TY - JOUR
T1 - Constructing conformal maps of triangulated surfaces
AU - Williams, G. Brock
PY - 2012/6/1
Y1 - 2012/6/1
N2 - We describe a means of computing the uniformizing conformal map from a triangulated surface whose triangles are realized as Euclidean triangles in R 3 onto a fundamental domain in the unit disc D, plane C, or sphere S 2. Mapping such triangulated surfaces arises in a number of applications, such as conformal brain flattening. We use the circle packing technique of Bowers, Hurdal, Stephenson, et al., to first create a quasiconformal approximation to the conformal map; then we apply a discrete form of conformal welding to reduce the distortion and converge to the conformal map in the limit.
AB - We describe a means of computing the uniformizing conformal map from a triangulated surface whose triangles are realized as Euclidean triangles in R 3 onto a fundamental domain in the unit disc D, plane C, or sphere S 2. Mapping such triangulated surfaces arises in a number of applications, such as conformal brain flattening. We use the circle packing technique of Bowers, Hurdal, Stephenson, et al., to first create a quasiconformal approximation to the conformal map; then we apply a discrete form of conformal welding to reduce the distortion and converge to the conformal map in the limit.
KW - Circle packing
KW - Conformal maps
KW - Conformal welding
UR - http://www.scopus.com/inward/record.url?scp=84856751607&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2012.01.023
DO - 10.1016/j.jmaa.2012.01.023
M3 - Article
AN - SCOPUS:84856751607
SN - 0022-247X
VL - 390
SP - 113
EP - 120
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -