Matrix Rotation About Origin
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From: Matt Thomas on 14 Jul 2010 14:29 Ben <benvoeveren(a)gmail.com> wrote in message <2069972631.29097.1279129690927.JavaMail.root(a)gallium.mathforum.org>... > function [m] = rotmat(a,b,c); > %calculates the rotation matrix in order XYZ in a right handed system > %the coordinate system is rotated, not the points! > > ca=cos(a); > sa=sin(a); > cb=cos(b); > sb=sin(b); > cc=cos(c); > sc=sin(c); > m1=[1 0 0;0 ca -sa;0 sa ca];%rotation only about x axis > m2=[cb 0 sb;0 1 0;-sb 0 cb];%rotation only about y axis > m3=[cc -sc 0;sc cc 0;0 0 1];%rotation only about z axis > % m1=[1 0 0;0 ca sa;0 -sa ca]; > % m2=[cb 0 -sb;0 1 0;sb 0 cb]; > % m3=[cc sc 0;-sc cc 0;0 0 1]; > m=m1*m2*m3; > > Thank you for the replies. I was in fact, looking at the rot90 command - I think now it designed for rotating images not matrices. In response to the code posted above, I need the program to change the values of my x,y,z points, not the coordinate system. This is because I will be doing more translation of these points later on. Is there no command for rotating a set of x,y points defined in a 2 column matrix about the origin of the x,y coordinate system? -matt
From: Matt J on 14 Jul 2010 15:43 "Matt Thomas" <matt.at(a)gmail.com> wrote in message <i1kvlh$2sv$1(a)fred.mathworks.com>... > In response to the code posted above, I need the program to change the values of my x,y,z points, not the coordinate system. =============== The two sound the same to me. > Is there no command for rotating a set of x,y points defined in a 2 column matrix about the origin of the x,y coordinate system? ======== Create a rotation matrix, similar to what has been described to you (or see below).You can multiply the 2 column matrix with the rotation matrix. function R=R2d(x) %2D Rotation matrix counter-clockwise. % %R=R2d(deg) % %Input is in degrees. % %See also Rx,Ry,Rz,,R3d,M2d,M3d R= [cosd(x),-sind(x); sind(x),cosd(x)];
From: Charles McPherson on 21 Jul 2010 15:38
Matt, What you describe is a 2D rotation transformation which is normally performed by multiplying the (x,y) data points of the original coordinate system by a 2X2 rotation transformation matrix. Because it's a simple 2X2, the rotation can be easily expressed a a simple linear equation as well. This equation for a clockwize rotation by an angle, theta, is: x_prime = x*cos(theta) + y*sin(theta); y_prime = -x*sin(theta) + y*cos(theta); where x_prime and y_prime are where the x,y moves to. Usually, I do coordinate transformation using matrix algebra because it's clean and simple. Check out the Wiki at <http://en.wikipedia.org/wiki/Transformation_matrix#Rotation> "Matt Thomas" <matt.at(a)gmail.com> wrote in message <i1krpq$iud$1(a)fred.mathworks.com>... > Hi All - > > I have a matrix that I need to rotate a specified number of degrees about the x,y origin. I have found resources for matrix rotation for 90 degrees but I need a way to do it a user specified amount (say, for example, 5 degrees). > > Can anyone point me in the right direction? > > Thanks! > > matt |