Winamp & Shoutcast Forums > AVS Polehedra...

 3rd December 2005, 16:27 #1 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Polehedra... I'm trying to find an algorithm to model three dimensional regular to semiregular polyhedra using the Wythoff symbol . I've seen it done manually on Mathematica, but I use Maple and, well, Mathematica pales in comparison...
 4th December 2005, 07:25 #2 QuadHeliX Major Dude     Join Date: Jan 2003 Location: Washington State Posts: 1,133 cant wait to see it!
 4th December 2005, 16:24 #3 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 I'm trying to find out what Maple does to do it, but that's kind of a stretch. I't going to be tough to actually fill the the faces and all...
 9th December 2005, 06:01 #4 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 filling faces is easy with triangle ape. for the trivial (triangle fan) way to draw any polygon just use two adjacent vertices for two of the triangle vertices, and the centre point of the polygon for the third (average of all vertices). breaks on concave polys tho... since there is no way to reverse get them from points... -- Jheriko 'Everything around us can be represented and understood through numbers'
 9th December 2005, 18:43 #5 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 I must admit, I never did triangle APE before... I need a rundown, it sounds like a possibility. Certified Spam Connoisseur.
 9th December 2005, 20:37 #6 UIUC85 Senior Member     Join Date: Oct 2003 Posts: 272 It's more or less like superscope, but instead of having just one point, you assign 3. So in a ssc we have (x,y) to define but with the triangle ape we have (x1,y1) (x2,y2) (x3,y3). If you can do a ssc, this isn't much different.
 9th December 2005, 20:45 #7 StevenRoy Senior Member     Join Date: Jun 2005 Location: USA Posts: 129 It's not that different from Superscope; you mainly just set x1, y1, x2, y2, x3, and y3, instead of just the one point (x and y) with the Superscope. Also, to change the color, set "red1", "green1", and "blue1", instead of just "red", "green" and "blue". I think it's this way because there might (fat chance) be a later version which will let you use different colours for each point, and it will shade. (This would be cool, but probably too slow to be practical.) There is also a "zbuf" variable you can set to 1 to enable a simple form of Z-buffering. With this enabled, you can set the z1 variable to the distance to control the "Z-order" of the triangles. This is often quicker and easier than doing full depth-sorting for 3d scenes. Am I forgetting anything?
 9th December 2005, 21:10 #8 PAK-9 Major Dude     Join Date: Oct 2002 Location: The United Kingdom of Great Britain and Northern Ireland Posts: 1,374 /Points to the guide http://PAK-9.deviantart.com ...innit
 10th December 2005, 13:17 #9 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Ok, does it draw just a triangle or fill it in?
 10th December 2005, 16:47 #10 Grandchild Senior Member     Join Date: Oct 2005 Location: Germany Posts: 333 it fills it in, that's the thrill to it!
 10th December 2005, 21:10 #11 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Tres nice. What about 3D? Or is Z-Buffering 3D...Bear with me... Hahaha...trivial (triangle fan)...Get it? tri Hahahaha! That's so funny! Hahahaha! Last edited by JFASI; 10th December 2005 at 21:32.
 11th December 2005, 13:15 #12 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 There is a more efficient, and less trivial way. Which is to make a triangle fan from one vertex... it reduces the number of triangles by 1, but its not as easy to see how to implement, and looks ugly when subdivided/tesselated. You can use 'z' to implement a flat z-buffer. i.e. one z value gets drawn per triangle. -- Jheriko 'Everything around us can be represented and understood through numbers'
 11th December 2005, 13:43 #13 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 So it'd be tricky for polyhedra...
 11th December 2005, 13:53 #14 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 not really. its long winded to write, but you can prove that for any convex solid, back face culling is enough to correctly occlude the faces. its basically common sense, imagine holding out a polyhedron. the only faces you can see are the ones pointing within 90 degrees the opposite of your view direction, the ones you cant see are all facing away in the remaining 180 degrees. you can do this test with a dot product and checking its sign... its in lots of presets, look at 'starfighter redux' in wfc2 i would recommend 'jet wash', but the code is in huge avstrans-ed blocks. in fact any of the model presets i have ever made probably contain it. you need to introduce 'occlusion' before z buffer is really necessary. e.g. convex objects that can have two triangles overlapping in 2d projection, both facing the viewer. or multiple objects, where one passes infront of the other. -- Jheriko 'Everything around us can be represented and understood through numbers'
 11th December 2005, 17:21 #15 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Ok, that's an idea, but still, I need to figure out how to get the Wythoff symbol or even the Schalffi symbol to yeild a polyhedron. Tough stuff...
 11th December 2005, 22:19 #16 StevenRoy Senior Member     Join Date: Jun 2005 Location: USA Posts: 129 Yeah, all this is well and good, but how do we figure out where to put the freakin' points in the first place!?
 11th December 2005, 23:07 #17 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Exactly. I'm still thinking...
 11th December 2005, 23:36 #18 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 Forget those symbols and things... too elaborate. Here are a couple of simple examples using a dodecahedron... I will add a couple more tomorrow, but I am tired right now. ftp://jheriko.kicks-ass.net:69/AVS/Jheriko/examples/ The platonic solids are all pretty easy to construct, and using some more geometry you can truncate them and stellate them into lots of other stuff. Also there are some other special cases that are interesting... check out these old packs of mine, feel free to steal the vertices: http://www.deviantart.com/deviation/720677/ http://www.deviantart.com/deviation/743266/ http://www.deviantart.com/deviation/911279/ -- Jheriko 'Everything around us can be represented and understood through numbers'
 12th December 2005, 20:09 #19 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Cool thanks. There is a bit of fun math that turns symbols into polydehra, but I don't quite get it... I'm a junior in high school, you see... Certified Spam Connoisseur.
 13th December 2005, 00:00 #20 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 well.. the way the symbol works is by defining vertices on the inside of a sphere. but its not particularly useful unless you have a method of finding a convex hull... etc... its long winded. easier to work out a specific polyhedron that you want, and use it... -- Jheriko 'Everything around us can be represented and understood through numbers'
 13th December 2005, 01:18 #21 JFASI Major Dude     Join Date: Jan 2005 Location: I was hoping you could tell me Posts: 1,350 Well, I cound use the brute ofrce method, where it just screws around for a while, but that would be no good for a visualization. Besides, for simple coding, AVS syntax is just ugly. Certified Spam Connoisseur.
 13th December 2005, 23:02 #22 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 You only need to generate a polyhedron once. Brute force it and stick it in the megabuf. Why make it so hard tho? Every specific polyhedron has a simple construction method. -- Jheriko 'Everything around us can be represented and understood through numbers'
 14th December 2005, 02:49 #23 jheriko Forum King     Join Date: Aug 2002 Location: a twist in the fabric of space Posts: 2,150 not quite perfect, but i did the dm example. i can't be bothered to fix it right now... i can't work out why its broken... probably from looking at it for too long: ftp://jheriko.kicks-ass.net:69/AVS/J...%20DM%203D.avs it gets the k correctly, but the texturing is messed up, and i had to make the camera face backwards in the dm for some reason... i will work it out later... -- Jheriko 'Everything around us can be represented and understood through numbers'
 Winamp & Shoutcast Forums > AVS Polehedra...