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How do you convert a vector to a quaternion?
First we convert the 3D vector into a quaternion, to do this we set the imaginary parts of the quaternion to the x,y and z values of the vector, the real part of the quaternion is set to zero. This quaternion is therefore not normalised like the quaternion representing the rotation.
What makes up a quaternion in math3d?
Each quaternion is composed of a vector (xyz) and a scalar rotation (w). Although their values are not very intuitive, they are used instead of the Euler angles to: It is advised not to use the x, y, z, w values directly, unless you really know what you are doing.
What is the formula for a quaternion transform?
Probably the most important result on this page is the formula for representing rotations in 3 dimensions using quaternions (although we will also discuss how to use quaternions for other transforms on this page). This formula for 3D rotations is:
How to calculate the rotation of a quaternion?
This formula for 3D rotations is: P out and P in are points in 3D space represented by the i, j and k parts of a quaternion (real part =0) conj () is a conjugate function explained on this page. We sometimes write conj (q) as q’.
So take the cross product of your direction vector D and up vector U for the side vector S then cross D and S for a new Un. Then use D, Un, S as rows (or columns depending on how your calculation rule is set up) as a matrix. Matrix to quaternion is well known math.
How do you rotate a quaternion?
This can be easily understood by the equivalent axis-angle representation. Any quaternion can be written as q=cos(ϕ/2)+sin(ϕ/2)k, where k is a unit vector representing the axis of rotation and ϕ is the angle in radians.
How do you multiply a vector and a quaternion?
As for the multiplication with a vector, you just extend the vector to a quaternion by setting a quat’s real component to zero and its ijk components to the vector’s xyz. Then you do the quaternion multiplications to get v’, and then extract the ijk components again.
How to convert a direction vector to a quaternion?
So take the cross product of your direction vector D and up vector U for the side vector S then cross D and S for a new U n. Then use D, U n, S as rows (or columns depending on how your calculation rule is set up) as a matrix. Matrix to quaternion is well known math.
Can a direction vector be a defined rotation?
A direction vector is not a defined rotation, it still has an infinite number of possible solutions. See there is no information for how to rotate around the axis. Two, vectors is possible as is a vector and a rotation (with a meaningful center) and in fact a fully defined matrix.
How to convert a lookat matrix to a quaternion?
(more efficient) Convert the LookAt matrix into a quaternion and conjugate it instead of applying glm::inverse, since the result is a unit quat and for such quats the inverse is equal to the conjugate. Thanks for contributing an answer to Stack Overflow!
When to use a quaternion in a camera?
When using quaternions to store the orientation of an object (be it a camera or anything else), usually this rotation quat is used to calculate the vectors which define its local-space (left-handed one in the below example):