TY - GEN
T1 - Mean value Bézier maps
AU - Langer, Torsten
AU - Belyaev, Alexander
AU - Seidel, Hans Peter
PY - 2008
Y1 - 2008
N2 - 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 Bézier 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. © 2008 Springer-Verlag Berlin Heidelberg.
AB - 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 Bézier 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. © 2008 Springer-Verlag Berlin Heidelberg.
KW - Bézier surfaces
KW - Computer Graphics
KW - Curves and Surfaces
KW - Mathematical foundations of CAGD
KW - Mean value coordinates
KW - Shape representation
UR - http://www.scopus.com/inward/record.url?scp=70349336852&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-79246-8_18
DO - 10.1007/978-3-540-79246-8_18
M3 - Conference contribution
SN - 3540792457
SN - 9783540792451
VL - 4975 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 231
EP - 243
BT - Advances in Geometric Modeling and Processing : 5th International Conference, GMP 2008, Proceedings
T2 - 5th International Conference on Geometric Modeling and Processing
Y2 - 23 April 2008 through 25 April 2008
ER -