Planar conformal mappings of piecewise flat surfaces. (English) Zbl 1069.30011
Hege, Hans-Christian (ed.) et al., Visualization and mathematics III. Outgrowth of the 3rd international workshop, Berlin, Germany, May 22–25, 2002. Berlin: Springer (ISBN 3-540-01295-8/hbk). 3-34, 425-426 (2003).
B. Rodin and D. Sullivan [J. Differ. Geom. 26, 349–360 (1987; Zbl 0694.30006)] proved the convergence of a circle packing scheme to the Riemann mapping of an arbitrary simply-connected domain in \(\mathbb C\) to the unit disk. The authors consider piecewise flat quadrilaterals and ask for a method to conformally map them to rectangles. Detailed investigations of approximating circle packings are illustrated by many beautiful pictures. Applications on mappings of the human brain are also presented.
For the entire collection see [Zbl 1014.00012].
For the entire collection see [Zbl 1014.00012].
Reviewer: Helmut Köditz (Hannover)
MSC:
| 30C35 | General theory of conformal mappings |
| 52C26 | Circle packings and discrete conformal geometry |
| 30F45 | Conformal metrics (hyperbolic, Poincaré, distance functions) |
| 05B40 | Combinatorial aspects of packing and covering |
| 68U05 | Computer graphics; computational geometry (digital and algorithmic aspects) |
