Modeling with Ambient B-Splines.

Intro -- 1 Introduction -- 2 Related Work -- 2.1 Surface modeling -- 2.1.1 Simplicial surfaces -- 2.1.2 Parametric surfaces -- 2.1.3 Implicit surfaces -- 2.2 Approximation of functions on manifolds -- 3 The Ambient B-Spline Method -- 3.1 Basic concept -- 3.2 Approximation power -- 4 Realization of the Ambient B-Spline Method -- 4.1 Preliminaries -- 4.1.1 B-splines -- 4.1.2 Dual functionals and quasi-interpolants -- 4.2 Implementation -- 4.3 Examples -- 4.3.1 Geoid -- 4.3.2 Stanford Bunny -- 4.3.3 Cow model -- 5 Hierarchical Approximation -- 5.1 Hierarchical grids and B-splines -- 5.2 Approximation by hierarchical overlays -- 5.3 Approximation by linearly independent hierarchical B-splines -- 5.3.1 Hierarchical quasi-interpolant -- 5.3.2 Stability -- 5.3.3 Implementation aspects of hierarchical B-splines -- 6 Revised Examples Using Adaptive Refinement -- 6.1 Geoid -- 6.2 Stanford Bunny -- 6.3 Cow model -- 7 Curvature Analysis -- 7.1 Introduction -- 7.2 The generalized curvature tensor -- 7.3 Three different setups -- 7.3.1 Parametrized surfaces -- 7.3.2 Implicit surfaces -- 7.3.3 Space deformation -- 7.4 Examples -- 7.4.1 Stanford Bunny and cow model -- 7.4.2 Rounded cube -- 8 Further Issues -- 8.1 Parameter correction -- 8.2 Bootstrapping -- 9 Conclusion and Outlook.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.