Advances in Geometric Modeling and Processing: 6th by Bernard Mourrain, Scott Schaefer, Guoliang Xu

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 awarded have been rigorously reviewed and chosen from a complete of 30 submissions. The papers hide a large spectrum within the quarter of geometric modeling and processing and handle issues corresponding to suggestions of transcendental equations; quantity parameterization; tender curves and surfaces; isogeometric research; implicit surfaces; and computational geometry.

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In this case, the two parameterizations T (t) and T (θ) are related by simple equation θ t = tan . 2 (9) Theorem 1 also leads to the natural decomposition of the support function of the Tschirnhausen cubic into a sum of an even and an odd rational function n31 − 3n1 + 2 2 n31 − 3n1 = + . 3n22 3n22 3n22 (10) Consequently, the Tschirnhausen cubic is a convolution (see Figure 2) of a centrally symmetrical curve (of degree 6) with even rational support and a cubic curve with linear normals, see [8] for general theory.

This contour is an iso-surface of the form: tk (x) = tj (x) ≥ tm (x), ∀m = k, j (1) Figure 5(a) illustrates the classification method and the resulting contours in a 2D cell. In this example, only two materials are present at the cell corners, which we label as + (red) and − (green). Figure 5(b) and 5(c) shows the two bi-linear functions t+ (x) and t− (x), respectively. Figure 5(d) shows a plot of the maximum of these two functions, where the white curve indicates the contour. Figure 6(a) shows another 2D example in which the four corner of the cell have three distinct materials, red, green and blue.

The Mathematics of Surfaces IX, pp. 348–371. Springer, Heidelberg (2000) 9. : Real rational curves are not unit speed. Computer Aided Geometric Design 8, 151–158 (1991) 10. : Curves with chord length parameterization. Computer Aided Geometric Design 26, 342–350 (2009) 11. : A circle-preserving variant of the four-point subdivision scheme. , Schumaker, L. ) Mathematical Methods for Curves and Surfaces, pp. 275–286. Nashboro Press (2005) 12. : Complex rational B´ezier curves. Computer Aided Geometric Design 26, 865–876 (2009) 13.

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