Dune Surfaces: A Spatial Visualization Technique for Medial Axes in the Plane or on the Sphere

Peter Calvache
Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012)
Pages 439–442 Short Papers


ent a technique by which the decomposition of surface areas through medial axes can be visualized in a fuzzy manner, in contrast to the discrete manner that medial axes normally impose. By mapping the closest-distance value of each point on the surface to its height-coordinate, remarkably aesthetic surfaces are constructed that uniquely relate the surface points to their nearest points on the shapes. We call the resulting manifolds "Dune Surfaces" because of the resemblance to sand dunes. We apply this technique of visualization, on a large scale, to the continents of the earth and, on a small scale, to the hotly disputed Spratly Islands in the South China Sea.