# xyz2R: Create a rotation matrix from 3 angles about new axes in the... In nvctr: The n-vector Approach to Geographical Position Calculations using an Ellipsoidal Model of Earth

## Description

The rotation matrix `R_AB` is created based on 3 angles `x`, `y` and `z` about new axes (intrinsic) in the order x-y-z. The angles (called Euler angles or Tait-Bryan angles) are defined by the following procedure of successive rotations:

1. Given two arbitrary coordinate frames `A` and `B`, consider a temporary frame `T` that initially coincides with `A`. In order to make `T` align with `B`, we first rotate `T` an angle `x` about its x-axis (common axis for both `A` and `T`).

2. Secondly, `T` is rotated an angle `y` about the NEW y-axis of `T`.

3. Finally, codeT is rotated an angle `z` about its NEWEST z-axis. The final orientation of `T` now coincides with the orientation of `B`.

The signs of the angles are given by the directions of the axes and the right hand rule.

## Usage

 `1` ```xyz2R(x, y, z) ```

## Arguments

 `x` Angle of rotation about new x axis (rad) `y` Angle of rotation about new y axis (rad) `z` Angle of rotation about new z axis (rad)

## Value

3x3 rotation matrix (direction cosine matrix) such that the relation between a vector v decomposed in A and B is given by: v_A = R_AB * v_B

## References

Kenneth Gade A Nonsingular Horizontal Position Representation. The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.

`R2xyz`, `zyx2R` and `R2zyx`.
 `1` ```xyz2R(rad(10), rad(20), rad(30)) ```