Modeling with Ambient B Splines is popular PDF and ePub book, written by Nicole Lehmann in 2013, it is a fantastic choice for those who relish reading online the Computers genre. Let's immerse ourselves in this engaging Computers book by exploring the summary and details provided below. Remember, Modeling with Ambient B Splines can be Read Online from any device for your convenience.
Modeling with Ambient B Splines Book PDF Summary
The present thesis introduces a new approach for the generation of CK-approximants of functions defined on closed submanifolds for arbitrary k ∈ N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we even obtain Ck-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and Ck, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a Ck-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R2 and verify its practicality by application-oriented examples in R3. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface.
Detail Book of Modeling with Ambient B Splines PDF
- Author : Nicole Lehmann
- Release : 20 September 2024
- Publisher : Logos Verlag Berlin GmbH
- ISBN : 9783832536022
- Genre : Computers
- Total Page : 126 pages
- Language : English
- PDF File Size : 9,8 Mb
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