Stupid HTML failed the first time. :(machiavelli_impNovember 15 2008, 11:20:09 UTC
Wow, Kushiel's Dart meets graph theory. And I thought Anafiel Delauney couldn't get any more interesting. Well, I suppose he could have survived. :) (The events of Dart if Delaunay hadn't died for a while would be a wonderful piece of fanfic. Hint, hint to all ficcers out there.)
I think the triangulation ties in more closely with Anafiel if it is defined in terms of graph theory rather than geometry.
Define a graph G as a collection of vertices (dots) connected by edges (lines without a direction) or arcs (lines with a direction). Forget about arcs for a minute, so a graph is just a mathematical join-the-dots. If two vertices are connected by only one edge then that edge is a bridge. It is also possible to connect a single vertex with itself: draw an edge that starts and finishes at the same vertex and doesn't intersect with any other edges. This is a loop (for obvious reasons if you draw it). Easy so far, right?
A face of the graph is a maximal portion of the plane for which any two points can be connected by a curve C such that
( ... )
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I think the triangulation ties in more closely with Anafiel if it is defined in terms of graph theory rather than geometry.
Define a graph G as a collection of vertices (dots) connected by edges (lines without a direction) or arcs (lines with a direction). Forget about arcs for a minute, so a graph is just a mathematical join-the-dots.
If two vertices are connected by only one edge then that edge is a bridge. It is also possible to connect a single vertex with itself: draw an edge that starts and finishes at the same vertex and doesn't intersect with any other edges. This is a loop (for obvious reasons if you draw it).
Easy so far, right?
A face of the graph is a maximal portion of the plane for which any two points can be connected by a curve C such that ( ... )
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