By Bernard Mourrain, Scott Schaefer, Guoliang Xu
This publication constitutes the refereed court cases of the sixth foreign convention on Geometric Modeling and Processing, GMP 2010, held in Castro Urdiales, Spain, in June 2010. The 20 revised complete papers provided have been conscientiously reviewed and chosen from a complete of 30 submissions. The papers disguise a large spectrum within the quarter of geometric modeling and processing and tackle subject matters comparable to options of transcendental equations; quantity parameterization; soft curves and surfaces; isogeometric research; implicit surfaces; and computational geometry.
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Extra info for Advances in Geometric Modeling and Processing: 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings
70, 1089–1111 (2001) 13. : Pythagorean Triples in Unique Factorization Domains. Amer. Math. Monthly 79, 503–505 (1972) 14. : Geometric Hermite interpolation with Tschirnhausen cubics. Journal of Computational and Applied Mathematics 81, 299–309 (1997) 15. : Construction and shape analysis of PH quintic Hermite interpolants. Comp. Aided Geom. Design 18, 93–115 (2001) 16. : A Class of Surfaces Closed under Five Important Geometric Operations, Technical report no. : Constructing acceleration continuous tool paths using pythagorean hodo17.
Given a grid cell whose corners have associated nonnegative scalars si and material labels mi , the following method can be used to determine the material label of a point x inside the cell. Here, index i ranges from 0 to 7, representing the eight corners of a cell. • For each distinct material label k present in the cell, construct a set of scalars tk associated with the corners of the cell via the following rule: tki = si if k = mi tki otherwise =0 • Compute the values of the tri-linear interpolant tk (x) for each distinct label k.
Mourrain, S. Schaefer, and G. ): GMP 2010, LNCS 6130, pp. 29–42, 2010. c Springer-Verlag Berlin Heidelberg 2010 30 ˇ ˇ ır E. Cernohorsk´ a and Z. S´ support function and then fully describe all possible data which can be interpolated and give the number of solutions. We thus solve the interpolation problem in a top-down way and extend results of . The remainder of this paper is organized as follows. In Section 2 we recall some basic facts about PH curves and support function. In Section 3 we determine the support function and suitable parameterization of the Tschirnhausen cubic.
Advances in Geometric Modeling and Processing: 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings by Bernard Mourrain, Scott Schaefer, Guoliang Xu