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- Efi Fogel, Dan Halperin
- ALENEX
- 2006

We present an exact implementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R. Our implementation is complete in the sense that it does not assume general position. Namely, it can handle degenerate input, and it produces exact results. We also present applications of the Minkowski-sum computation to answer collision and… (More)

- Efi Fogel, Dan Halperin, Christophe Weibel
- Discrete & Computational Geometry
- 2009

We present a tight bound on the exact maximum complexity of Minkowski sums of polytopes in R. In particular, we prove that the maximum number of facets of the Minkowski sum of k polytopes with m1,m2, . . . ,mk facets respectively is bounded from above by

- Ron Wein, Efi Fogel, Baruch Zukerman, Dan Halperin
- Comput. Geom.
- 2007

Arrangements of planar curves are fundamental structures in computational geometry. Recently, the arrangement package of Cgal, the Computational Geometry Algorithms Library, has been redesigned and re-implemented exploiting several advanced programming techniques. The resulting software package, which constructs and maintains planar arrangements, is easier… (More)

- Efi Fogel, Daniel Cohen-Or, Revital Ironi, Tali Zvi
- Web3D
- 2001

In this paper a Web architecture for 3D content delivery is presented. The architecture is based on a progressive compression representation integrated into the X3D framework. The architecture is designed to enhance the Internet user experience by delivering 3D content quickly, reliably, and with high quality. The progressive compressed stream enables… (More)

- Eric Berberich, Efi Fogel, Dan Halperin, Kurt Mehlhorn, Ron Wein
- ESA
- 2007

We introduce a general framework for sweeping a set of curves embedded on a two-dimensional parametric surface. We can handle planes, cylinders, spheres, tori, and surfaces homeomorphic to them. A major goal of our work is to maximize code reuse by generalizing the prevalent sweep-line paradigm and its implementation so that it can be employed on a large… (More)

- Efi Fogel, Dan Halperin, Ron Wein
- Geometry and Computing
- 2012

Why should wait for some days to get or receive the cgal arrangements and their applications a step by step guide book that you order? Why should you take it if you can get the faster one? You can find the same book that you order right here. This is it the book that you can receive directly after purchasing. This cgal arrangements and their applications a… (More)

- Efi Fogel, Dan Halperin
- IEEE Transactions on Automation Science and…
- 2008

Assembly partitioning with an infinite translation is the application of an infinite translation to partition an assembled product into two complementing subsets of parts, referred to as subassemblies, each treated as a rigid body. We present an exact implementation of an efficient algorithm to obtain such a motion and subassemblies given an assembly of… (More)

- Efi Fogel, Dan Halperin
- Symposium on Computational Geometry
- 2005

We present an exact imp ementation of an efficient algorithm that computes Minkowski sums of convex polyhedra in R<sup>3</sup>. Our implementation is complete in the sense that it does not assume general position, namely, it can handle degenerate input, and produces exact results. Our software also includes applications of the Minkowski-sum computation to… (More)

- Eric Berberich, Efi Fogel, Dan Halperin, Michael Kerber, Ophir Setter
- Mathematics in Computer Science
- 2010

We describe the algorithms and implementation details involved in the concretizations of a generic framework that enables exact construction, maintenance, and manipulation of arrangements embedded on certain two-dimensional orientable parametric surfaces in three-dimensional space. The fundamentals of the framework are described in a companion paper. Our… (More)

- Efi Fogel, Ron Wein, Dan Halperin
- ESA
- 2004

Arrangements of planar curves are fundamental structures in computational geometry. We describe the recent developments in the arrangement package of Cgal, the Computational Geometry Algorithms Library, making it easier to use, to extend and to adapt to a variety of applications. This improved flexibility of the code does not come at the expense of… (More)