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Conference Paper

Mean Value Bézier Maps

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

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

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

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https://rdcu.be/dITRn
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Citation

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


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-1C30-1
Abstract
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.