User:Dllu/sandbox

Todo
Personal todo list in no particular order.


 * Diagrams for Island of stability should get similar colour schemes. The isometric illustration should be redone to be not so huge in filesize and also fix factual accuracies. Also, make this in SVG format: dllu (t,c) 05:19, 10 March 2013 (UTC)
 * The monochrome picture File:Island of Stablity derived from Zagrebaev.png looks good. dllu (t,c) 06:14, 21 December 2014 (UTC)


 * Expand stuff on flight control for quadrotor. dllu (t,c) 05:19, 10 March 2013 (UTC)
 * I don't feel like doing this anymore. Maybe in the distant future. dllu (t,c) 06:14, 21 December 2014 (UTC)


 * Convert all trajectory traces on Swinging Atwood's machine to SVG format using my new RK4 simulator that's more accurate. dllu (t,c) 05:19, 10 March 2013 (UTC)
 * ✅ dllu (t,c) 02:49, 21 March 2013 (UTC)


 * Rewrite Particle Filter article and Monte Carlo localization. dllu (t,c) 20:44, 21 March 2013 (UTC)
 * Work is currently in progress at User:dllu/sandbox/Monte Carlo localization. dllu (t,c) 23:39, 24 March 2013 (UTC)
 * ✅ eh good enough. dllu (t,c) 09:18, 25 March 2013 (UTC)
 * Must write "gentle introduction". dllu (t,c) 11:32, 5 April 2013 (UTC)


 * Rewrite robot localization. Oh my god this is a mess! so much work to do areuhgaeorgjadfhasodfjasdfasd dllu (t,c) 10:18, 23 March 2013 (UTC)
 * Start Markov localization. Monte Carlo localization and grid-based localization (and in a sense, EKF localization) all use the Markov principle. dllu (t,c) 01:05, 27 March 2013 (UTC)
 * Vectorise File:Scallop Diagram.jpg. dllu (t,c) 22:07, 30 March 2013 (UTC)
 * File:Scallop Diagram2.svg is available. dllu (t,c) 06:14, 21 December 2014 (UTC)


 * Vectorise File:Teletherapy Capsule.jpg. dllu (t,c) 22:07, 30 March 2013 (UTC)
 * ✅ dllu (t,c) 09:58, 4 April 2013 (UTC)


 * Vectorise File:Tri-star.gif. dllu (t,c) 00:28, 9 April 2013 (UTC)
 * ✅. User:Conundrumer has graciously created a superior gif animation. It is not a vector format but an animated raster file is clearly better than a static vector file since Wikipedia does not support animated SVG. dllu (t,c) 23:05, 27 August 2013 (UTC)


 * Write an article on point set registration. dllu (t,c) 23:05, 27 August 2013 (UTC)
 * Work in progress at user:dllu/sandbox/Point Set Registration. dllu (t,c) 23:07, 27 August 2013 (UTC)
 * ✅. Now awaiting peer reviews. dllu (t,c) 01:36, 31 August 2013 (UTC)


 * Expand Minkowski sum. dllu (t,c) 23:00, 5 March 2014 (UTC)
 * Expand visibility polygon. dllu (t,c) 03:14, 9 May 2014 (UTC)
 * Expansion under way. dllu (t,c) 05:31, 10 May 2014 (UTC)
 * Need to add stuff for output-sensitive algorithms. I wonder if I should make "Lower envelope" an article by itself? dllu (t,c) 06:14, 21 December 2014 (UTC)


 * Create better didactic animation for BML traffic model. dllu (t,c) 06:14, 21 December 2014 (UTC)

Regular Polygons
This image illustrates an example of Combinations of regular polygons that can meet at a vertex.

For Euclidean tilings, the internal angles of the polygons meeting at a vertex must add to 360 degrees. There are seventeen combinations of regular polygons whose internal angles add up to 360 degrees, each being referred to as a species of vertex; in four cases there are two distinct cyclic orders of the polygons, yielding twenty-one types of vertex. Only eleven of these can occur in a uniform tiling of regular polygons. In particular, if three polygons meet at a vertex and one has an odd number of sides, the other two polygons must be the same. If they are not, they would have to alternate around the first polygon, which is impossible if its number of sides is odd. These arrangements are here enumerated:


 * 3 polygons of sides 3 7 42
 * 3 polygons of sides 3 8 24
 * 3 polygons of sides 3 9 18
 * 3 polygons of sides 3 10 15
 * 3 polygons of sides 3 12 12
 * 3 polygons of sides 4 5 20
 * 3 polygons of sides 4 6 12
 * 3 polygons of sides 4 8 8
 * 3 polygons of sides 5 5 10
 * 3 polygons of sides 6 6 6
 * 4 polygons of sides 3 3 4 12
 * 4 polygons of sides 3 4 3 12
 * 4 polygons of sides 3 3 6 6
 * 4 polygons of sides 3 6 3 6
 * 4 polygons of sides 4 4 4 4
 * 4 polygons of sides 3 4 4 6
 * 4 polygons of sides 3 4 6 4
 * 5 polygons of sides 3 3 3 3 6
 * 5 polygons of sides 3 3 3 4 4
 * 5 polygons of sides 3 3 4 3 4
 * 6 polygons of sides 3 3 3 3 3 3