# DCM2euler

Below is a demonstration of the features of the DCM2euler function

## Contents

```clear; close all; clc;
```

## Syntax

[a]=DCM2euler(Q);

## Description

This function is the inverse of the euler2DCM function. The Euler angles a are derived based on the input rotatin tensor Q.

## Examples

Plot settings

```fontSize=25;
```

## Retrieving the Euler andles from a rotation tensor

Get example patch data

```[F,V]=parasaurolophus;
```

Defining sets of true Euler angles for X, Y and Z axis rotation

```a_true=[0.25*pi 0.25*pi -0.25*pi]
```
```a_true =

0.7854    0.7854   -0.7854

```

Use euler2DCM function to define the rotation tensor

```[Q]=euler2DCM(a_true);
```

Use DCM2euler to retrieve the Euler angles

```a_fit=DCM2euler(Q)
```
```a_fit =

0.7854    0.7854   -0.7854

```

## Handling symbolic expressions

```try
syms a b c

a_true=[a b c]
Q=euler2DCM(a_true);

a_fit=DCM2euler(Q)

catch
warning('Symbolic toolbox likely missing')
end
```
```
a_true =

[ a, b, c]

a_fit =

[ -atan2(-cos(b)*sin(a), cos(a)*cos(b)), -atan2(-sin(b), (cos(a)^2*cos(b)^2 + cos(b)^2*sin(a)^2)^(1/2)), -atan2(-cos(b)*sin(c), cos(b)*cos(c))]

``` GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

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GIBBON: The Geometry and Image-based Bioengineering add-On. A toolbox for image segmentation, image-based modeling, meshing, and finite element analysis.

Copyright (C) 2019 Kevin Mattheus Moerman

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