Rotating a line given the angle and a vector

I have 2 points (x1, y1) and (x2, y2). I want to rotate it clockwise by 123 deg and find the co-ordinate (x2', y2') after rotation. Can anyone help?

Answer 1

[KSSV]

p1 = rand(2,1) ;
p2 = rand(2,1) ;
%%rotation matrix 
th = 123*pi/180 ;
R = [cos(th) -sin(th) ;sin(th) cos(th)] ;
%%rotate points
pr2 = R*p2 ;
figure
hold on
plot([p1(1) p2(1)],[p1(2) p2(2)] ,'r') ;
plot([p1(1) pr2(1)],[p1(2) pr2(2)] ,'b') ;

Read about rotation matrix: https://en.wikipedia.org/wiki/Rotation_matrix

[Ravindra P N]

Thanks. I can use cosd(th) instead of doing *pi/180. It works.

[bio lim]

Yes, you can.

[KSSV]

off course you can..

[RMH]

THIS DOES NOT WORK AS WRITTEN (and yes I'm necroposting, but this was my 1st result in google when I searched this problem). Here's why: You cannot rotate a POINT, you need to rotate a VECTOR. Test with dot product definiton:

(Wikipedia Link)

rearrange and solve for theta (and use acosd for degrees):

th = acosd(dot(v1,v2)/(norm(v1)*norm(v2)))

Now, create your vectors by subtracting P2x-P1x, P2y-P1y, and do same for v2.

v1 = [p2(1)-p1(1); p2(2)-p1(2)];
v2 = [pr2(1)-p1(1); pr2(2)-p1(2)];

If you now run the code KSSV posted above, you will NOT achieve the same angle of rotation that you put in. That's because you tried to rotate a point. Now try this:

v2_correct = R*v1;
th_correct = acosd(dot(v1,v2_correct)/(norm(v1)*norm(v2_correct)))

You'll see exactly the input that you put in. And to convert from a vector back to X and Y points, just use the new vector, and:

P1 = P1;  %P1 is simply your "origin" point.
P2_correct = [P1(1)+v2(1) ; P1(2)+v2(2)] 

Note that to do matrix math correctly, R is a 2x2, and v1 needs to be a 2x1 (2 rows 1 column). Else matlab will throw an error.

Again, sorry to comment on an old post, but I was searching for the solution to this problem for myself and this was the first google link I came across. Hope this helps someone!

Answer 2

[bio lim]

Rotate it to respect to what? If you are simply rotating points in the XY Cartesian plane counter-clockwise through 123 degrees about the origin around the Z axis, then just use a simple rotation matrix .

[Ravindra P N]

rotate With respect to x axis

[bio lim]

You can't rotate something with respect to an axis. You can rotate it about/around an axis, but you rotate something with respect to something that has a position.