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          Institute: MPI für Informatik     Collection: Computer Graphics Group     Display Documents



ID: 428144.0, MPI für Informatik / Computer Graphics Group
Mean Value Bézier Maps
Authors:Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter
Language:English
Publisher:Springer
Place of Publication:Berlin
Date of Publication (YYYY-MM-DD):2008
Title of Proceedings:Advances in Geometric Modeling and Processing : 5th International Conference, GMP 2008
Start Page:231
End Page:243
Title of Series:Lecture Notes in Computer Science
Place of Conference/Meeting:Hangzhou, China
(Start) Date of Conference/Meeting
 (YYYY-MM-DD):
2008-04-23
End Date of Conference/Meeting 
 (YYYY-MM-DD):
2008-04-25
Audience:Experts Only
Intended Educational Use:No
Abstract / Description: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.
Last Change of the Resource (YYYY-MM-DD):2009-03-25
External Publication Status:published
Document Type:Conference-Paper
Communicated by:Hans-Peter Seidel
Affiliations:MPI f�r Informatik/Computer Graphics Group
Identifiers:LOCALID:C125756E0038A185-95E5933EF8BCA8D2C12573D4005C6D92-...
URL:http://dx.doi.org/10.1007/978-3-540-79246-8_18
DOI:10.1007/978-3-540-79246-8_18
ISBN:978-3-540-79245-1/0302-9743
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