Wednesday, December 25, 2024

[aeuwpoaz] graphs from points

minimum spanning tree, Delaunay triangulation, traveling salesman path, traveling salesman circuit, Euclidean Steiner tree.

on a plane, sphere, flat torus, flat Klein bottle.

(it feels strange to call it the Euclidean Steiner Tree problem when on a non-Euclidean manifold such as a sphere.  however, we do need the modifier to specify the problem is about points in space and not the Steiner Tree problem on graphs.)

3D: Delaunay is no longer a triangulation but a graph, the dual of Voronoi as it always is.

in 3D space, 3D flat torus, 3-sphere.

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