Rotation of a set of points onto the X axis

Question

Nancy 2012-3-2

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Hi Guys,

I know this is a simple problem but I am just not to able to figure out how to do it. I dont know if the code I have written is correct. So my problem. I have a set of 4 points in a 2D plane. The points are linear and can be fit to a line in the form on y=m*x+b. Usually b=0. So these fitted line will pass through the origin. The points are in all quadrants. So the fitted lines look like they radite out of the origin. I want to rotate all these points onto the x axis. I am having trouble finding out the exact angle of rotation since this would depend on the quadrant the points/fitted line lie in.

Can you please tell me if my code is right. It is very crude.

My points are in matrix X. It is a 2 row 4 column matrix. Row 1 has X coordinates and row 2 has corresponding Y coordinates.

%Fit a line to the points
 poly=polyfit(X(1,1:4),X(2,1:4),1);
 theta=atan(poly(1));
%computation of angle of rotation based on quadrant trajectory %lies. If in first or fourth it is -theta and if in second or third %it is -(pi+theta)
sumx=sum(X(1,:));
sumy=sum(X(2,:));
if (sumx>0)
theta=-theta;
else
theta=-(pi+theta);
end
%computation of rotation matrix. rotation is about X axis
rot = [cos(theta) -sin(theta); sin(theta) cos(theta)];
Xrot=rot*X;

Your help is greatly appreciated.

Nancy

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Answer 1

Honglei Chen 2012-3-2

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I'm not sure why you need to play with theta, unless you care about the orientation. If you just want the line to become horizontal, rotate an angle of -theta should serve the purpose.

The reason that it does not lie on the x axis is because the rotation matrix is centered on origin. Therefore, once rotated, you need to move it onto the x axis.

I modified your program a little bit and put it below. I just used the -theta and the main change is at the end, where I compensate for the displacement after I did rot*X

% Test data
X = [-2 -1 1 2;0 -1 -3 -4];
%--- Your program starts ---
%Fit a line to the points
poly=polyfit(X(1,1:4),X(2,1:4),1);
theta0=atan(poly(1));
theta=-theta0;
%computation of rotation matrix. rotation is about X axis
rot = [cos(theta) -sin(theta); sin(theta) cos(theta)];
Xrot=rot*X-poly(2)*cos(theta0);   % <- change here
% --- Your program ends ---
% plot
plot(X(1,:),X(2,:),Xrot(1,:),Xrot(2,:))

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Nancy 2012-3-2

My data set involves a lot of set of points. It seems to work ok. There are still some points that dont fall on the positive X axis. I want to know if my code is correct or if there is a more elegant way to do this.