TY - JOUR
T1 - Signed Lp-distance fields
AU - Belyaev, Alexander
AU - Fayolle, Pierre-Alain
AU - Pasko, Alexander
PY - 2012
Y1 - 2012
N2 - We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal high practical potential of our approach.
AB - We introduce and study a family of generalized double-layer potentials which are used to build smooth and accurate approximants for the signed distance function. Given a surface, the value of an approximant at a given point is a power mean of distances from the point to the surface points parameterized by the angle they are viewed from the given point. We analyze mathematical properties of the potentials and corresponding approximants. In particular, approximation accuracy estimates are derived. Our theoretical results are supported by numerical experiments which reveal high practical potential of our approach.
UR - https://www.scopus.com/pages/publications/84868206907
U2 - 10.1016/j.cad.2012.10.035
DO - 10.1016/j.cad.2012.10.035
M3 - Article
SN - 0010-4485
VL - 45
SP - 523
EP - 528
JO - Computer-Aided Design
JF - Computer-Aided Design
IS - 2
ER -