WIP - Tectonic Plate building

[Master TMO]

I can easily wrap your map on a globe for you, if it would help at all.

[Hai-Etlik]

Well I haven't been generating the boundaries. I used the spherical Voronoi approach to get a general arrangement of plates, then drew the boundaries in by hand.

Interesting, I did a bit of work on a Spherical Voronoi generator for this sort of thing at one point but never got it to work right.

[Master TMO]

I think I can build a spreadsheet that randomly places centroids, and then finds the points of intersection, even weighting them so that it's not necessarily equidistant. Note that that doesn't mean draw the plate boundaries from intersection to intersection though, although that's something we could work on adding once the start and end points of each boundary is.

[Master TMO]

I think I have it so that it finds the weighted centroids for each triplet of plate origins, although the weighting formula may need tweaking. I couldn't quite handle the spherical trigonometry to the point of solving the equations into a nice, neat formula, so it starts with a reasonable guess and iterates across the map seeking the centerpoint. This method does pose the possibility that it will find a localized low spot rather than the actual centerpoint, but until I become a lot more competent at spherical trig, it's the best I can do. I do have a BS in Math, but I haven't ever had to use it much since I graduated, and even if we did cover spherical trig in a college course, I've never touched it since, and it's all been forgotten.

The next bit I need to do is teach it to draw the weighted boundary line between two of these centroids, and then how to pick out the boundaries to use to make the plates.

I am making it harder on myself though- the plate definition is a pair of points rather than a single one. I'm using an oval as the concept, rather than a circle.

[Master TMO]

Still working slowly on figuring out the best process to draw these boundaries. Today I wrote the code for finding the weighted midway point between any 2 plate cores, and filtering out those that shouldn't be drawn because they are too far away or another plate is between them.

Now all I have to do is figure out how which Voronoi centroids to connect with which midpoints. I don't think that will be too difficult, once I add the filtering code to the Voronoi centroids so that I know which ones should be used and which should be thrown away. I currently can't do that because I was filling in all the Voronoi centroids, even for plates on opposite sides of the planet. The filter should make it easy. (I hope)

[Master TMO]

Here is a partially-completed version. The midway and centroid pts are scaled by the weights, but the lines themselves are not yet. But, it does show the algorithms are roughly correct. Wheeee!!!

[Master TMO]

Some tangible progress at last. I used Excel charts to build the general algorithms, but they reached their practical limit before I finished, so I've started down the ImageMagick path. It took a few days, but I finally figured out how to send commands to ImageMagick to create an image file. Unfortunately the direct connection method from VBA didn't work, so I have my macros exporting to a text file that ImageMagick can process and turn into an image.

I need to work on the algorithms a bit more, now that I can actually see some output from the work. So keep an eye on this thread for more details in the next couple of weeks.

[Master TMO]

Here is an output from the process. Only 6 continental plates this time, because one of the changes I need to make is some intelligence on the random placement of plate cores. It is quite happy to have overlapping plate cores, which causes all kinds of havoc with the map formulas. Being done in Excel VBA it does take a while to create a large map, doing it one pixel at a time, but what the hey.

As you can see, there are still some weird looking stuff in it, definitely not realistic continental plate shaped. That's okay for now. That's just that the math concept that's been solely in my head until now still needs some tweaking, and the lack of any rules on plate core placement. Hopefully some tweaking here and there can resolve those.



The brown, btw, indicates a 'lower density' plate that would have a continent on it. Mind you, I hadn't quite envisioned a plate ever being quite that shape... I think those will disappear with more plates being thrown into the mix.

[gilgamec]

I think I can build a spreadsheet that randomly places centroids, and then finds the points of intersection, even weighting them so that it's not necessarily equidistant. Note that that doesn't mean draw the plate boundaries from intersection to intersection though, although that's something we could work on adding once the start and end points of each boundary is.

Interesting, I did a bit of work on a Spherical Voronoi generator for this sort of thing at one point but never got it to work right.

I've also fiddled with tectonic plates in true spherical geometry. While I could never get the physics for plate collision to work right, I got the plate assignment working fine. I used stripack, a library for calculating Voronoi cells on a sphere; it's in FORTRAN, but if you're not quite up to that, the page links to other projects which do the same thing in Matlab and C++. If that still doesn't work, let me know, and I'll look at dredging up some of my old code into a command-line version.
Good luck!