2-D Meshgrid Rotation Matrix Multiplication

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Sordin
Sordin 2017-4-2
评论： Walter Roberson 2017-4-3
I am trying to rotate the coordinates of a 182x182 mesh grid by means of multiplication with the rotation matrix:
The following code works fine:
[x0,y0] = meshgrid(x,x);
for i = 1:length(theta)
X = x0.*cosd(-i) + -y0.*sind(-i);
Y = x0.*sind(-i) + y0.*cosd(-i);
end
However, I get errors when I try to perform this using the following matrix multiplication:
Here is my code:
[x0,y0] = meshgrid(x,x);
for i = 1:length(theta)
R = [cosd(-i) -sind(-i); sind(-i) cosd(-i)];
[X,Y]'=R.*[x0;y0];
end
And this is the error:
[X,Y]=R.*[x0;y0];
The expression to the left of the equals sign is not a valid target for an assignment.
And when I remove the transpose operator, it says:
Error using .*
Too many output arguments.
What is wrong here? How can I perform this operation using matrix multiplication?
Any guidance is greatly appreciated.

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采纳的回答

Stephen23
Stephen23 2017-4-2
编辑：Stephen23 2017-4-2
Firstly you are using the wrong multiplication operator: you need to use matrix times *, not element-wise times .*.
Secondly you are trying to implicitly split the output of this multiplication into parts. But the output of that multiplication is one column vector. Therefore you need to allocate the output to one variable:
Z = R*[x0;y0]
When you write [X,Y] = ... then you are telling MATLAB that the operation has two output variables. But a multiplication does not have two outputs, it only has one.
You have other bugs in your code as well, such as using i as the input to sin and cos, whereas you should use theta(i).
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Sordin
Sordin 2017-4-3
Thank you for your message. But Matlab still gives the following error when using .* : 'Matrix dimensions must agree'. This was the code:
n = size(Image,1);
x = linspace(-1,1,n);
[x0,y0] = meshgrid(x,x);
for i = 1:length(theta)
R = [cosd(-i) -sind(-i); sind(-i) cosd(-i)];
XY = R.*[x0(:),y0(:)];
X = XY(1,:);
Y = XY(2, :);
end
I wonder if there is any other way to implement this using multiplication with R?

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Walter Roberson
Walter Roberson 2017-4-2
You have
[X,Y]'=R.*[x0;y0];
You need to replace this with something like
XY = R * [x0;y0];
X = XY(1);
Y = XY(2);
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Walter Roberson
Walter Roberson 2017-4-2
If your R is truly 2 x 2 and your x0 and y0 are scalars, then R * [x0; y0] is correct. Perhaps your R is not 2 x 2 or perhaps your x0 or y0 are not scalars.
Sordin
Sordin 2017-4-3
I'm very confused because R is definitely a 2x2 matrix:
R = [cosd(-i) -sind(-i); sind(-i) cosd(-i)]
For instance, for θ=1, the output is:
R =
0.9998 0.0175
-0.0175 0.9998
And x0 and y0 should be scalars because they are defined as:
n = size(Image,1);
x = linspace(-1,1,n);
[x0,y0] = meshgrid(x,x)
Why is it that this method doesn't work but the following non-matrix approach does?
X = x0.*cosd(-i) + -y0.*sind(-i);
Y = x0.*sind(-i) + y0.*cosd(-i);
Thank you.

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