# 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.

## Examples

## 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') axisGeom; camlight headlight; gdrawnow;

* GIBBON* www.gibboncode.org

*Kevin Mattheus Moerman*, [email protected]

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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) 2006-2023 Kevin Mattheus Moerman and the GIBBON contributors

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