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MathGroup Archive 2004

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RE: ParametricPlot2D

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46806] RE: [mg46790] ParametricPlot2D
  • From: "David Park" <djmp at earthlink.net>
  • Date: Tue, 9 Mar 2004 04:30:49 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Easy with DrawGraphics from my web site below.

Needs["DrawGraphics`DrawingMaster`"]

First we draw the 3D surface with z==0 and convert the Polygons to 2D
polygons.

surface =
    ParametricDraw3D[{u - v^2, u v, 0}, {u, -1, 1}, {v, -1,
          1}] /. {x_?NumberQ, y_?NumberQ, _?NumberQ} -> {x, y};

Then we draw the resulting surface in 2D. Mathematica outlines Polygons in
3D but does not outline them in 2D. The DrawGraphics routine PolygonOutline
will add the edges. I used LightGray so the edges would be subdued.

Draw2D[
    {LightBlue, surface,
     surface // PolygonOutline[LightGray]},
    Frame -> True,
    PlotLabel -> "Parametric 2D Area",
    Background -> Linen,
    ImageSize -> 350];

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/


From: Narasimham G.L. [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net

Is it possible to plot like :)  ParametricPlot2D {x,y}=f(u,v), where
u,v are two parameters? At present, I am plotting by setting z=0 in a
3D plot e.g.,
ParametricPlot3D[{u-v^2,u v,0},{u,-1,1},{v,-1,1},ViewPoint->{0,0,4}] ;
But it adds colour to the domain that would have become a surface in
3D had z been non-zero. Actually I like to see clean plots, no matter
if there are self-intersections.What is the simplest plot command
recommended in such cases?



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