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Construction of smooth maps with mean value coordinates

Langer, Torsten and Seidel, Hans-Peter

MPI-I-2007-4-002. May 2007, 22 pages. | Status: available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:
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.
References to related material:

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  AUTHOR = {Langer, Torsten and Seidel, Hans-Peter},
  TITLE = {Construction of smooth maps with mean value coordinates},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-2007-4-002},
  MONTH = {May},
  YEAR = {2007},
  ISSN = {0946-011X},