matlab - Why does my 3 axes system coordinate orientation change x with y values? -

i using matlab , euler angles in order reorient 3axes coordinate system. specifically,

rz = [cos(ψ) sin(ψ) 0;-sin(ψ) cos(ψ) 0;0 0 1]; ry = [cos(φ) 0 -sin(φ);0 1 0;sin(φ) 0 cos(φ)]; rx = [1 0 0;0 cos(θ) -sin(θ);0 sin(θ) cos(θ)]; rtotal = rz*ry*rz 

then loop through old system coordinates (x,y,z) , make vector coord_old. reoriented system (xn,yn,zn)

for i=1:size(num,1)     coord_old = [x(i,1);y(i,1);z(i,1)];     coord_new = rtotal*coord_old;     xn(i,1) = coord_new(1,1);     yn(i,1) = coord_new(2,1);     zn(i,1) = coord_new(3,1); end 

my issue when θ,φ,ψ≃0 x->-y , y->x , when θ,φ≃0 , ψ=90 x , y not rotate! means when x,y should rotate don't , when shouldn't rotate stay were!

--edit-- example, when ψ=20.0871, φ=0.0580 , θ=0.0088 these results

see x->-y , y->x while z doesn't change @ all! thoughts?

ok, see 2 main problems here:

1. rtotal = rz*ry*rz not want since rz multiplied twice. think mean rtotal = rz*ry*rx.
2. your rotation matrix seems incorrect. check this wikipedia artice correct signs.

here corrected rotation matrix:

rz = [cos(psi) -sin(psi) 0; sin(psi) cos(psi) 0;      0 0 1]; ry = [cos(phi) 0 sin(phi);  0 1 0;                    -sin(phi) 0 cos(phi)]; rx = [1 0 0;                0 cos(theta) -sin(theta); 0 sin(theta) cos(theta)]; rtotal = rz*ry*rx; 

with matrix correct results:

x=1; y=2; z=3; psi=0; phi=0; theta=0; [xn,yn,zn] >> 1 2 3  x=1; y=2; z=3; psi=90/180*pi; phi=0; theta=0; [xn,yn,zn] >> -2 1 3 

and here full graphical example of cube in 3d-space:

% create cube (not in origin) dvert = [0 0 0; 0 1 0; 1 1 0; 1 0 0 ; ...           0 0 1; 0 1 1; 1 1 1; 1 0 1];      dside = [1 2 3 4; 2 6 7 3; 4 3 7 8; ...          1 5 8 4; 1 2 6 5; 5 6 7 8]; dcol  = [0 0 1; 0 0.33 1; 0 0.66 1; ...          0 1 0.33; 0 1 0.66; 0 1 1];  % rotation angles psi   = 20  /180*pi;    % z phi   = 45  /180*pi;    % y theta = 0   /180*pi;    % x  % rotation matrix rz = [cos(psi) -sin(psi) 0; sin(psi) cos(psi) 0;      0 0 1]; ry = [cos(phi) 0 sin(phi);  0 1 0;                    -sin(phi) 0 cos(phi)]; rx = [1 0 0;                0 cos(theta) -sin(theta); 0 sin(theta) cos(theta)]; rtotal = rz*ry*rz;  % apply rotation dvertnew = rtotal * dvert';  % plot cubes figure; patch('faces',dside,'vertices',dvert,'facecolor','flat','facevertexcdata',dcol);  patch('faces',dside,'vertices',dvertnew','facecolor','flat','facevertexcdata',dcol);   % customize view grid on; axis equal; view(30,30);