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Is there a way to speed up this rendering? I have to make this call many times in order to make an animation of some dynamics on the graph g. Thus dynamics are carried in the list var. Each entry in var has the 25,000 values of a function that is defined on the nodes of g. The first entry gives those 25,000 values at the first time point, the second gives them at the second time point, etc. The only thing changing is the coloring of the graph but not the graph itself. The graphs I am looking at look like knotted snarls. The parameters (sphere radius, ImageSize, maxvar, etc) are fixed.

GraphPlot3D[g, VertexRenderingFunction -> ({ColorData["TemperatureMap"][
  Rescale[var[[t]], {0, maxvar}][[#2]]], 
  Sphere[#1, 2.5]} &), ImageSize -> 1000, 
  PreserveImageOptions -> True]

It looks like it will take some 15 hours to do the rendering for a simulation that took a few minutes. Is there some way to take advantage of the fact that g is fixed? Or is there some other approach entirely that would give the same output in less time? I'd like to be able to do about 1-2000 frames of this. Each frame takes over a minute.

Most of the values contained in var don't change much from time point to time point either. var takes on only integer values. Perhaps there is something I could do by computing dvar = var[[t]]-var[[t-1]] . dvar would be zero over most of the graph.

Another thing that might save a little time is that I don't need to render most of the edges as they can't be seen anyway. There are about 30 edges that I would want to render. I have no idea how to render a subset of the edges. I don't know if it would save much time but I guess I can check that by setting EdgeRenderingFunction->None ?

Here is the sample code requested by bbgodfrey.

g = Graph[{1 <-> 2, 2 <-> 3, 3 <-> 4, 4 <-> 5, 5 <-> 6, 6 <-> 7, 
7 <-> 8, 8 <-> 9, 9 <-> 10, 1 <-> 10, 4 <-> 10}]
var = {{}, {}};
var[[1]] = ConstantArray[0, 10];
var[[1, 6 ;;]] = RandomInteger[{8, 10}, 5];
dvar = ConstantArray[0, 10];
dvar[[4 ;; 5]] = 10;
var[[2]] = var[[1]] + dvar;
var[[1]]
var[[2]]
maxvar = Max[var];
GraphPlot3D[g, 
   VertexRenderingFunction -> ({ColorData["TemperatureMap"][
   Rescale[var[[1]], {0, maxvar}][[#2]]], Sphere[#1, 2.5]} &), 
   ImageSize -> 1000, PreserveImageOptions -> True] // Timing
GraphPlot3D[g, 
   VertexRenderingFunction -> ({ColorData["TemperatureMap"][
   Rescale[var[[2]], {0, maxvar}][[#2]]], Sphere[#1, 2.5]} &), 
   ImageSize -> 1000, PreserveImageOptions -> True] // Timing
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    $\begingroup$ Please provide an executable sample code with all variables defined. 5 nodes and 2 steps should be sufficient. By the way, I believe that [g] should be replaced by [g. $\endgroup$ – bbgodfrey Dec 14 '14 at 2:47
  • $\begingroup$ Sorry for all the edits. I added "dvar" to highlight the idea that not much of var changes from time step to time step. $\endgroup$ – JEP Dec 14 '14 at 3:18
  • $\begingroup$ In the GraphEmbedding docs there is an example on how to use GraphicsComplex to draw a graph. That could be faster $\endgroup$ – Dr. belisarius Dec 14 '14 at 5:38
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    $\begingroup$ Somewhat related: mathematica.stackexchange.com/q/66445/131 $\endgroup$ – Yves Klett Dec 14 '14 at 12:21
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I suggest you try the following. Set your two plots in the Question to p1 and p2. Then,

col = Map[ColorData["TemperatureMap"][#] &, Rescale[var[[2]], {0, maxvar}]];
ans = MapIndexed[(#1 /. (RGBColor[__] -> col[[Last[#2]]])) &, p1 // InputForm, {6}]; ans[[1]]

reproduces p2 without calling GraphPlot3D, which should be faster. This process can, of course, be used for each subsequent plot. Please let me know, if it actually is significantly faster. (Warning: I have not tested this in detail, and it may not give correct results in all cases. If it provides a significant time improvement, we can chase any bugs.)

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  • $\begingroup$ It is much faster. I"m doing a large scale test now. $\endgroup$ – JEP Dec 14 '14 at 12:12
  • $\begingroup$ @JEP, I noticed this morning that my solution also modifies the color of edges, as can be seen by reducing the Sphere radius to ,say, 0.5. If this is an issue for you, I can fix it without much difficulty. $\endgroup$ – bbgodfrey Dec 14 '14 at 16:41
  • $\begingroup$ I"ll let you know. I've been away all day and am just back now. So far I've been unable to write this to a file so I haven't watched the animation yet. The individual frames that I've looked at appear to be alright but it tends to crash Mathematica when its saving the output. I'll probably have to run it tomorrow on a desk top machine. My MacBook Air has a lot of problems doing this. $\endgroup$ – JEP Dec 15 '14 at 3:56
  • $\begingroup$ I just discovered I was supposed to accept answers. This answer is now accepted and I apologize for taking so long to do it. It was VERY helpful. $\endgroup$ – JEP Jan 20 '15 at 16:17
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Since you are only drawing Spheres (like @belisarius mentioned), GraphEmbedding and Graphics3D will be enough to do this (GraphicsComplex may not help that much in this situation).

For example,

g = RandomGraph[{100, 150}];
coord = GraphEmbedding[g, Automatic, 3];
colors = ColorData["TemperatureMap"] /@ RandomReal[{0, 1}, 100];;

spheres = MapThread[{#, Sphere[#2, 2.5]} &, {colors, coord}];

Graphics3D[spheres, ImageSize -> 1000, PreserveImageOptions -> True]

enter image description here

If you also draw some edges:

Using Graph3D:

subedges = {1 <-> 2, 2 <-> 3, 3 <-> 4};
edges = {None, Thread[subedges -> "Line"]};

Graph3D[g, VertexShapeFunction -> (Sphere[#, 2.5] &), 
 VertexStyle -> Thread[VertexList[g] -> colors], 
 EdgeShapeFunction -> edges, VertexCoordinates -> coord, 
 ImageSize -> 1000, PreserveImageOptions -> True]

Graphics3D:

ispheres = MapIndexed[{#, Sphere[#2[[1]], 2.5]} &, colors];
Graphics3D[
 GraphicsComplex[coord, {ispheres, Line[Tube @@@ subedges]}], 
 ImageSize -> 1000, PreserveImageOptions -> True]
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