Surface plot of function over triangular domain

Hello,

I would like to create a surface plot over a triangular domain. The result should be a curved triangle. I have a little example here:

syms x y 

z = x^2+y^2;

ezsurf(x,y,z);
hold on

% triangular domain with P(x,y)

P1 = [1,1];
P2 = [2,0.5];
P3 = [4,4];

plot([P1(1);P2(1);P3(1);P1(1)],[P1(2);P2(2);P3(2);P1(2)]);

All z values for x,y combinations inside the triangle shall be plotted. The rims should not look like steps. Do you have any suggestions?

Thanks a lot.

Ps: I am using Symbolic Math Toolbox (as you might see)

[Gaudio]

Hello everybody,

I was able to solve my Problem with DelaunayTriangulation and inpolygon.

Best, Gauido

[Noah Stam]

Can you elaborate on your solution? :P

Answer 1

[Bruno Luong]

P1 = [1,1];
P2 = [2,0.5];
P3 = [4,4];
zfun = @(x,y) x.^2+y.^2;

% Create triangular mesh of triangla P1,P2,P3
n=20;
[I,J]=meshgrid(linspace(0,1,n));
keep=I+J <= 1+eps;
IJ = [I(keep),J(keep)];
K = 1-sum(IJ,2);
F=delaunay(IJ);
IJK = [IJ,K];
XY=IJK*[P1;P2;P3];
x=XY(:,1);
y=XY(:,2);

trisurf(F,x,y,zfun(x,y))

[Noah Stam]

Thanks a lot!

[Bruno Luong]

You are welcome. Please accept the answer if it helps. Thanks