# kabschRotationMatrix

Below is a demonstration of the features of the kabschRotationMatrix function

## Contents

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

## Syntax

[Q]=kabschRotationMatrix(V1,V2);

## Description

This function uses the "Kabsch" algorithm to determine the rotation tensor to best rotate the coordinates V1 to V2.

## Example 1: Determine the rotation between two coordinate sets

```[F,V1] = parasaurolophus; % Example geometry for first coordinate set

Qt = euler2DCM([0.25*pi 0.25*pi 0.25*pi]) %Example true rotation

V2 = V1 * Qt'; %Create rotated second set
```
```Qt =

0.5000   -0.5000    0.7071
0.8536    0.1464   -0.5000
0.1464    0.8536    0.5000

```

Using the Kabsch algorithm to determine the rotation matrix

```Q = kabschRotationMatrix(V1,V2) %Determine rotation between V1 and V2

V3 = V2 * Q;
```
```Q =

0.5000   -0.5000    0.7071
0.8536    0.1464   -0.5000
0.1464    0.8536    0.5000

```

Visualisation

```cFigure;
gpatch(F,V1,'bw','b',0.5)
gpatch(F,V2,'gw','g',0.5)
gpatch(F,V3,'rw','r')

gdrawnow;
```

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, [email protected]

GIBBON footer text

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

Copyright (C) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.