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Mean Value Bézier Maps

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44882

Langer,  Torsten
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44112

Belyaev,  Alexander
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zitation

Langer, T., Belyaev, A., & Seidel, H.-P. (2008). Mean Value Bézier Maps. In F. Chen, & B. Jüttler (Eds.), Advances in Geometric Modeling and Processing: 5th International Conference, GMP 2008 (pp. 231-243). Berlin: Springer.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-1C30-1
Zusammenfassung
Bernstein polynomials are a classical tool in Computer Aided Design to create smooth maps with a high degree of local control. They are used for the construction of B\'ezier surfaces, free-form deformations, and many other applications. However, classical Bernstein polynomials are only defined for simplices and parallelepipeds. These can in general not directly capture the shape of arbitrary objects. Instead, a tessellation of the desired domain has to be done first. We construct smooth maps on arbitrary sets of polytopes such that the restriction to each of the polytopes is a Bernstein polynomial in mean value coordinates (or any other generalized barycentric coordinates). In particular, we show how smooth transitions between different domain polytopes can be ensured.