[Zz] Translation and rotation of the Cartesian coordinate system

Translation and rotation of the Cartesian coordinate system:

Http://www.oschina.net/question/565065_67286

Http://xinxing124.blog.163.com/blog/static/30170195201162815851981/

Comments: although the X and Y axes are only a label, they always feel awkward when the X axis is an vertical axis and the Y axis is a horizontal axis!

 

Coordinate System Conversion:

Http://blog.sina.com.cn/s/blog_429a1dbf010009vg.html

View code

% Matlab File: Tcoord.m% Transformation for different coordnate systemsA=load('p1.dat');   % A is a matrix of n*3. Each row is the three components% of a point in the original coordinate system.T=load('T1.dat');   % T is a matrix of 3*4. The first three column vectors% denote the three axis vectors of the new coordinate system. The fourth column% is the position of the new origin.n=size(A,1); % Rows of Matrix A.At=repmat(T(:,4)',n,1);Y=T(:,1:3)'*(A-At)';   % the new coordinate values. 3*nfprintf(1,'The new coordinate values are stored in the file of p2.dat\n');fid=fopen('p2.dat','w+');fprintf(fid,'%12.8f %12.8f %12.8f\n',Y); % n*3fclose(fid);

 

MATLAB Functions of coordinate transformation:

Http://shiaohoo.blogbus.com/logs/53777599.html

View code

Function B = transcoord3 (a) % function: 3D coordinate-> 2D coordinate x_axis = a (2, :)-A (1, :); y_axis = A (3, :)-A (1, :); z_axis = cross (x_axis, y_axis); y_axis = cross (x_axis, z_axis); x_axis = x_axis/norm (x_axis ); y_axis = y_axis/norm (y_axis); z_axis = z_axis/norm (z_axis); transmatrix = [x_axis; y_axis; z_axis]; Len = length (a); for I = 1: len r_vector = a (I, :)-A (1, :); B (I, :) = r_vector/transmatrix; end

View code

Function [A, AFA] = transcoord (A, center, angle) % function: 2D coordinate transformation, translation and rotation Len = length (a); for I = 1: len A (I, 1) = a (I, 1)-center (1); a (I, 2) = a (I, 2)-center (2 ); end for I = 1: Len r = SQRT (A (I, 1) * a (I, 1) + a (I, 2) * a (I, 2 )); k = a (I, 2)/A (I, 1); If a (I, 1) <0 AFA = atan (k) + PI; elseif a (I, 1)> 0 AFA = atan (k); else AFA = PI/2; end AFA = AFA + angle; A (I, 1) = r * Cos (AFA ); A (I, 2) = r * sin (AFA); end

The Code has inspired me a lot! But should "AFA = AFA + angle" be "AFA = afa-angle?

 

Rotation Transformation of the coordinate system:

Http://blog.sina.com.cn/s/blog_5f853eb10100zx2z.html

Derivation of coordinate rotation transformation formula:

Http://blog.csdn.net/Tangyongkang/article/details/5484636

The above two theories are very clear!

 

Coordinate rotation:

Http://blog.163.com/yhtian619@126/blog/static/1625512802010717112643721/

There seems to be a problem with the formula!