TY - GEN
T1 - On Integral-Based (Transfinite) Laplace Coordinates
AU - Belyaev, Alexander G.
AU - Fayolle, Pierre-Alain
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/5/7
Y1 - 2021/5/7
N2 - In this theoretical work, we analyze general constructions for integral-based (transfinite, continuous) barycentric coordinates and consider a simple variational principle to arrive at a continuous version of the Laplace barycentric coordinates. We demonstrate how our approach leads to a general description of the integral-based barycentric coordinates and establish links with Dirichlet energy minimization problems for conical surfaces. Both the 2D and 3D cases are studied. An application to a surface generation problem is briefly considered.
AB - In this theoretical work, we analyze general constructions for integral-based (transfinite, continuous) barycentric coordinates and consider a simple variational principle to arrive at a continuous version of the Laplace barycentric coordinates. We demonstrate how our approach leads to a general description of the integral-based barycentric coordinates and establish links with Dirichlet energy minimization problems for conical surfaces. Both the 2D and 3D cases are studied. An application to a surface generation problem is briefly considered.
UR - http://www.scopus.com/inward/record.url?scp=85116329278&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-76798-3_22
DO - 10.1007/978-3-030-76798-3_22
M3 - Conference contribution
AN - SCOPUS:85116329278
SN - 9783030767976
T3 - Lecture Notes in Computational Science and Engineering
SP - 341
EP - 357
BT - Numerical Geometry, Grid Generation and Scientific Computing
A2 - Garanzha, Vladimir A.
A2 - Kamenski, Lennard
A2 - Si, Hang
PB - Springer
T2 - 10th International Conference on Numerical Geometry, Grid Generation, and Scientific Computing celebrating the 130th anniversary of B. N. Delaunay
Y2 - 25 November 2020 through 27 November 2020
ER -