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Construction of smooth maps with mean value coordinates

Langer, Torsten and Seidel, Hans-Peter

May 2007, 22 pages.

Status: available - back from printing

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.

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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},