# Effective Computational Geometry for Curves and Surfaces by Jean-Daniel Boissonnat, Monique Teillaud

By Jean-Daniel Boissonnat, Monique Teillaud

The reason of this booklet is to settle the rules of non-linear computational geometry. It covers combinatorial facts constructions and algorithms, algebraic matters in geometric computing, approximation of curves and surfaces, and computational topology.

Each bankruptcy offers a state-of-the-art, in addition to an educational advent to big techniques and effects. the focal point is on equipment that are either good based mathematically and effective in practice.

References to open resource software program and dialogue of power purposes of the awarded strategies also are included.

This booklet can function a textbook on non-linear computational geometry. it is going to even be helpful to engineers and researchers operating in computational geometry or different fields, like structural biology, three-dimensional scientific imaging, CAD/CAM, robotics, and graphics.

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**Additional resources for Effective Computational Geometry for Curves and Surfaces**

**Sample text**

As in [284, 145], our choices have been heavily inspired by the Cgal kernel design [204] which is extensible and adaptable. Indeed, one of its features is the ability to apply primitives like geometric predicates and constructions to either the geometric objects which are provided by our kernel, or to user-deﬁned objects. The curved kernel is parametrized by a LinearKernel parameter and derives from it, in order to include all needed functionality on basic geometric objects, like points, line segments, and so on.

The rest of this section introduces several of them. For the complete speciﬁcations and discussions we refer the reader to [163, 167, 333]; a comprehensive documentation of the packages with a variety of examples can be found in [2]. The Arrangement package consists of a few components. The main component is the Arrangement 2

It is also possible to issue point-location queries on such arrangements, as the set of predicates the ArrBasicTraits 2 concept comprises is suﬃcient for the various point-location strategies detailed in the previous section. The only exception is the “landmarks” strategy, which requires a traits class that models the reﬁned ArrangementLandmarkTraits 2 concept — the details of which are omitted here. The concept ArrXMonotoneTraits 2 reﬁnes the concept ArrBasicTraits 2 by several construction operations, namely, computing the intersection points of two x-monotone curves and splitting an x-monotone curve at a given point in its interior.