Sorry for my stupidity, but I cannot figure out what *you* are talking about, either, Warren. Could you please quote what it is you're responding to, or at least paraphrase it in your own words? Thanks, Dan On 2013-05-20, at 1:46 PM, Warren D Smith wrote:
Sorry for my stupidity, but I cannot figure out what you are talking about.
First, for electrical circuits, whatever you wanted to do with a planar dual is useless if the graph is nonplanar (which for a complicated circuit, it always will be).
Second, for trusses, if we have a V-vertex planar graph it has E edges where E<=3*V-6. Now seems to me, if you demand zero vector force at each vertex (2D universe) that is 2 equations per vertex, but you've got E unknown forces. So if E>2*V, such as E=3*V-6, then how are you going to solve for the forces? No comprende. Maybe you have in mind an "outerplanar" graph (all vertices on one face). Then looks like can do. Seems like the solution for general planar graph is going to be highly non-unique but by minimizing elastic energy over all solutions, you'd uniquify.