How can I rotate a set of points by an angle around its origin?

I have a set of data points that I would like to rotate around its origin by 45 degrees.

I already have the following code:

ITM = [sl.x sl.y]; %81x2 matrix

x_centre = sl.x(1); %rotate around its origin
y_centre = sl.y(1);

centre = transpose(repmat([x_centre; y_centre], 1, length(sl.x))); %transpose to get 81x2 matrix

theta = pi/4 %45 degrees
R = [cos(theta -sun(theta); sin(theta cos(theta)];
vo = R*(v - centre) + centre;
x_rotated = vo(1, :);
y_rotated = vo(2, :);

However, I get the error "incorrect dimensions for matrix multiplication".

Using '.*' doesn't solve the issue either.

How could I rotate these 81 points around its origin by 45 degrees?

Answer 1

[Alan Stevens]

Do you mean like this?

ITM = [461400.0758	617474.3059
461400.8069	617475.4609
461400.8069	617475.4609
461402.3069	617477.6334
461402.9793	617478.8059
461402.9793	617478.8059
461404.8069	617481.0369
461404.8069	617483.4696
461405.5181	617484.3059
461405.7293	617484.8059
461407.3069	617487.1909
461408.1	617488.3059
461408.3069	617488.6369
461409.3069	617489.7196
461410.5885	617491.8059
461410.5885	617491.8059
461412.3069	617493.1334
461413.2552	617494.8059
461413.2552	617494.8059
461414.3069	617495.5946
461416.0758	617497.8059
461417.1689	617499.3059
461417.6109	617500.3059
461418.5758	617501.8059
461419.3069	617503.1369
461419.4793	617504.3059
461420.3069	617506.1564
461420.8069	617506.8576
461421.6977	617507.8059
461422.8069	617509.6334
461422.85	617509.8059
461424.3069	617511.4696
461424.3069	617511.4696
461426.6418	617513.8059
461427.3069	617514.8369
461427.8069	617516.1909
461428.4477	617517.8059
461428.725	617518.3059
461429.8069	617519.7484
461430.499	617521.3059
461431.4793	617522.3059
461431.4793	617522.3059
461432.8069	617523.4369
461434.3069	617525.8317
461434.8069	617526.4709
461435.2758	617526.8059
461436.3069	617527.5753
461437.3069	617528.4214
461440.1431	617529.8059
461440.1431	617529.8059
461441.4793	617530.3059
461444.0375	617532.3059
461444.0375	617532.3059
461444.9793	617532.8059
461446.225	617534.3059
461448.1913	617536.3059
461448.1913	617536.3059
461449.8069	617538.0423
461449.8069	617538.0423
461451.7473	617539.8059
461452.5913	617540.8059
461453.7243	617542.3059
461453.7243	617542.3059
461455.2552	617543.3059
461456.2389	617544.3059
461458.1689	617545.8059
461458.6273	617546.8059
461459.6689	617548.8059
461460.1801	617549.8059
461460.8069	617551.4438
461461.5181	617552.8059
461461.9758	617554.3059
461462.3758	617555.3059
461462.8931	617556.3059
461463.6418	617557.3059
461465.3069	617559.0214
461465.3069	617559.0214
461466.1518	617559.8059
461468.3069	617561.3446
461469.4758	617562.8059
461469.7293	617563.3059];


x_centre = ITM(1,1);
y_centre = ITM(1,2);
x = ITM(:,1)-x_centre;
y = ITM(:,2)-y_centre;
v = [x y];

theta = pi/4; %45 degrees
R = [cos(theta) -sin(theta); sin(theta) cos(theta)];  %%%%%%%%%%%%%%%
vo = v*R;
x_rotated = vo(:,1)+x_centre;
y_rotated = vo(:,2)+y_centre;

plot(ITM(:,1),ITM(:,2),'.',x_rotated,y_rotated,'o')
xlabel('x'),ylabel('y')
legend('initial','rotated')

[Siegmund Nuyts]

This is perfect! Thanks a lot for your help