Do you know what the formula is for the 3D rotation of the perspective of a 3D object in a 2D space. For example, imagine that we got a picture of a 3D object. So, we have the projected picture of that 3D object in a 2D space. Next time, we rotate the 3D object by z-axis and got another projected picture in 2D space. What will be the formula of the transformation of each point in the second 2D projected picture with respect to the first one in a 2D space.
Actually, two 2D projected pictures of the 3D rotated object are being compared.
[Math] The formula for 3D rotation of the perspective of an image in 2D space
3dgeometryrotationstransformation
Related Solutions
Composition of Euler angles is not simple.
Convert your Euler-angles to rotation matrices, and multiply them together.
R1 = rotate 90° around y-axis — Rotates to left side
R2 = rotate 14° around x-axis
R3 = rotate -14° around y-axis
R4 = rotate -32° around z-axis
R = R4 × R3 × R2 × R1Recover the angles
x' = arctan2(R3,2,R3,3) = arctan2(cos(y)·sin(x), -sin(y))
y' = -arcsin(R3,1) = -arcsin(cos(y)·cos(x))
z' = arctan2(R2,1,R1,1) = arctan2(cos(z)·sin(x) - sin(z)·sin(y)·cos(x), -sin(z)·sin(x) - cos(z)·sin(y)·cos(x))
In your specific case, this evaluates to:
x' = 44.1°
y' = 70.3°
z' = 13.9°
Stick your thumb of your right hand along the direction of the rotation axis. A positive angle is along the way your fingers point.
Like this
http://electron9.phys.utk.edu/Collisions/rotational_motiondetails.htm
Best Answer
This is indeed undefined when you are missing the depth information.
If the rotation axis is fixed, all points are moving on ellipses of various extents, as seen on these cylinders, so the new positions aren't completely undefined.
If you have two pictures of the same object, stereoscopy allows you to reconstruct the 3D model.