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MathGroup Archive 2005

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Re: Question about Plotting with boundary constriants

  • To: mathgroup at smc.vnet.net
  • Subject: [mg58236] Re: [mg58225] Question about Plotting with boundary constriants
  • From: "David Park" <djmp at earthlink.net>
  • Date: Fri, 24 Jun 2005 02:49:55 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

HC,

There was a similar question on MathGroup just two weeks ago.

http://forums.wolfram.com/mathgroup/archive/2005/Jun/msg00496.html

One method is to multiply your function f[x,y] by a Boole function defining
the triangular region. This gives a somewhat jagged boundary to the boundary
region. To make it reasonably smooth you have to go to a large number of
PlotPoints, which also generally forces you to get rid of the 'mesh'.

The methods I presented in the link above uses two different methods to give
a smooth boundary region with a normal number of PlotPoints. One method uses
variable substitution to turn a variable domain iterator into a fixed domain
interator and then uses ParametricPlot3D to plot the function. The second
method uses a grid of polygons that fits the boundary and then raises the
grid to a 3D surface. Both of these methods use the DrawGraphics Mathematica
package at my web site below.

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




From: HUAFANG CUI [mailto:huafangc at seas.upenn.edu]
To: mathgroup at smc.vnet.net


Hi,

I have a question about plotting a 3d graph with some boundary constraints.

for example,

feasible area of function f(x, y) is 0 <= x <= 1 and 0 <= y <= 1-x.

Thanks alot.

HC



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