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From: CENGIZ on 10 Feb 2010 06:38
Hello Roger,

Your answer was helpful to me too. I have a very similar problem. I was wondering how i can make a 3d plot using a triangular domain. suppose that i need to plot z values for all (x,y) values within the triangular region (a1,b1), (a2,b2), and (a3,b3). I tried to use the parametrization technique you gave here, but could not figure out how to apply to my situation. Any thoughts would be appreciated.

Best...

"Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message <fum3cu$r2t$1(a)fred.mathworks.com>...
> "Bookie" <u43093(a)uwe> wrote in message <831044a106ed5(a)uwe>...
> > Hi,
> >
> > I was wondering how I can make a 3D plot using non-rectandular data for
> x
> > and y. My x-y domain can be described with limits: a <= x <= b AND 0
> <= y <=
> > m*x + b. Then z, forming the surface of the plot, will be a function of x
> > and y. So the shadow of the plot will not look like a rectangle but some
> > other 4-sided polygon. Thanks for you help in advance!
> >
> > Bookie
> ----------
> In the 'surf' and 'surfc' functions it isn't necessary that the x-y domain
> covered be a rectangle. It is only necessary that there be a two-parameter
> representation of the desired surface in which the parameters fill a
> rectangular space. In your example, you could use parameters, ix and iy
> where
>
> [ix,iy] = meshgrid(1:p,1:q); % Use a p by q mesh of ix & iy values
> x = a + (ix-1)*(b-a)/(p-1); % a <= x <= b
> y = (iy-1).*(m*x+b)/(q-1); % 0 <= y <= m*x+b
> z = (Whatever your function of x and y is)
> surf(x,y,z)
>
> There is an example of a sphere generated by 'surf' in the function reference
> to matlab. Study it to see how the parameterization works. In particular note
> that what you call the "shadow" is a circle in this case.
>
> Roger Stafford
>
From: Luigi Giaccari on 11 Feb 2010 11:28
"Bookie" <u43093(a)uwe> wrote in message <831044a106ed5(a)uwe>...
> Hi,
>
> I was wondering how I can make a 3D plot using non-rectandular data for x
> and y. My x-y domain can be described with limits: a <= x <= b AND 0 <= y <=
> m*x + b. Then z, forming the surface of the plot, will be a function of x
> and y. So the shadow of the plot will not look like a rectangle but some
> other 4-sided polygon. Thanks for you help in advance!
>
> Bookie
>

I hope one of these works

http://www.mathworks.com/matlabcentral/newsreader/create_message?reply_id=711429

http://www.advancedmcode.org/how-to-plot-a-coloured-surface-from-3d-scatter.html

http://www.advancedmcode.org/surface-recostruction-from-scattered-points-cloud-mycrustopen.html

http://www.advancedmcode.org/surface-recostruction-from-scattered-points-cloud-mycrust-robust.html



http://www.advancedmcode.org
From: Roger Stafford on 26 Feb 2010 23:07
"CENGIZ " <cengizucbenli(a)gmail.com> wrote in message <hku5qs$81c$1(a)fred.mathworks.com>...
> Hello Roger,
>
> Your answer was helpful to me too. I have a very similar problem. I was wondering how i can make a 3d plot using a triangular domain. suppose that i need to plot z values for all (x,y) values within the triangular region (a1,b1), (a2,b2), and (a3,b3). I tried to use the parametrization technique you gave here, but could not figure out how to apply to my situation. Any thoughts would be appreciated.
>
> Best...

Hello Cengiz. Sorry for the delay. I didn't notice your question when it appeared Feb. 10.

With a triangle whose vertices are (a1,b1), (a2,b2), and (a3,b3) in the x-y plane, you can generate points falling within the triangle parametrically using two parameters p and q defined by:

x = p*a1 + (1-p)*(q*a2 + (1-q)*a3)
y = p*b1 + (1-p)*(q*b2 + (1-q)*b3)

with p and q in the rectangular (actually square) region

0 <= p <= 1
0 <= q <= 1

(This does have the disadvantage that points will be clustered more densely near the (a1,b1) vertex.)

Roger Stafford
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