surf plot question

Altair Forum User

Here are two file

 

The equations are same but the surf plot is different.

 

Can you explain the plot process between them?

 - I can understand meshgrid method.

  But I can't understand the second method.

 

 

 

[first - meshgrid]

clear;
close all;
clc;
x=[0:0.1:2*pi];
y=x;
[X,Y] = meshgrid(x,y);
z=sin(X).*cos(Y);
figure(1);
s=surf(X, Y, z);
 

 

[second - without meshgrid] - This is in the help manual at surf command

clear;
close all;
clc;
a=[0:0.1:2*pi];
b=a;
c=sin(a')*cos(b);
% z=sin(x)*cos(y); 이렇게 하면 error 난다, size 정보가 맞아아 그래프가 그려짐
% sin cos 의 결과가 행렬의 곱셈이기에 

figure(2);
s=surf(a, b, c);

 

 

 

 

 

manoj kandukuri

Hi SeokSan,

 

Meshgrid of x and y vectors would give you the rows of the output array X which are copies of the vector x; columns of the output array Y are copies of the vector y.

in your 1st example: X values are replicates of vector x and Y values are replicates of vector y' (transpose of vector y), giving you X & Y as square matrices with data points representing in 2Dplane (something like Cartesian coordinates)

So when you calculate z (in your 1st example) you're doing element-wise multiplication of sin(X) (which is x vector repeated Horizontally) and cos(Y) (which is y vector repeated vertically) 

in your 2nd example approach, while calculating c you're doing matrix multiplication of sin(a') (which is x vector repeated vertically) and cos(b) (which is y vector repeated Horizontally) 
which is not the same mathematical operation as your 1st approach. that is why you see 2 different graph's. 

 

so to achieve the same result with these 2 approaches; you need to surface plot of c' (transpose of matrix c)
surf(a,b,c')

 

or change the logic little bit

a=[0:0.1:2*pi];
b=a';
c=cos(b)*sin(a);

figure(2)
surf(a,b,c)

 

Hope this helps!

 

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