# 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*, gibbon.toolbox@gmail.com

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License: https://github.com/gibbonCode/GIBBON/blob/master/LICENSE

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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