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MathGroup Archive 1998

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Re: Mathematica Plot [help]


  • To: mathgroup@smc.vnet.net
  • Subject: [mg10563] Re: Mathematica Plot [help]
  • From: bruck@pacificnet.net (Ronald Bruck)
  • Date: Tue, 20 Jan 1998 16:54:06 -0500
  • Organization: University of Southern California
  • References: <68s834$5mq@smc.vnet.net> <694bal$km0@smc.vnet.net>

In article <694bal$km0@smc.vnet.net>, Allan Hayes
<hay@haystack.demon.co.uk> wrote:

:Wei Xu wrote:
:
:> I want to draw a surface, say sin[x,y],  defined on a triangular domain,
:> say, x:[0,1], y:[0,1] and x+y <=1.
...

:Find a parameterization of the region, Rxy, that you wish to plot f[x,y]
:over.
:
:    {s,t} -> {x[s,t], y[s,t]}
:
:taking a rectangle  [smin,smax] x [tmin, tmax] onto R[x,y].
:
:Plot
:
:ParametricPlot3D[{x[s,t],y[s,t],f[x[s,t],y[s,t]},
:  {s,smin,smax},{t,tmin,tmax}]
:
:For your example take
:
: x[s_,t_] := s
: y[s_,t_] :=  s t
: f[x_,y_] := Sin[x y]

The problem with this solution--I use it myself--is that the short line
segments will be divided into the same number of subintervals as the
long line segments.  (And some of the polygons can be trivial, which
can lead to problems when sending the output to another rendering
package--MathLive is a particular problem.)

What's really needed is a package that will triangulate a region with
roughly-equal-sized triangles, then draw the surface.  I dunno how to
automate such a procedure.  Presumably the finite-element people have
software which does this?

--Ron Bruck

--Now 800% ISDN from this address
  (2B channels + STAC compression)



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