Surface Plots on randomly distributed points

Dear All,

I am trying to plot a 2D function z=f(x,y) on randomly distributed points using surf command. The code I have written is given below

clear all
close all
clc
N = 1600
X = rand(N, 1); Y = rand(N, 1); 
Pe = 1000;
T_exact = zeros(N, 1);
a = (Pe + sqrt(4*pi^2+Pe^2))/2;
b = (Pe - sqrt(4*pi^2+Pe^2))/2;
T_exact = sin(pi * Y) .* (exp(b * X) - exp(a * (X - 1) + b))/(1-exp(b - a));
X_t = vec2mat(X, sqrt(N)); Y_t = vec2mat(Y, sqrt(N));
T_exact_t = vec2mat(T_exact, sqrt(N));
exact_Solution = surf(X_t, Y_t, T_exact_t);
xlabel('\rightarrow X'), ylabel('\rightarrow Y'), zlabel('\rightarrow T'), grid on, colorbar
set(gca,'fontsize', 15)
set(findall(gca, 'Type', 'Line'),'LineWidth',2);

The graph is not smooth. Can anyone tell me what should I do?

Answer 1

[Stephan]

Hi,

consider the following small example:

N = 10;
X = rand(N, 1);
Y = rand(N, 1);
Z = X*Y';
surf(X, Y, Z);

results in:

.

Now try:

N = 10
X = sort(rand(N, 1));
Y = sort(rand(N, 1));
Z = X*Y';
surf(X, Y, Z);

which results in:

.

Check your code and think about what can be sorted (without creating meaningless calculations!) - then you should get a better result

Best regards

Stephan

[Ali Baig]

Dear Stephen,

I have attempted in quite a number of different ways, but I am not getting the right plot.

[Stephan]

i dont have access to vec2mat function, since i do not have the Communications Toolbox - please load up a .mat-file containing these values

 X_t
 Y_t
 T_exact_t

Could you also explain why you change X (1600x1) to X_t (40x40)?

i guess you should do something like this:

N = 49 % Do not use 1600...
X = sort(rand(N, 1));
Y = sort(rand(N, 1)); 

[m,n] = meshgrid(1:numel(X),1:numel(Y));

Pe = 1000;
T_exact = zeros(N, 1);
a = (Pe + sqrt(4*pi^2+Pe^2))/2;
b = (Pe - sqrt(4*pi^2+Pe^2))/2;
T_exact = sin(pi .* Y(n)) .* (exp(b .* X(m)) - exp(a .* (X(m) - 1) + b))./(1-exp(b - a));

surf(X, Y, T_exact);

which gives: