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

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S
S 2021 年 9 月 3 日
コメント済み: darova 2021 年 9 月 8 日
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.

採用された回答

darova
darova 2021 年 9 月 5 日
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)
  4 件のコメント
S
S 2021 年 9 月 8 日
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
darova 2021 年 9 月 8 日
You are welcome. Let me know if it works

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