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On the design of CGAL a computational geometry algorithms library
 Softw. – Pract. Exp
, 1998
"... 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 90 (15 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. Copyright c ○ 1999 John Wiley & Sons, Ltd. KEY WORDS: computational geometry; software library; C++; generic programming;
Multivariate analysis of spatial patterns: a unified approach to local and global structures
 ENVIRONMENTAL AND ECOLOGICAL STATISTICS
, 1995
"... We propose a new approach to the multivariate analysis of data sets with known sampling site spatial positions. A betweensites neighbouring relationship must be derived from site positions and this relationship is introduced into the multivariate analyses through neighbouring weights (number of n ..."
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Cited by 5 (1 self)
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We propose a new approach to the multivariate analysis of data sets with known sampling site spatial positions. A betweensites neighbouring relationship must be derived from site positions and this relationship is introduced into the multivariate analyses through neighbouring weights (number of neighbours at each site) and through the matrix of the neighbouring graph. Eigenvector analysis methods (e.g., principal component analysis, correspondence analysis) can then be used to detect total, local and global structures. The introduction of the Dcentring (centring with respect to the neighbouring weights) allows us to write a total variance decomposition into local and global components, and to propose a unified view of several methods. After a brief review of the matrix approach to this problem, we present the results obtained on both simulated and real data sets, showing how spatial structure can be detected and analysed. Freely available computer programs to perform computations and graphical displays are proposed.
Animation of Geometric Algorithms: A Video Review
 DEC Systems Research Center, Research Report
, 1993
"... Geometric algorithms and data structures are often easiest to understand visually, in terms of the geometric objects they manipulate. Indeed, most papers in computational geometry rely on diagrams to communicate the intuition behind the results. Algorithm animation uses dynamic visual images to expl ..."
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Cited by 4 (0 self)
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Geometric algorithms and data structures are often easiest to understand visually, in terms of the geometric objects they manipulate. Indeed, most papers in computational geometry rely on diagrams to communicate the intuition behind the results. Algorithm animation uses dynamic visual images to explain algorithms. Thus it is natural to present geometric algorithms, which are inherently dynamic, via algorithm animation. The accompanying videotape presents a video review of geometric animations; the review was premiered at the 1992 ACM Symposium on Computational Geometry. The video review includes singlealgorithm animations and sample graphic displays from "workbench" systems for implementing multiple geometric algorithms. This report contains short descriptions of each video segment. vi Preface This booklet and the accompanying videotape contain animations of a variety of computational geometry algorithms. Computational geometry has existed as a field for almost two decades, and int...
The Design of MMM: A Model ManageMent System for Time Series Analysis
 Proceedings of DAGS'95
, 1995
"... Time series analysis and prediction is turning into an interdisciplinary subject where data and methods are being contributed from a broad variety of disciplines, including economics, physics, computer science, and statistics. Model management systems were originally designed for operations research ..."
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Cited by 2 (1 self)
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Time series analysis and prediction is turning into an interdisciplinary subject where data and methods are being contributed from a broad variety of disciplines, including economics, physics, computer science, and statistics. Model management systems were originally designed for operations research applications. With thousands of methods and gigabytes of data now available on the Internet, however, such systems may become a crucial component for the efficient organization and exchange of any computerbased work in these areas. This paper introduces the model management system MMM that combines model management with the World Wide Web (WWW) to provide an infrastructure for interdisciplinary, worldwide distributed research on time series analysis. In particular, MMM will provide a platform to make related research results applicable and verifiable. 1 Introduction With the increasing availability of highcapacity wide area computer networks, the sharing of data among distributed teams i...
Visualization of Geometric Algorithms in an Electronic Classroom
, 1997
"... This paper investigates the visualization and animation of geometric computing in a distributed electronic classroom. We show how focusing in a welldefined domain makes it possible to develop a compact system that is accessible to even naive users. We present a conceptual model and a system, GASPI ..."
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Cited by 1 (1 self)
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This paper investigates the visualization and animation of geometric computing in a distributed electronic classroom. We show how focusing in a welldefined domain makes it possible to develop a compact system that is accessible to even naive users. We present a conceptual model and a system, GASPII, that realizes this model in the geometric domain. The system allows the presentation and interactive exploration of 3dimensional geometric algorithms over the network. Key words: Algorithm animation, Visualization in Education, Geometric algorithms. 1 Introduction A large part of computer science education deals with algorithms and datastructures. Though algorithms are dynamic in nature, most instructors choose static ways to describe them. It has been shown that visualization can be a powerful tool in the teaching of algorithms [7]. An algorithm animation can expose properties of an algorithm that are otherwise hard to grasp, and help get some intuition into the way the algorithm oper...
DCEL: A Polyhedral Database And Programming Environment
, 1996
"... In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate ..."
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In this paper we describe the DCEL system: a geometric software package which implements a polyhedral programming environment. This package enables fast prototyping of geometric algorithms for polyhedra or for polyhedral surfaces. We provide an overview of the system's functionality and demonstrate its use in several applications. Keywords: geometric software, databases, programming environments, polyhedra. 1. Introduction Computational geometry has offered a large amount of algorithms during the last two decades. Software implementation of these algorithms makes them valuable not only for theoreticians but also for practitioners in academia and industry. This is in many cases the appropriate tool for choosing the best algorithm for a specific problem in a given context: hardware platform, operating system, programming language, typical inputs of the application, robustness considerations, etc. The importance of applied computational geometry is now being recognized. 10 Dedicated ...
Geometry Freedom in Geometric Computation  Towards HigherOrder Genericity through Purely Combinatorial Geometric Algorithms
"... Any geometric algorithm can be dissected into combinatorial parts and geometric parts. The two parts intertwine in both the description and the implementation of the algorithm. We consider the benefits of relaxing this tight coupling. Coordinate freedom is widely considered the most important princi ..."
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Any geometric algorithm can be dissected into combinatorial parts and geometric parts. The two parts intertwine in both the description and the implementation of the algorithm. We consider the benefits of relaxing this tight coupling. Coordinate freedom is widely considered the most important principle in designing and implementing geometric systems. By ensuring that client code not manipulate individual coordinates and by developing two foundations for homogeneous and Cartesian coordinates, switching from one to the other can be easily performed after the system has been completed. We take another step and show that geometry freedom is possible. By removing the geometric classes from the implementation of a geometric algorithm, the algorithm becomes purely combinatorial. An arbitrary Euclidean or spherical geometry is then used as a parameter to the combinatorial algorithm to produce a geometric system in that geometry. Geometric freedom is helpful, for instance, when a geographic input is no longer constrained to a small area of Earth and one wishes to use spherical instead of Euclidean geometry. We apply geometry freedom to three classical problems. For the first two problems—convex hulls and Delaunay triangulations—the algorithms become generic with respect to the geometry. For the third—binary space partitioning—the algorithm becomes generic with respect to both the geometry and the dimension.