Effective Computational Geometry for Curves and Surfaces - download pdf or read online

By Jean-Daniel Boissonnat, Monique Teillaud

ISBN-10: 3540332588

ISBN-13: 9783540332589

The motive of this ebook is to settle the rules of non-linear computational geometry. It covers combinatorial info constructions and algorithms, algebraic concerns in geometric computing, approximation of curves and surfaces, and computational topology.

Each bankruptcy offers a cutting-edge, in addition to an academic creation to special thoughts 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 provided options also are included.

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

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Extra resources for Effective Computational Geometry for Curves and Surfaces

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Halperin, L. Kettner, M. Teillaud, R. Wein, N. Wolpert that handles a specific family of curves of interest and a specific representation suitable for their application, as long as it conforms to the requirements of the appropriate concept. , Cgal kernel, Leda kernel, user defined), and the number type used by the arithmetic operations carried out by the predicates and constructions of the traits class. Traits classes developed for handling curves of higher degree may also differ in the underlying algebraic methods used for answering predicates and computing intersection points.

Wolpert Compare to right: Given two arcs a ¯1 and a ¯2 (as above) and one of their inter(0) (0) (x) (x) section points u, we begin by defining f1 (x) = pq11(x) and f2 (x) = pq22(x) . We start with m = 1, and compute for k = 1, 2 the mth order derivative (m) (m−1) (m) (m) fk = fk . If f1 (ux ) = f2 (ux ), then we can determine the comparison result. Otherwise we conclude the multiplicity of u is greater than m, so we increment m and repeat the derivation process. We will need deg(p1 q2 − p2 q1 ) iterations at most, as this is the maximal multiplicity of an intersection point.

Halperin, L. Kettner, M. Teillaud, R. Wein, N. Wolpert that handles a specific family of curves of interest and a specific representation suitable for their application, as long as it conforms to the requirements of the appropriate concept. , Cgal kernel, Leda kernel, user defined), and the number type used by the arithmetic operations carried out by the predicates and constructions of the traits class. Traits classes developed for handling curves of higher degree may also differ in the underlying algebraic methods used for answering predicates and computing intersection points.

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


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