By Juncong Lin, Xiaogang Jin, Zhengwen Fan, Charlie C. L. Wang (auth.), Falai Chen, Bert Jüttler (eds.)
This e-book constitutes the refereed court cases 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 offered have been rigorously reviewed and chosen from a complete of 113 submissions. The papers conceal a large spectrum within the zone of geometric modeling and processing and deal with subject matters reminiscent of curves and surfaces, electronic geometry processing, geometric function modeling and popularity, geometric constraint fixing, geometric optimization, multiresolution modeling, and functions in laptop imaginative and prescient, snapshot processing, clinical 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
However, these surfaces don’t lie in the same continuity class as G1 surfaces and can therefore not be compared with. It would be interesting to have convergent G1 surfaces or even practical G2 schemes, but this seems still to be an actual research problem . In this paper a new surface scheme for G1 interpolation of irregular quad meshes by tensor product B´ezier patches is presented. The surface construction is based on a 1-to-4 split of the parameter domain for each surface patch. This technique has already been used successfully in the case interpolating triangular G1 surfaces .
Bicubic G1 Interpolation of Irregular Quad Meshes Using a 4-Split 29 Bi + Bi+2 A1 + A2 + A3 + A4 Ai + Ai+1 , C= = . 2 2 4 i=1,. . ,4. The subscripts are taken modulo 4, see Figure 3. It remain 4 degrees of freedom. In our implementation we choose A1 , A2 , A3 , A4 as dof. Bi = 4 Results and Implementation Issues The interpolation method oﬀers several parameters as degrees of freedom, which can be used for shape design and optimization. Let us brieﬂy discuss the possibility to ﬁx them. There are two groups of parameters which act on diﬀerent parts of the surface.
347–356 (1990) 14. : Smooth interpolation of a mesh of curves. 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.
Advances in Geometric Modeling and Processing: 5th International Conference, GMP 2008, Hangzhou, China, April 23-25, 2008. Proceedings by Juncong Lin, Xiaogang Jin, Zhengwen Fan, Charlie C. L. Wang (auth.), Falai Chen, Bert Jüttler (eds.)