Lefschetz S.'s Transformations of Manifolds with a Boundary PDF

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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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Transformations of Manifolds with a Boundary by Lefschetz S.


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