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How to calculate a rotation matrix to align vector a to?
Let’s call the function that will do this rotateAlign (). This is an extremely useful operation to align an object in a given direction. Let’s assume we already have the following function for rotating around a given (normalised) axis u by a given angle angleRadians (specified in radians):
How to find camera position and rotation from a 4×4 matrix?
This seems to be a 4×4 homogeneous transformation matrix. How do I extract the camera position and rotation in world co-ordinates using this matrix? On the left I have shown a cam and its viewing a 3d object, and I take a photo of this 3D object from the cam. THe right is what I want.
Where does the camera go in a matrix?
The conventions that I’m used to are that in camera space, the camera is situated at the origin, and has axes that look like this: In other words, the camera is looking along the positive Z axis, and the Y axis is up.
How to find the orientation of the camera?
The orientation of the camera is given simply by RT. So if the “in” axis is the z-axis, for instance, then the vector pointing in the direction the camera is pointing is RT[0 0 1] = (0.718, − 0.595, 0.36).
How to calculate the rotation from a to B?
Given our unit vectors, we note that cosθ = A ⋅ B, and sinθ = | | A × B | |. Thus G = ( A ⋅ B − ‖A × B‖ 0 ‖A × B‖ A ⋅ B 0 0 0 1). This matrix represents the rotation from A to B in the base consisting of the following column vectors: Those vectors are all orthogonal, and form an orthogonal basis.
How to calculate rotation matrix for curve 2?
In my test case, curve 2 is simply curve 1 with the following rotation matrix applied: (just a 60 degree rotation around the x axis). The rotation matrix computed by my code to align the two vectors again is: [ [ 1. -0.32264329 0.27572962] [ 0.53984249 1. -0.35320293] [-0
How to find a unique rotation matrix between two coordinate systems?
Since you have the plane (not only the normal vector), a way to find a unique rotation matrix between two coordinate system would be: do the non-unique rotation twice! Find a orthogonal vector in the same plane of interest with A and B respectively.