How do you convert quaternions to degrees?
quat = eul2quat( eul ) converts a given set of Euler angles, eul , to the corresponding quaternion, quat . The default order for Euler angle rotations is “ZYX” . quat = eul2quat( eul , sequence ) converts a set of Euler angles into a quaternion. The Euler angles are specified in the axis rotation sequence, sequence .
What is the conjugate of a quaternion?
Conjugate. The conjugate of a quaternion number is a quaternion with the same magnitudes but with the sign of the imaginary parts changed, so: conj(a + b i + c j + d k) = a – b i – c j – d k.
How to convert a quaternion to a matrix?
If a quaternion is represented by qw + i qx + j qy + k qz , then the equivalent matrix, to represent the same rotation, is: This page discusses the equivalence of quaternion multiplication and orthogonal matrix multiplication. Jay Ryness has kindly sent me this alternative method which calculates the result as a Product of two 4×4 matrices:
When to use quaternion multiplication and orthogonal matrix multiplication?
Quaternion multiplication and orthogonal matrix multiplication can both be used to represent rotation. If a quaternion is represented by qw + i qx + j qy + k qz , then the equivalent matrix, to represent the same rotation, is: This page discusses the equivalence of quaternion multiplication and orthogonal matrix multiplication.
Why are quaternions used instead of Euler angle matrices?
Quaternions are often used instead of Euler angle rotation matrices because “compared to rotation matrices they are more compact, more numerically stable, and more efficient” (Source: Wikipedia ).
What are the four values of a quaternion?
The four values in a quaternion consist of one scalar and a 3-element unit vector. Instead of a, b, c, and d, you will commonly see: q 1, q 2, and q 3 correspond to an axis of rotation about which the angle of rotation is performed. Other ways you can write a quaternion are as follows: