If you need to calculate a rotation matrix from Euler angles, you will have realised that it is not easy to find something usable in C#. It is necessary to rely on development tools such as Unity or similar to find ready-made functions.

Today we are going to look at a solution written in C# which will allow us to solve the problem without too much headaches .

What I am presenting here does not make use of special libraries, so it can be **compiled in .NET Core**, which guarantees portability on all operating systems supported by the Microsoft framework.

If you are looking for a solution to do the reverse operation, i.e. to

derive Euler angles from a rotation matrix, please refer to this article.

## Euler Angles to Rotation Matrix

Without wasting any time, here is the solution that allows you, starting from 3 Euler angles (rotation with respect to the X, Y and Z axis), to obtain the relative rotation matrix. The result is strictly dependent on the type of convention you need to use when applying the rotations. In the code in question, I take into account the **3 classic rotation sequences**: *XYZ*, *ZYZ* and *ZYX*.

To begin with, **let us define two enums** that will make the code more readable. In **lines 1 – 5**, we define the various types of **angle units** that we want to manage, in our case degrees and radians. On **lines 7 – 12**, we describe the various **axis rotation sequences** that we will be managing.

**The function**, as described by the signature in **line 14**, takes as input:

- an
**array of doubles of 3 elements**containing the Euler angles; - the
**type of rotation**of the axes; - the
**unit of measurement**of the angles passed as first parameter**;**

and returns a 3 x 3 matrix containing the rotation matrix.

To test the code we have just written, we write a simple program that performs the calculation of the rotation:

- Rx = 180;
- Ry = 0;
- Rz = 180.

The output result will be the 3 x 3 matrix in which the **elements** are stored in **row-major order** (i.e. row by row).

rotM[0,0] |
rotM[0, 1] |
rotM[0, 2] |
---|---|---|

rotM[1,0] |
rotM[1,1] |
rotM[1,2] |

rotM[2,0] |
rotM[2,1] |
rotM[2,2] |

## Conclusions

The *rotation matrix* is nothing more than a matrix operator that allows a vector to be rotated around a given axis in space. It is a very useful tool in several application fields, such as in robotics in solving inverse kinematics problems or in reference system transformations.

In this short article, we have presented a solution in C# that allows the calculation of the rotation matrix from a configuration of Euler angles.

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