Effective Computational Geometry for Curves & Surfaces - Boissonnat & Teillaud Part 12 doc

... accommodate non-uniform sampling the pivoting process can be re- peated with a larger value for α. Conformal α-shapes. Conformal α-shapes were introduced in [81] to circumvent the uniformity limitations ... been used for. Whenever the information has been provided by the authors, we indicate so. Greedy [94]. Information provided by D. Cohen-Steiner. Algorithm Greedy has been mar- keted by...

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... 223 Editors ABC Effective Computational Jean-Daniel Boissonnat Monique Teillaud With 120 Figures and 1 Table Geometry for Curves and Surfaces 6 E. Fogel, D. Halperin, L. Kettner, M. Teillaud, R. ... algorithmic foundations for effective computational geometry for curves and surfaces. This book covers two main approaches. In a first part, we discuss exact geometric...

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... [85, 196, 312] . For simplicity of exposition we describe the three-dimensional variant for arrangements of triangles. Let T = {t 1 ,t 2 , ,t n } be a collection of triangles in 3-space. For a curve ... single point. We transform the requirement that the predicates will evaluate to sufficiently-far-from- zero values into a geometric distance require- ment. An outer tangency between C 1 an...

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... corresponding part in the join tree 306 G.Rote,G.Vegter W u (q) consists of all regular integral curves with ω-limit equal to p and - limit equal to q. In particular, a Morse-Smale function on a two-dimensional manifold ... same α-limit and the same ω-limit. Therefore, it makes sense to refer to these points as the α-limit and ω-limit of the integral curve. It follows from Lemma 1.2 th...

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... MPI-I- 200 1-1 -0 03, Max-Planck-Institut f¨ur Informatik, Stuhlsatzenhausweg 85, 6 6123 Saarbr¨ucken, Germany, August 2001. [55] 309. M. Seel. Planar Nef Polyhedra and Generic High-dimensional Geometry. PhD thesis, ... Guha. Computational topology. In B.Chazelle,J.E.Goodman,andR.Pollack,editors,Advances in Discrete and Computational Geometry - Proc. 1996 AMS-IMS-SIAM Joint Sum...

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... components. The main com- ponent is the Arrangement 2 <Traits,Dcel> 12 class-template. It represents the planar embedding of a set of x-monotone planar curves that are pairwise dis- joint in their ... independent part that implements the predicates and constructions for the sweep-line algorithm based upon the one-curve and two -curves analysis, as described in Sect. 1.3.1; see...

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... O(n d+ε ) for any ε>0, where the constant of proportionality depends on ε, d and η. The vertices, edges and 2-faces of the diagram can be computed in randomized expected time O(n d+ε ) for any ε>0. This ... algorithmic results for arrangements of curves and surfaces can be found in Sharir and Agarwal’s book [ 312] , see also their more recent survey [15]. Earlier combinatorial...

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... sufficiently far apart, is close to a medial sphere of S (for the Hausdorff distance). We have therefore bounded the one-sided Hausdorff distance from the λ-medial axis (Voronoi diagram) of an ε-sample P ... that on each V I , for all i<j, δ i (x) <δ j (x)iffx ∈ b i ij and δ i (x)=δ j (x)iffx ∈ b ij . The induction follows. 94 J-D. Boissonnat, C. Wormser, M. Yvinec Lemma 3. For any dist...

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... roots ∆ 1 > 0 ∧T>0 ∧ ∆ 2 > 0 {1, 1, 1, 1} ∆ 1 > 0 ∧(T ≤ 0 ∨ ∆ 2 ≤ 0) {} ∆ 1 < 0 {1, 1} ∆ 1 =0∧ T>0 {2, 1, 1} ∆ 1 =0∧ T<0 {2} ∆ 1 =0∧ T =0∧∆ 2 > 0 ∧R =0{2, 2} ∆ 1 =0∧ T =0∧∆ 2 > ... β =(q, ]c, d[), assuming for simplicity that α and β are simple roots of p and q.Ifb<c(resp. d<a)wehaveα<β(resp. β<α). Let us assume now that a<c<b<d(the other case...

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