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MathGroup Archive 1996

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Re: Display Functions defined by Barycentric Coordinates

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4786] Re: Display Functions defined by Barycentric Coordinates
  • From: rubin at msu.edu (Paul A. Rubin)
  • Date: Mon, 16 Sep 1996 23:51:16 -0400
  • Organization: Michigan State University
  • Sender: owner-wri-mathgroup at wolfram.com

In article <508fp4$14k at dragonfly.wolfram.com>,
   pyu at leland.Stanford.EDU (Pok-Yin Yu) wrote:
->
->Dear All:
->
->Does anyone have experience on displaying functions 
->defined on triangles via barycentric coordinates?
->
->I need to know, for example, how to constrain the
->plotting range to an non-rectangular domain.
->
->thanks,
->Thomas
->
->
You can define the function only for those arguments in the domain.  For 
instance, suppose want a function f(x,y) = (x-1)^2 + (y-1)^2, with 
triangular domain {(x,y) | 1 <= x, 1 <= y, x + y <= 10}.  I can do the 
following:

In[]:= f[x_, y_] := (x-3)^2 + (y-3)^2 /;
         x >= 1 && y >= 1 && x + y <= 10
In[]:= Plot3D[ f[x, y], {x, 0, 10}, {y, 0, 10} ];

Note that f[] is undefined outside my triangle.  Plot3D spits up a bunch of 
diagnostic messages (which you can suppress with the Off[] command if they 
bother you), then plots the surface.  The only catch is that, since the 
plot elements are rectangles with edges parallel to the x- and y-axes, the 
diagonal boundary x + y <= 10 makes for a ragged edge to the plot.  Try it 
and you'll see what I mean.

-- Paul

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
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