Forever Reading (again) + additional crazy

Research is slow. Apparently, finding good viewpoints is meant to be as slow. Most of the techniques I have looked at concentrate on viewpoints which do not cause occlusions, which is computationally expensive. Occlusions are undesirable as it can hide information within the graph, however, I am under the impression these approaches work well for smaller graphs, but are less effective in larger graphs.

NB: there are many methods which use these good/bad viewpoints and have different approaches to calculating them

Larger graphs are very likely to have occlusions, no matter which angle the drawing is observed. Although still offering the better viewpoints (by calculating the viewpoint with less occlusions), I am starting to see why it is not used (or at least referenced) in other placement/drawing algorithms where the viewpoint is left to the user.

There are other approaches which I have yet to research but a naive first glances suggests this area is lacking interest from researchers looking for a quicker and more ideal methods for finding viewpoints based on more than one criteria (see Purchase for multi-criteria and Eades for implementing more criteria in graph drawing.

Now for some monthly Carl Crazy; when looking at graphs, the more we can see, the more we can normally understand about the graph, even in cases where edge crossings can be seen. For example, rotating a cube so it is observed at a 45degree angle, we understand a lot more about the cube than if viewed head on (you could argue a planar drawing does this with no crossings, but the graph is warped and edge lengths suffer).

Using this same crazy, if you look at an edge within a graph, you ideally want to have the view perpendicular to it (or you will be looking at it from an angle which shortens the edge) in order to see it. If we look at this on the whole, we would be looking for the average direction of all edges within the graph. If the view was perpendicular to this, the observer would be looking at a view which offered the maximum view of all edges in the graph, albeit with occlusions/crossings.

<EDIT> This is a rather silly version of Kamada and Kawai 88, albeit ignoring the normals of the image and instead choosing to use the average edge direction to rotate the graph. In practise, this isn't as adequate as one would have hoped, with large numbers of occlusions and edge crossings. May be best to stick to Eades et al.Best Viewpoints for 3D Graph Drawings).

Of course I will continue reading, but I will test the crazy regardless due to the speed increase it offers.

That's pretty much all for this post, here's a picture of some output to liven this otherwise boring post up:

finan512.graph, drawn using 3D quadtree and 2D contraction approx. with different forces for each. The testing of parameters will hopefully find output for 'quadtree' which closer resembles that by Yifan Hu (although currently it is very close to his output of MSE(2). )