– Computational geometry – From theory to practice , From linear objects to curved objects . Monique Teillaud HABILITATION

Géométrie algorithmique - De la théorie à la pratique,Des objets linéaires aux objets courbes. (Computational geometry - From theory to practice,From linear objects to curved objects)

Towards an Open Curved Kernel

Our work goes towards answering the growing need for the robust and efficient manipulation of curved objects in numerous applications. The kernel of the cgal library provides several functionalities which are, however, mostly restricted to linear objects. We focus here on the arrangement of conic arcs in the plane. Our first contribution is the design, implementation and testing of a kernel for...

Extending the Qualitative Trajectory Calculus Based on the Concept of Accessibility of Moving Objects in the Paths

Qualitative spatial representation and reasoning are among the important capabilities in intelligent geospatial information system development. Although a large contribution to the study of moving objects has been attributed to the quantitative use and analysis of data, such calculations are ineffective when there is little inaccurate data on position and geometry or when explicitly explaining ...

Design of the CGAL 3D Spherical Kernel and application to arrangements of circles on a sphere

This paper presents a cgal kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the design of the kernel concept is developed, following the best practices for the design of kernels geared towards curved objects. Second, we show how two di erent frameworks can be combined: one for the general setting, and one dedicated to the cas...

Triangulations in CGAL

This paper presents the main algorithmic and design choices that have been made to implement triangulations in the computational geometry algorithms library Cgal.