       Re: Plotting functions with undefined values

• To: mathgroup at smc.vnet.net
• Subject: [mg43772] Re: Plotting functions with undefined values
• From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
• Date: Sat, 4 Oct 2003 02:04:51 -0400 (EDT)
• References: <blgk0b\$jb2\$1@smc.vnet.net> <blj62u\$1hg\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```"Bo Le" <bole79 at email.si> wrote:
> You can define your function with the If clause:
>
> f[x_,y_,m_]:=If[y==1-x,0,(m+x+1)/(x+y-1)];
>
> Plot3D[ f[x,y,1],{x,0,1},{y,0,1} ]

But unfortunately that produces a graph which is _even more deceptive_ than
naively using just

f[x_,y_,m_]:= (m+x+1)/(x+y-1); Plot3D[f[x,y,1],{x,0,1},{y,0,1}]

Let me suggest something which produces a graph which is a fair
representation. And, although certainly not as nice as David Park's
solution, mine is substantially simpler:

f[x_,y_,m_]:= If[x+y != 1,(m+x+1)/(x+y-1)]; Plot3D[f[x,y,1],{x,0,1},{y,0,1}]

Of course, there are various comments generated before the graph, but the
graph produced is, as I said, a fair representation. Another possibility
(perhaps closer to what Bo Le had in mind), would be to use

f[x_,y_,m_]:=If[y==1-x,ComplexInfinity,(m+x+1)/(x+y-1)];
Plot3D[f[x,y,1],{x,0,1},{y,0,1}]

which again gives a graph having no spurious portions of the surface.

David Cantrell

> "Ronaldo Prati" <rcprati at bol.com.br> wrote in message
> news:blgk0b\$jb2\$1 at smc.vnet.net...
> > I need to plot the function pos[m_] = (m + x -1)/(x+y-1), where
> > 0<=pos<1, x and y are between 0 and 1 but x+y-1!=0. My problem is
> > that I could not input this constrain. When plot the function using
> > Plot3D, at the region where x+y = 1 several erros of infinith
> > expression 1/0 encountred are given. I'm not interested in plotting the
> > region where x+1 occurs, but the region where the function has a true
> > value (the graphic appers, but with a straigh region where it is
> > undef). How can i solve it?

```

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