TAILIEUCHUNG - Effective Computational Geometry for Curves & Surfaces - Boissonnat & Teillaud Part 3

Tham khảo tài liệu 'effective computational geometry for curves & surfaces - boissonnat & teillaud part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 40 E. Fogel D. Halperin L. Kettner M. Teillaud R. Wein N. Wolpert the term arcpoint for either an endpoint of an arc or an intersection point. An arcpoint is represented by a root of a system of two bivariate polynomial equations. Finding this root reduces to the algebraic operation solve that computes the common roots of two given bivariate polynomials. The basic operations necessary to implement geometric predicates and constructions are kept at a high level not imposing any specific algebraic tool. The main operations can then be rephrased as compare that compares two algebraic numbers x_critical_points that computes the critical points of a bivariate polynomial sigmat that computes the sign of a bivariate polynomial evaluated at the root of a system of bivariate equations. Comparisons can be carried out exactly and efficiently using algebraic methods adapted to algebraic numbers of low degree 116 144 . This is explained in Chap. 3. It is crucial to note however that the concepts are general enough to allow also completely different methods such as interval analysis that will be used together with exact algebraic methods for filtering purposes. How To Speed Up Your Arrangement Computation in Cgal When the curves to be inserted into an arrangement are x-monotone and pairwise disjoint in their interior to start with then it is more efficient in running time and less demanding in traits-class functionality to use the non-intersection insertion-functions instead of the general ones. The main trade-off among point-location strategies is between time and storage. Using the naive or walk strategies for example takes more query time but saves storage space and requires less time for maintaining the auxiliary structures. If point-location queries are not performed frequently but other modifying functions such as removing splitting or merging edges are then using a point-location strategy that does not require the maintenance of auxiliary structures such as the .

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