A Möbius-invariant power diagram and its applications to soap bubbles and planar Lombardi drawing

DOI10.1007/s00454-014-9627-0zbMath1302.52021OpenAlexW1990695568MaRDI QIDQ471143

David Eppstein

Publication date: 14 November 2014

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00454-014-9627-0

zbMATH Keywords

power diagramcircle packinghyperbolic geometrygraph drawingsoap bubblesLombardi drawing

Mathematics Subject Classification ID

Circle packings and discrete conformal geometry (52C26)

Related Items

Arrangements of orthogonal circles with many intersections, Limitations on realistic hyperbolic graph drawing, Bipartite and Series-Parallel Graphs Without Planar Lombardi Drawings, Angles of arc-polygons and lombardi drawings of cacti, Realization and connectivity of the graphs of origami flat foldings, Arrangements of orthogonal circles with many intersections, Minimal surfaces from infinitesimal deformations of circle packings

Uses Software

• CirclePack

Cites Work

• Small grid embeddings of 3-polytopes
• A polynomial time circle packing algorithm
• The structure of singularities in soap-bubble-like and soap-film-like minimal surfaces
• Double bubbles minimize
• The honeycomb conjecture
• Proof of the double bubble conjecture
• On some structural properties of fullerene graphs
• Incremental convex planarity testing
• A circle packing algorithm
• Steinitz Theorems for Orthogonal Polyhedra
• Drawing Trees with Perfect Angular Resolution and Polynomial Area
• Planar and Poly-arc Lombardi Drawings
• Force-Directed Lombardi-Style Graph Drawing
• Proof of the planar triple bubble conjecture
• Representations of Planar Graphs
• Power Diagrams: Properties, Algorithms and Applications
• Dividing a Graph into Triconnected Components
• Are large perimeter- minimizing two-dimensional clusters of equal-area bubbles hexagonal or circular?
• Universal Point Sets for Drawing Planar Graphs with Circular Arcs
• On Diagrams Representing Maps
• On Hamiltonian Circuits
• Lombardi Drawings of Graphs
• Drawing 3-Polytopes with Good Vertex Resolution
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