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On the design of CGAL a computational geometry algorithms library
 SOFTW. – PRACT. EXP
, 1999
"... CGAL is a Computational Geometry Algorithms Library written in C++, which is being developed by research groups in Europe and Israel. The goal is to make the large body of geometric algorithms developed in the field of computational geometry available for industrial application. We discuss the major ..."
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Cited by 97 (16 self)
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CGAL is a Computational Geometry Algorithms Library written in C++, which is being developed by research groups in Europe and Israel. The goal is to make the large body of geometric algorithms developed in the field of computational geometry available for industrial application. We discuss the major design goals for CGAL, which are correctness, flexibility, easeofuse, efficiency, and robustness, and present our approach to reach these goals. Generic programming using templates in C++ plays a central role in the architecture of CGAL. We give a short introduction to generic programming in C++, compare it to the objectoriented programming paradigm, and present examples where both paradigms are used effectively in CGAL. Moreover, we give an overview of the current structure of the CGALlibrary and consider software engineering aspects in the CGALproject.
Efficient Exact Geometric Computation Made Easy
, 1999
"... We show that the combination of the Cgal framework for geometric computation and the number type leda_real yields easytowrite, correct and efficient geometric programs. ..."
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Cited by 23 (5 self)
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We show that the combination of the Cgal framework for geometric computation and the number type leda_real yields easytowrite, correct and efficient geometric programs.
Triangulations in CGAL
 COMPUTATIONAL GEOMETRY: THEORY & APPLICATIONS, 22:519, 2002. SPECIAL ISSUE SOCG00
, 2002
"... This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library Cgal. ..."
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Cited by 3 (0 self)
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This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library Cgal.
La bibliothèque d'algorithmes géométriques CGAL
, 1998
"... Cgal est une biblioth#que d'algorithmes g#om#triques, d#velopp#e dans le cadre d'un projet Esprit LTR. Le but de cette biblioth#que est de rendre les algorithmes g#om#triques d#veloppes par la communaut# de g#om#trie algorithmique disponibles pour une utilisation dans l'industrie, ..."
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Cgal est une biblioth#que d'algorithmes g#om#triques, d#velopp#e dans le cadre d'un projet Esprit LTR. Le but de cette biblioth#que est de rendre les algorithmes g#om#triques d#veloppes par la communaut# de g#om#trie algorithmique disponibles pour une utilisation dans l'industrie, ainsi que par les chercheurs et les praticiens du domaines et des domaines connexes. Les buts en sont AEexibilit#, eOEcacit#, correction, et robustesse. Le design de la biblioth#que est pr#sent# de fa#on synth#tique, tout en montrant les techniques qui permettent de concilier au mieux ces exigences apparemment contradictoires. Ces techniques sont pour une large part inspir#es de la programmation g#n#rique et de la Standard Template Library (STL) de C++.
Efficient Exact Geometric Computation Made Easy
"... Abstract We show that the combination of the Cgal framework for geometric computation and the number type leda real yields easytowrite, correct and efficient geometric programs. 1 Introduction The implementation of geometric algorithms is notoriously difficult. Geometric algorithms are usually des ..."
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Abstract We show that the combination of the Cgal framework for geometric computation and the number type leda real yields easytowrite, correct and efficient geometric programs. 1 Introduction The implementation of geometric algorithms is notoriously difficult. Geometric algorithms are usually designed for the socalled &quot;Real RAMmodel &quot; which assumes exact real arithmetic (in the sense of mathematics). When real arithmetic is simply replaced by imprecise floatingpoint arithmetic, geometric algorithms that are provably correct with real arithmetic may crash or compute garbage. There are two ways to resolve this dilemma: one may either design new algorithms that work correctly even with imprecise arithmetic or implement the real RAM.
971 Copyright Virtual Concept FEAdriven Geometric Modelling for Meshless Methods
"... orthogonal Fixed Grids (FG) for 2manifold construction in quasimeshless methods for Finite Element Analysis are presented. A Piecewise Linear (PL) or Boundary Representation (BRep) B is assumed to be the boundary of a solid S ⊂ R3. On the other hand, R3 is partitioned into a 3dimensional array o ..."
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orthogonal Fixed Grids (FG) for 2manifold construction in quasimeshless methods for Finite Element Analysis are presented. A Piecewise Linear (PL) or Boundary Representation (BRep) B is assumed to be the boundary of a solid S ⊂ R3. On the other hand, R3 is partitioned into a 3dimensional array of cubic, uniform cells Ci,j,k. Cells Ci,j,k with Ci,j,k ∩ S ≠Φ and Ci,j,k ∩ S ≠ Ci,j,k are particularly important for FG applications. These are the cells Ci,j,k intersecting B, which happen to be Neither Inside nor Outside (NIO) of B. The boundary ∂(Ci,j,k ∩ S) of Ci,j,k ∩ S must be calculated from ∂Ci,j,k and B for a large number of cells Ci,j,k, which makes the normal boolean operations unpractical. The article illustrates with examples the immersion of BRep models in Fixed Grids, visits the downstream results of the stressstrain calculations using FG and explains how this approach is used in Product Design Optimization. Key words: meshless methods; geometric modelling; orthogonal boolean operations; Fixed Grid, finite element analysis. Glossary B A PL 2manifold without border (a 2D object). S S is the union of B and its interior, hence B = ∂S (S is a 3D object). F Face of B, F is PL. Ci,j,k Cubic, ith, jth, kth cell in the X, Y, and Z directions respectively, with faces parallel to the XY, XZ and YZ planes (Ci,j,k is a 3D object). FG The collection of the Ci,j,k, with i, j, k ∈ [1...N] NIOi,j,k The portion of S confined to Ci,j,k, i.e., NIOi,j,k =