How to plot a pentatope in Maple!

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How to plot a pentatope in Maple!

Postby [In:TkZ] » Mon Jan 29, 2007 1:44 pm

I want to plot a pentatope (4-simplex) (using Maple).

Can anyone help or explain the method to me?

Thank you very much!
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Postby bo198214 » Tue Jan 30, 2007 12:08 pm

Simply draw 5 points and connect each two by a line?
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Postby [In:TkZ] » Tue Jan 30, 2007 1:11 pm

ah, and how to plot a pentatope that can rotate in 4d?
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Postby papernuke » Wed Jan 31, 2007 5:28 am

What's maple? A game or a 3d, 2d, or 4d drawing thing?
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Postby Keiji » Wed Jan 31, 2007 8:02 am

http://en.wikipedia.org/wiki/Maple_%28software%29

It's a program like Mathematica.
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Postby PWrong » Wed Jan 31, 2007 9:32 am

I've often wondered how to graph 4D objects in mathematica. I think I could figure out the programming, if I knew the maths of it.

Do you have to use some kind of raytracing thing?
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Re: How to plot a pentatope in Maple!

Postby Hugh » Wed Jan 31, 2007 11:37 am

[In:TkZ] wrote:I want to plot a pentatope (4-simplex) (using Maple).

Can anyone help or explain the method to me?

You could probably find out by asking Maplesoft directly:

http://www.maplesoft.com/contact/index.aspx
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Postby bo198214 » Wed Jan 31, 2007 1:15 pm

I think there is no standard package that can that stuff for you.
You have to reinvent the wheel like all those 4d applet/raytracing writers out there, but this time in maple.

First think about your used projection (perspective, parallel, orthogonal, etc). From 4d to 3d and from 3d to 2d.
If you simply want to make a wirefrime model, you project the 5 points in 4d to 2d and then draw a line between each two of them.
4d Rotation algorithm can you find somewhere here on the forum (though I dont know how to write interactive maplets).

Its all a lot of effort, if you have specific questions, turn back to the forum :)

@Pwrong come on, you know the maths of it!!!
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Postby [In:TkZ] » Thu Feb 01, 2007 8:08 am

Thank you very much.
I'll try it then!
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Postby bo198214 » Thu Feb 01, 2007 12:35 pm

Then good luck!
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Postby PWrong » Thu Feb 01, 2007 3:07 pm

Well, I know the maths necessary for it, but not the actual formulas for raytracing. I don't know about the different kinds of projection either. I suppose if you just had a set of points in 3D, you'd draw a line from the origin to the point, work out the polar coordinates and map from (theta, phi) to (x,y). I guess you could make closer points bigger too. Is that the only way to do it, or can you just send all the points to a plane with a matrix?
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plotting a pentatope

Postby jmichae3 » Sat Jul 14, 2007 5:22 am

If you want Euclidian space (I derived this off of Wikipedia):
x=R*cos(angle1)
y=R*sin(angle1)*cos(angle2)
z=R*sin(angle1)*sin(angle2)*cos(angle3)
w=R*sin(angle1)*sin(angle2)*sin(angle3)

you can scale this to n dimensions.

what I would like to find out, is how to manipulate the angles so that I can plot the points of a polytope.
public class z{public z(){System.out.println("Hi");} public static void main(String[] args){z p=new z();}}
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Postby Keiji » Sat Jul 14, 2007 9:45 pm

uhum, that doesn't look like a 5-simplex to me. For one it only has 4 dimensions and secondly from all the trig it looks like a toratope ;)
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Postby bo198214 » Sat Jul 14, 2007 10:12 pm

If not a glome.
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Postby moonlord » Sat Jul 28, 2007 5:40 pm

Agreed. Glome it is.
"God does not play dice." -- Albert Einstein, early 1900's.
"Not only does God play dice, but... he sometimes throws them where we cannot see them." -- Stephen Hawking, late 1900's.
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