rotateframe

Define a point in three dimensions. The coordinates of a point are always specified in the order x, y, and z. For convenient visualization, define the point on the x-y plane.

x = 0.5;
y = 0.5;
z = 0;
plot(x,y,"ko")
hold on
axis([-1 1 -1 1])

Create a quaternion vector specifying two separate rotations, one to rotate the frame 45 degrees and another to rotate the point -90 degrees about the z-axis. Use rotateframe to perform the rotations.

quat = quaternion([0,0,pi/4; ...
                   0,0,-pi/2],"euler","XYZ","frame");
               
rereferencedPoint = rotateframe(quat,[x,y,z])

rereferencedPoint = 2×3

    0.7071   -0.0000         0
   -0.5000    0.5000         0

Plot the re-referenced points.

plot(rereferencedPoint(1,1),rereferencedPoint(1,2),"bo")
plot(rereferencedPoint(2,1),rereferencedPoint(2,2),"go")

Define two points in three-dimensional space. Define a quaternion to re-reference the points by first rotating the reference frame about the z-axis 30 degrees and then about the new y-axis 45 degrees.

a = [1,0,0];
b = [0,1,0];
quat = quaternion([30,45,0],"eulerd","ZYX","point");

Use rotateframe to reference both points using the quaternion rotation operator. Display the result.

rP = rotateframe(quat,[a;b])

rP = 2×3

    0.6124   -0.3536    0.7071
    0.5000    0.8660   -0.0000

Visualize the original orientation and the rotated orientation of the points. Draw lines from the origin to each of the points for visualization purposes.

plot3(a(1),a(2),a(3),"bo");

hold on
grid on
axis([-1 1 -1 1 -1 1])
xlabel("x")
ylabel("y")
zlabel("z")

plot3(b(1),b(2),b(3),"ro");
plot3(rP(1,1),rP(1,2),rP(1,3),"bd")
plot3(rP(2,1),rP(2,2),rP(2,3),"rd")

plot3([0;rP(1,1)],[0;rP(1,2)],[0;rP(1,3)],"k")
plot3([0;rP(2,1)],[0;rP(2,2)],[0;rP(2,3)],"k")
plot3([0;a(1)],[0;a(2)],[0;a(3)],"k")
plot3([0;b(1)],[0;b(2)],[0;b(3)],"k")