Effective Computational Geometry for Curves & Surfaces - Boissonnat & Teillaud Part 1 docx

... 223 Editors ABC Effective Computational Jean-Daniel Boissonnat Monique Teillaud With 12 0 Figures and 1 Table Geometry for Curves and Surfaces 6 E. Fogel, D. Halperin, L. Kettner, M. Teillaud, R. ... of line-segments, containing various kinds of degeneracies — see [11 1, Sect. 2 .1] and [2 51, Sect. 10 .7]. Sweeping Non-Linear Curves Already Bentley and Ottmann observed...

Ngày tải lên: 10/08/2014, 02:20

... polynomial 408332484x 4 + 519 39673y 4 − 664779204x 3 y − 2 410 1506y 3 x +56 418 5724x 2 y 2 − 250 019 406x 3 + 17 767644y 3 +2 211 20964x 2 y − 12 3026 916 y 2 x + 16 6 919 19x 2 + 476 415 2y 2 +14 4 410 04xy + 10 482900x + 2305740y 17 63465. ... z)=88x 2 +45y 2 +67z 2 − 66xy − 25xz +12 yz − 24x +2y +29z − 5 , B(x, y, z) = 13 9x 2 + 14 1y 2 +71z 2 − 15 7xy +97xz − 11 1yz − 3x −6y...

Ngày tải lên: 10/08/2014, 02:20

... and conic arcs (Fig. 1. 11) , cubic curves (Fig. 1. 12), and quartic curves as they result from projections of in- tersection and silhouette curves of quadrics in space (Sect. 1. 5.2). The conics implementation ... curve- type independent part that implements the predicates and constructions for the sweep-line algorithm based upon the one-curve and two -curves analysis, as descr...

Ngày tải lên: 10/08/2014, 02:20

... computations give ω. 2 Curved Voronoi Diagrams 87 1. the point ˜m i ∈ R d(d +1) 2 defined as ˜m u,u i = − 1 2 M u,u i , for 1 ≤ u ≤ d; ˜m u,v i = −M u,v i , for 1 ≤ u<v≤ d, 2. the point ˆp i =(M i p i , ... half-cones. This intersection is a quadratic hypersurface (in fact, a sheet of a two sheet hyperboloid) contained in a hyperplane. Indeed, we have C 1 :(x d +1 + r 1 ) 2...

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... sides b 1 12 and b 2 12 have been assigned. Consider now the labeling of the sides of b 1i , for some i>2: let x be a point in the non empty set b 2i \b 12 . First assume that x ∈ b 1 12 . Lemma ... probability (1 −β) k 1 . Let n l be the number of objects in Θ  . The expected number N  of objects that are visited at level  is bounded as follows: N  ≤ n   k =1 k (1 −β)...

Ngày tải lên: 10/08/2014, 02:20

... 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 ... H d , ,H j 1 , h d , ,h j with h j =0and H j 1 =0.Letk = deg(H j 1 ).Then: • If k<j 1, letH k = δ j−k coef k (H j 1 ) j 1 k h j 1 k j H j 1 , h j 1 =1. For l ∈ N w...

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... values: δ 0 <σ 1 <µ 1 < ···<σ l <δ 1 , where µ i := σ i +σ i +1 2 for i =0, ,l 1, and δ 0 ,δ 1 are any value such that ]δ 0 ,δ 1 [ contains Σ. We denote by α 0 < ···<α m this ... |N| 1 E 1 ± E 2 u(E 1 ) · l(E 2 )+l(E 1 ) · u(E 2 ) l(E 1 ) · l(E 2 ) E 1 · E 2 u(E 1 ) · u(E 2 ) l(E 1 ) · l(E 2 ) E 1 /E 2 u(E 1 ) · l(E 2 ) l(E 1 ) · u(E 2 )...

Ngày tải lên: 10/08/2014, 02:20

... works for surfaces with self- intersections, fold lines, or other singularities. On the other hand, it makes 1 http://www.cse.ohio-state.edu/˜tamaldey/surfremesh.html 5 Meshing of Surfaces 19 5 The ... vertical parts explicitly.) For simplicity of exposition, we will also assume that the curve or surface is bounded. The algorithm can also deal with curves and surfaces that 5 Me...

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... S. A B C D E F G A B C D E F G 0 10 0 200 0 10 0 10 0 10 0 0 10 0 200 10 0 10 0 0 200 10 0 10 0 10 0 A B C D E F G A B C D E F G 0 10 0 200 0 10 0 10 0 10 0 0 10 0 200 10 0 − 10 0 0 200 10 0 10 0 10 0 10 0 0 10 0 10 0 0 f g 0 Fig. 5.23. Critical points ... = ˆ f 1 (0). The algorithm consists in building a tetrahedral mesh T such that the output mesh ˆ S is isotopic to...

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... Giesen the curves to A 3 1 and A 3 contacts, and the points to A 4 1 and A 3 A 1 contacts. Moreover, one has the following incidences. At an A 4 1 point, six A 1 2 sheets and four A 3 1 curves meet. ... A 3 1 curves meet. Along an A 3 1 curve, three A 2 1 sheets meet. A 3 curves bound A 2 1 sheets. At last, the point where an A 2 1 sheet vanishes is an A 3 A 1...

Ngày tải lên: 10/08/2014, 02:20