# Rotate the plot at 45 degree

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Sharah on 29 Sep 2016
Commented: Ryan Webb on 1 Sep 2022
Can anyone tell me how to rotate the plot from the following image so that the now the linear reference line will be a straight vertical line, and the red and green line will fall on the left side of the plot?
for a reference the red and green line is just a data that I plot with different slope.

Jakub Rysanek on 4 Oct 2016
I would simply rotate all data using the planar (2D) transform with respect to the origin:
angle = pi/4;
reference_line = [0 1 2 3 4 5 6];
data_x = [0 1 2 3 4 5 6];
data_y = [0 1.1 2.2 3.3 4.4 5.5 6.6];
% 2D rotation
x2 = data_x*cos(angle)-data_y*sin(angle);
y2 = data_y*cos(angle)+data_x*sin(angle);
figure;
hold on;
p1=plot(reference_line,reference_line,'marker','none','linestyle','--');
p2=plot(data_x,data_y,'-r');
p3=plot(x2,y2,'-b');
p4=plot(zeros(1,7),reference_line,'-k');
set(gca,'ylim',[0 6],'xlim',[-6 6]);
axis square;
legend([p1,p2,p3,p4],{'Reference line','Original data','Rotated data','Vertical line'},'Location','southwest');

Walter Roberson on 29 Sep 2016
Create an hgtransform, set the axes parent to be the transform, set the rotation matrix for the transform to have the appropriate rotation.
Note: this will transform the axes too, rotating the entire plot.
If you want just the data to be rotated then the easiest single way would probably:
[th, r] = cart2pol(x, y);
[nx, ny] = pol2cart(th+pi/4, r);
Your x and y arrays will need to be the same size for this to work, so if you have multiple columns in your y array (one column per line) and a vector x, then use repmat(x(:), 1, size(y,2)) as the x for the rotation.
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Ryan Webb on 1 Sep 2022
Can you clarify on "set the axes parent to be the transform"
set(ax,'Parent',t)
gives the error:
Error using matlab.graphics.axis.Axes/set
Axes cannot be a child of Transform.