Contents
How do you code a quaternion rotation?
Quaternion construction: q = { cos(theta/2.0), // This is the angle component sin(theta/2.0) * x, // Remember, angle is in radians, not degrees! sin(theta/2.0) * y, // These capture the axis of rotation sin(theta/2.0) * z};
How do you convert Euler to quaternion?
quat = eul2quat( eul , sequence ) converts a set of Euler angles into a quaternion. The Euler angles are specified in the axis rotation sequence, sequence . The default order for Euler angle rotations is “ZYX” .
What quaternion means?
Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three dimensional space. Specifically, they encode information about an axis-angle rotation about an arbitrary axis.
How to transform a 3D vector into a quaternion?
So how do we use quaternions to transform one 3D vector into another? First we convert the 3D vector into a quaternion, to do this we set the imaginary pars of the quaternion to the x,y and z values of the vector, the real part of the quaternion is set to zero.
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’.
How are the pars of a quaternion normalised?
First we convert the 3D vector into a quaternion, to do this we set the imaginary pars 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.
Can a quaternion be used in a 3 dimensional space?
On this page we discuss how a given quaternion can be used to rotate points in 3 dimensional space. Although rotations in 3 dimensions have three degrees of freedom they are not a 3D vector space (we can’t combine them using vector addition).