By Bernard Mourrain, Scott Schaefer, Guoliang Xu
This publication constitutes the refereed court cases of the sixth overseas convention on Geometric Modeling and Processing, GMP 2010, held in Castro Urdiales, Spain, in June 2010. The 20 revised complete papers offered have been rigorously reviewed and chosen from a complete of 30 submissions. The papers disguise a large spectrum within the zone of geometric modeling and processing and tackle subject matters similar to suggestions of transcendental equations; quantity parameterization; gentle curves and surfaces; isogeometric research; implicit surfaces; and computational geometry.
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Additional info for Advances in Geometric Modeling and Processing: 6th International Conference, GMP 2010, Castro Urdiales, Spain, June 16-18, 2010, Proceedings
Six of these 9 equations are trivially satisﬁed, since one of the ri and Ri vanish at each vertex. The remaining three equations guarantee the similarity of the triangles. In the remainder of the paper, we identify the reference triangle (A1 , A2 , A3 ) with the vertex triangle (v1 , v2 , v3 ) and the domain R2 containing it with the plane spanned by the vertex triangle. Consequently, the domain of the surface is the plane spanned by the vertex triangle. For any point Y ∈ R3 , we denote with (Y) = ||Y − v ||2 , = 1, 2, 3, (6) the squared distances to the vertices of the patch.
A Class of Surfaces Closed under Five Important Geometric Operations, Technical report no. : Constructing acceleration continuous tool paths using pythagorean hodo17. S´ graph curves. Mech. Mach. : Curves and surfaces represented by polynomial support func18. S´ tions. Theor. Comput. Sci. : Computing Minkowski sums via Support Function Repre19. S´ sentation. , Schumaker, L. ) Curve and Surface Design: Avignon 2006, pp. 244–253. : Hermite interpolation by hypocycloids and epicycloids with 20. S´ rational offsets.
For example, Dual Contouring  creates polygons from point and normal data stored on edges in the grid, and the works of [6,15] use a generalized Marching Cubes look-up table to polygonalize a multi-labeled cell. A work on smooth boundaries among multiple materials that is similar to our own is by Stalling et al. . In their approach, a tri-linear function f k (x, y, z) is deﬁned for each material k, and the boundary surfaces are located where the values of two or more functions are identical and higher than the remaining functions.