# Thread: lingering questions on Euler to matrix

1. ## lingering questions on Euler to matrix

When the distances of the unit circle are worked out for a set of Euler angles, what is this result called? Is this a 'positional' vector? A generic vector?

I would just like it spelled out how we go from Euler angles to distances. I know movement can be worked out with trig fx, but I want to (and have been advised to use) matrices for this.

Thank you for your time.

2. Originally Posted by technologist
When the distances of the unit circle are worked out for a set of Euler angles, what is this result called? Is this a 'positional' vector? A generic vector?

I would just like it spelled out how we go from Euler angles to distances. I know movement can be worked out with trig fx, but I want to (and have been advised to use) matrices for this.
What "distances"? Are you referring to the components of a vector in Cartesian coordinates?

A set of Euler angles corresponds to a rotation (orthonormal matrix) rather than a direction (vector). A rotation requires three parameters to specify (e.g. yaw, pitch, roll), a direction only requires two (e.g. heading and elevation, which roughly correspond to yaw and pitch).

To convert Euler angles to a matrix, you need to be clear on which axis is which (is the Z axis up or forward? Or backward?), the order in which the rotations are applied, and the sign of each rotation (is a positive angle clockwise or anticlockwise?). There is no universal "correct" answer to any of these.

Once you have established the conventions, you'd typically convert each rotation to a matrix then multiply them.

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