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, ease-of-use, 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 object-oriented programming paradigm, and present examples where both paradigms are used effectively in CGAL. Moreover, we give an overview of the current structure of the CGAL-library and consider software engineering aspects in the CGAL-project. Copyright c ○ 1999 John Wiley & Sons, Ltd. KEY WORDS: computational geometry; software library; C++; generic programming;

ion There are times when the amount of data produced by a program overwhelms the user. When this happens, an animation confuses more than it educates. If the algorithm is complex, and uses several different data structures and sub-algorithms, the user may get lost in the details and not see the over-all picture. In such cases, the programmer should condense complicated parts of the scene into simpler items, like boxes. This is the approach taken in several videos we have reviewed. Time can also be abstracted, if several phases of an algorithm are omitted and only the final result of several program steps is presented. An ideal system should include facilities that help the programmer implement this sort of abstraction. Ideally, all the detail should be accessible to the user if he/she needs to see it. This is called semantic zooming. Sometimes, of course, it may be desirable to present the viewer with large amounts of information. This occurs when several sorts are simultaneously c...

A set of spatial index JAVA TM applets is described that enable users on the worldwide web to experiment with a number of variants of the quadtree spatial data structure for different spatial data types, and, most importantly, enable them to see in an animated manner how a number of basic search operations are executed for them. The spatial data types are points, line segments, and rectangles. The search operations are finding nearest neighbors from an object of arbitrary type and shape, and retrieving all objects that overlap an object of arbitrary type and shape or are within a given distance of an object of arbitrary type and shape. The nearest neighbor and within queries retrieve their results in the order of their distance from the given query object. The representations and algorithms are visualized and animated in a consistent manner using the same primitives so that the differences between the effects of the representations can be easily understood. The applets can be found

This paper investigates the visualization and animation of geometric computing in a distributed electronic classroom. We show how focusing in a well-defined domain makes it possible to develop a compact system that is accessible to even naive users. We present a conceptual model and a system, GASP-II, that realizes this model in the geometric domain. The system allows the presentation and interactive exploration of 3-dimensional 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 data-structures. 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...

We present a new approach to the distributed visualization of geometric algorithms that emphasizes the position of the end user. Concepts are introduced that enable a more flexible usage of visualized geometric algorithms, while keeping the task of adapting existing algorithms to the new scheme as simple as possible. A main proposition is that interactivity should not be built into the visualized algorithms, but into the visualizing system. With this in mind, we devise a visualization model for geometric algorithms that incorporates strong algorithm execution control, flexible manipulation of geometric input/output data and adjustable view attributes. The new visualization model is implemented in the Vega system. Vega offers distributed visualization of geometric algorithms based on source code annotation and supports the standard libraries LEDA and CGAL.