By Juncong Lin, Xiaogang Jin, Zhengwen Fan, Charlie C. L. Wang (auth.), Falai Chen, Bert Jüttler (eds.)
This publication constitutes the refereed court cases of the fifth foreign 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 awarded have been conscientiously reviewed and chosen from a complete of 113 submissions. The papers hide a large spectrum within the quarter of geometric modeling and processing and deal with issues corresponding to curves and surfaces, electronic geometry processing, geometric function modeling and popularity, geometric constraint fixing, geometric optimization, multiresolution modeling, and purposes in laptop imaginative and prescient, picture processing, clinical visualization, robotics and opposite engineering.
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Additional resources for Advances in Geometric Modeling and Processing: 5th International Conference, GMP 2008, Hangzhou, China, April 23-25, 2008. Proceedings
2 b11 = F(v2 , w2 ) , b15 = F(v3 , w3 ) . Bounding the Distance Similar to the analysis in Section 3, we can rewrite Skm (v, w) and Fkm (v, w) into the quartic B´ezier forms as Equations (3) and (4), respectively. Thus for k , we have (v, w) ∈ Ωm 15 S(v, w) − F(v, w) = Skm (˜ v , w) ˜ − Fkm (˜ v , w) ˜ ≤ bi − bi Bi (˜ v , w). ˜ (9) i=1 Notice that Fkm is not the limit triangle of the triangular patch Skm but one portion of the extraordinary patch S’s limit triangle F. So we can not use the results for bi − bi derived in Section 3 directly.
P. Bonneau, and B. Caramiaux 9. : Eﬃcient, fair interpolation using catmullclark surfaces. In: SIGGRAPH 1993: Proceedings of the 20th annual conference on Computer graphics and interactive techniques, pp. 35–44 (1993) 10. : G1 interpolation of mesh curves. Computer-Aided Design 26(4), 259–267 (1994) 11. : Approximate continuity for parametric b´ezier patches. In: SPM 2007: Proceedings of the 2007 ACM symposium on Solid and physical modeling, Beijing, China, pp. 315–321 (2007) 12. : A G1 triangular spline surface of arbitrary topological type.
0 1 2 .. .. 1 2 0 .. . 1 2 1 2 −Φ0 ⎤⎡ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎦⎢ ⎣ ⎤ ∂S 1 ∂u1 (0, 0) .. ⎥ ⎥ ⎥ ⎥=O ⎥ ⎥ ⎦ ∂S n ∂un (0, 0) n 0 where the determinant is equal to Πi=0 cos( 2πk n ) − Φ , see . e. if Φ0 = cos( 2πk n ) ∂S i for some integer k. We set k = 1 in order to ensure that the vectors ∂ui (0, 0) span a plane and are ordered properly. Thus we have Φ0 = Φi (0) = cos 2π n . Then we have to look at the G1 conditions at the opposite mesh vertex where ui = 1. Here condition (2) implies cos 2π ni ∂S i 1 ∂S i 1 ∂S i−1 (0, 0) = (0, 0) + (0, 0), ∂u ¯i 2 ∂u ¯i+1 2 ∂u ¯i−1 where ni is the order of the vertex associated with S i (1, 0), and u ¯i = −ui , u ¯i+1 = ui+1 , u ¯i−1 = ui−1 .