[zz] 直角座標系的平移和旋轉

直角座標系的平移和旋轉：

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

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

點評：x, y軸雖然只是一種標號，但是x軸做縱軸，y軸做橫軸，始終感覺彆扭！

 

座標系轉換：

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);

 

座標變換之MATLAB函數分享:

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

View Code

function B = TransCoord3( A ) %   功能：三維座標 -> 二維座標 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 end

View Code

function [A,afa] = TransCoord( A, Center, Angle) %   功能：二維座標變換，平移和旋轉 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 end

代碼給我很大啟發！但是：“afa=afa+Angle” 應該為“afa=afa-Angle”吧？

 

座標系的旋轉變換：

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

座標旋轉變換公式的推導：

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

上面2篇理論講的很清楚！

 

座標旋轉：

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

公式好像有問題！