Effective Computational Geometry for Curves & Surfaces - Boissonnat & Teillaud Part 13 doc

... 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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... algorithm. 3-5 4 0-3 325 8-8 Springer Berlin Heidelberg New York Monique Teillaud Jean-Daniel Boissonnat INRIA Sophia-Antipolis 2004 route des Lucioles B.P. 93 06902 Sophia-Antipolis, France E-mail: Jean-Daniel .Boissonnat@ sophia.inria.fr Monique .Teillaud@ sophia.inria.fr Preface Computational ... algorithmic foundations for effective computational geometry for curves...

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... 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 and C 2 oc- curs when  (x 1 − ... divide curves to form x-monotone sub -curves) . • If an isolated vertex has the same selection mark as its surrounding face, then this vertex is redundant and is removed from...

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... 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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... Sophia-Antipolis, 2003. [136 , 137 , 138 , 139 ] 149. I. Z. Emiris and E. P. Tsigaridas. Methods to compare real roots of polyno- mials of small degree. Technical Report ECG-TR-24220 0-0 1, INRIA Sophia- Antipolis, ... computational geometry: CG im- pact task force report. Technical Report TR-52 1-9 6, Princeton Univ., Apr. 1996. [ 313] 87. B. Chazelle et al. Application challenges...

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... 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 [48] for details. Most ... 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 pairwi...

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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 ... quadratic hypersurfaces. These dia- grams can be computed through linearization, a technique to be described in full generality in Sect. 2.5. Apollonius (or Johnson-Mehl) diagram...

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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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