By Bernard Mourrain, Scott Schaefer, Guoliang Xu

ISBN-10: 3642134106

ISBN-13: 9783642134104

This booklet constitutes the refereed complaints 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 rigorously reviewed and chosen from a complete of 30 submissions. The papers hide a large spectrum within the sector of geometric modeling and processing and handle subject matters comparable to options of transcendental equations; quantity parameterization; tender curves and surfaces; isogeometric research; implicit surfaces; and computational geometry.

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**Extra resources for Advances in Geometric Modeling and Processing: 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings**

**Sample text**

The two possible choices of the sign of the third coordinate can be obtained by specifying the sign of the rational function q. We provide a geometric meaning for this result. Proposition 1. Consider the angle α(u, v) ∈ [−π, π] which satisfies tan α(u, v) = q(u, v). 2 (16) If u2 + v2 = 1, then α is the angle between the xy-plane and the sphere which passes through the point P(u, v) and the reference circle C. If u2 + v2 = 1, then P(u, v) lies on the reference circle C and α is the angle between the xy-plane and the tangent plane of the surface P at this point.

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. : Curves with rational chord-length parametrization. cz Abstract. The Tschirnhausen cubic represents all non-degenerate Pythagorean Hododgraph cubics. We determine its support function and represent it as a convolution of a centrally symmetrical curve and a curve with linear normals.

Moreover the convolution of curves corresponds to the addition of their support functions, see [18] for more details. 3 Support Function of the Tschirnhausen Cubic In this section we will determine the support function of the Tschirnhausen cubic and describe it as a convolution of a curve with odd rational support function and a curve with even rational support function. We will also parametrize the Tschirnhausen cubic by its normals. Theorem 1. The support function of the Tschirnhausen cubic is the restriction of the function (5) to the unit circle.

### 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

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