Thread Subject:

3D plot over a triangle region

Hello,

I have the following 3D funktion that I want to plot over a triangular region instead of a rectangular region. How can I solve this problem, and is it possible to z(max)=1

[x,y] = meshgrid(0:0.1:1);
z = x*(2*x.^2+2*y^2+2*(1-x-y).^2+3*y.*(1-x-y)-1);
figure
surf(x,y,z)

Best regards Anna

"Anna Larsen" <asla07@student.aau.dk> wrote in message
news:jfca3a$r4q$1@newscl01ah.mathworks.com...
> Hello,
> I have the following 3D funktion that I want to plot over a triangular
> region instead of a rectangular region. How can I solve this problem, and
> is it possible to z(max)=1

Set the values of z corresponding to (x, y) coordinates outside your
triangle to NaN.

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

You could:

1. mesh the triangle in finer resolution (You might take a look at 2D mesh generation in FEX)
2. Compute the function at the knots
3. Call trimesh or trisurf to plot

Bruno

"Anna Larsen" wrote in message <jfca3a$r4q$1@newscl01ah.mathworks.com>...
> I have the following 3D funktion that I want to plot over a triangular region instead of a rectangular region. How can I solve this problem, and is it possible to z(max)=1
>
> [x,y] = meshgrid(0:0.1:1);
> z = x*(2*x.^2+2*y^2+2*(1-x-y).^2+3*y.*(1-x-y)-1);
> figure
> surf(x,y,z)
- - - - - - - - -
  You could make a mesh of parameters s and t defined as follows. Let P1 = (x1,y1), P2 = (x2,y2), and P3 = (x3,y3) be the three vertices of your triangle. Then do:

 [s,t] = meshgrid(linspace(0,1,100));
 x = (1-sqrt(s))*x1 + sqrt(s).*((1-t)*x2+t*x3);
 y = (1-sqrt(s))*y1 + sqrt(s).*((1-t)*y2+t*y3);
 z = x.*(2*x.^2+2*y.^2+2*(1-x-y).^2+3*y.*(1-x-y)-1);
 z(z>1) = 1;
 surf(x,y,z)

(Note: The square root avoids having greater density near P1.)

Roger Stafford

"Anna Larsen" wrote in message <jfca3a$r4q$1@newscl01ah.mathworks.com>...
> Hello,
>
> I have the following 3D funktion that I want to plot over a triangular region instead of a rectangular region.

You can set the z data outside the triangular region to NaNs. Then they won't show up in the plot.

"Anna Larsen" wrote in message <jfca3a$r4q$1@newscl01ah.mathworks.com>...
>
>and is it possible to z(max)=1

Yes, there are many ways to reset the maximum value of the z array to 1.One option would be

z=z-max(z(:))+1

Since this approach and many others may or may not make sense for you, you should say what the purpose of doing this is.