How to rotate a surface(or a 2D plane) in 3D Cartesian coordinate ?

Hi everyone,

I am trying the tilt a 2 dimension plane or surface by some small incremental angle along a particular axis (1. about x - axis and 2. about y-axis) using the rotation matrix formula.

for example,

% the 3D volume has a dimension of -  64 x 64 x 64 
% the plane is placed inside the 3D volume and is defined as a set of points
    y = 24:1:40;                
    x(1, 1:size(y,2)) = 32;
    z(1, 1:size(y,2)) = 20;
    plane = [x; y; z];

So, when I try to rotate this plane about a particular axis using the rotation matrix, R = [cos(theta) -sin(theta) 0; sin(theta) cos(theta) 0; 0 0 1], I am not able to find the new values of the x, y and z point for the considered plane correctly.

I also have confusion about the rotation (pitch, yaw and roll).

Therefore, if someone could please help me understand the concept about the rotation and suggest a correct way to appraoch the problem.

Thank you.

Answer 1

[darova]

See this example:

R = @(a) [cosd(a) -sind(a); sind(a) cosd(a)];
t = 0:.1:2*pi;
[x,y] = pol2cart(t,5+sin(5*t));
line(x,y)
v1 = R(15)*[x;y];                   % rotate around Z axis
line(v1(1,:),v1(2,:),'color','r')

figure
z = x*0;
v2 = R(15)*[x;z];      % rotat around Y axis
plot(x,y)
line(v2(1,:),y,v2(2,:))
view(45,45)

[S]

Hey Darova,

Thank you very much for your help.

Buddy I have two doubt,

(1) when you rotated the plane about the y- axis or about the z-axis. why didn't you consider the y and z values respectively. Since the value for all point contained on the plane will change (x,y,z) except for few (about which we rotate it).

(2) why did you write z = x*0 ?

[darova]

(1) I didn't consider Z values when i rotated about Z axis because they won't change. The same thing with Y axis

(2) I created Z values. I assumed that a curve is plane (z=0)

[S]

Hey Darova ..

Thank you very much for answering my doubts ..

Let me try the approach you have suggested to solve my problem ..

Thanks once more

[darova]

You are welcome. Let me know if it works