@techreport{LangerSeidel2007,
TITLE = {Construction of smooth maps with mean value coordinates},
AUTHOR = {Langer, Torsten and Seidel, Hans-Peter},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2007-4-002},
NUMBER = {MPI-I-2007-4-002},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2007},
DATE = {2007},
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.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}