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MathGroup Archive 1996

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Re: Wireframes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4306] Re: Wireframes
  • From: Xah Lee <xah at best.com>
  • Date: Tue, 9 Jul 1996 00:47:42 -0400
  • Organization: Best Internet Communications
  • Sender: owner-wri-mathgroup at wolfram.com

Kathryn Lockwood wrote:
> 
> I would like to take a Stack of 2D outlined sections and create a 3D >wireframe.  Does anyone know if there is an already existing program or 
>algorithm that wil

An elementary approach is to raisd each of your 2D outline to a higher 
plane. This you do by replacing each point {x,y} in your 2D graphics 
primitive by {x,y,n}, where n is higher for each 2D outline.

suppose you crossSections is a bunch of ellipses with different 
eccentricity.

crossSections = First@ ParametricPlot[
	Evaluate@ Table[{i Cos at t, Sin at t}, {i,.5,1.5,.25}],
	{t, 0, 2 Pi},
	AspectRatio->Automatic,
	PlotStyle->{Hue[.75], Hue[0],Hue[.35,1,.7]}
];0;

(* now raise each ellipse to higher plane *)

crossSections = Table[
	replaceAll[ crossSections[[i]], rule[{x_?AtomQ,y_?AtomQ},{x,y,i}]],
	{i,Length@ crossSections}
];

crossSections = crossSections /. {replaceAll->ReplaceAll, rule->Rule};

(* show the result *)

Show[
	Graphics3D[ crossSections
	],
	AspectRatio->Automatic
];0;

If you also want lines that run across, it'll take some more 
programming.

You may find the package RuledSurfacePlot.m (MathSource# 0207-975) 
useful.
http://www.best.com/~xah/public_html/SpecialPlaneCurves_dir/MmaPackages_
dir/mmaPackages.html

 Xah
 xah at best.com; 74631.731 at compuserve.com
 http://www.best.com/~xah/SpecialPlaneCurves_dir/specialPlaneCurves.html
 Mountain View, CA, USA
 Quote of the day: I'm the Schizoid Man. --The Schizoid Man

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