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By Su, Hartung, Girod

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Hughes et. al [1] select those NURBS that describe the geometry, and mesh refinement steps or degree elevation enlarge the subspace while still preserving the original geometry. This is in analogy to the isoparametric approach, but on a global level. However, as long as the geometry function is exact and used as in the transformation rule (39), other choices for ψ1 , . . , ψn will also preserve the geometry. For instance, one could think of B-Splines instead of NURBS and thus avoid the rational terms.

Isogeometric analysis: Approximation, stability and error estimates for h-refined meshes. Mathematical Methods and Models in Applied Sciences 16, 1031–1090 (2006) 4. : Weak imposition of Dirichlet boundary conditions in fluid mechancis. Computer & Fluids 36, 12–26 (2007) 5. : Isogeometric fluid-structure interaction: theory, algorithms, and compuations. Computational Mechanics 43, 3–37 (2008) 6. : Studies of refinement and continuity in isogeometric structural analysis. Computer methods in applied mechanics and engineering 196, 4160–4183 (2007) 7.

5. Left: Part of the mesh around an EV of valency n = 5 for a bounded curvature variant of the Catmull-Clark scheme (degree 3). The characteristic ring in the first sector lies within the thick dark lines. Control points influencing the first derivatives in this region and required for the analysis are shown as circles. Right: The mesh around an EV of valency n = 8. The vertices for which differences are negative are encircled in grey. coordinate system are positive. However, for an EV of valency n = 8, shown on the right, not all differences are positive.

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A Channel Model for a Watermark Attack by Su, Hartung, Girod

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