, and other geometric application areas. Unlike nonconvex polygons or convex objects in space, for which many problems can be solved easily, polyhedra are notoriously difficult to handle efficiently, at least in the worst case.