By Juncong Lin, Xiaogang Jin, Zhengwen Fan, Charlie C. L. Wang (auth.), Falai Chen, Bert Jüttler (eds.)
This e-book constitutes the refereed complaints of the fifth overseas convention on Geometric Modeling and Processing, GMP 2008, held in Hangzhou, China, in April 2008.
The 34 revised complete papers and 17 revised brief papers provided have been rigorously reviewed and chosen from a complete of 113 submissions. The papers hide a large spectrum within the region of geometric modeling and processing and tackle issues akin to curves and surfaces, electronic geometry processing, geometric characteristic modeling and popularity, geometric constraint fixing, geometric optimization, multiresolution modeling, and purposes in laptop imaginative and prescient, photograph processing, medical visualization, robotics and opposite engineering.
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Additional info for Advances in Geometric Modeling and Processing: 5th International Conference, GMP 2008, Hangzhou, China, April 23-25, 2008. Proceedings
By symmetry, to compute the value of β(n), at most four distance bound functions corresponding to S11 , S12 , S21 , S22 are needed to be analyzed. Numerical results for β(n), 3 ≤ n ≤ 10 are given in Table 2. For regular Loop patches, the constant β(n) = 13 is optimum. But for extraordinary Loop patches, the constants can be improved through further subdividing the subpatches Skm . 5 Subdivision Depth Estimation Before estimating subdivision depth, we investigate the recurrence relation between the second order norms of the control meshes of S at diﬀerent levels.
Bi − bi . l=1 By symmetry, we only need to solve three constrained minimization problems. With the help of the symbolic computation of Mathematica, we have δ1 = δ11 = δ15 = 0 , δ2 = δ3 = δ7 = δ10 = δ12 = δ14 = 1 , 4 1 , 3 5 . δ5 = δ8 = δ9 = 12 δ4 = δ6 = δ13 = It follows that 15 B(v, w) = δi Bi (v, w) = v + w − v 2 − vw − w2 . i=1 We obtain a bound on the pointwise distance between S(v, w) and F(v, w): Theorem 1. For (v, w) ∈ Ω, we have S(v, w) − F(v, w) ≤ B(v, w)M , where B(v, w) = v + w − v 2 − vw − w2 is called the distance bound function of S(v, w) with respect to F(v, w).
Constructive Approx. 7, 221– 246 (1991) 15. : C 1 surface splines. SIAM Journal of Numerical Analysis 32(2), 645–666 (1995) 16. : C2 free-form surfaces of degree (3, 5). Computer Aided Geometric Design 19(2), 113–126 (2002) 17. : Visually smooth interpolation with triangular b´ezier patches. In: Farin, G. ) Geometric Modeling: Algorithms and new Trends, pp. 221–233. SIAM, Philadelphia (1987) 18. : Biquadratic g-spline surfaces. Computer Aided Geometric Design 12(2), 193–205 (1995) 19. : G1 interpolation of generally unrestricted cubic b´ezier curves.