# vectorOrthogonalPair

Below is a demonstration of the features of the `vectorOrthogonalPair` function

## Contents

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

## Syntax

`[a,d]=vectorOrthogonalPair(f);`

## Description

Based on the input vector f this function generates the normalized output vectors a and d which are orthogonal to eachother and to f. This function can be useful for describing local element axis systems based e.g. in FEBio (whereby the input vector defaults to e3).

## Examples

## Example 1: Creating a triplet of mutually orthogonal vectors

Creating example vectors

P=eye(3,3); %Vector origins V=euler2DCM([0.25*pi 0.25*pi 0.25*pi]); %Input Vectors, rotated directions % V=eye(3,3); %Input Vectors, x,y,z axes

Compute mutually orthogonal sets using `vectorOrthogonalPair`

[a,d]=vectorOrthogonalPair(V);

Visualize the sets

cFigure; title('Visualized vectors sets, input vectors=transparent, orthogonal=non-transparent'); quiverVec(P,V,2,'b','none',1,0.2); quiverVec(P,a,1,'r','none',1,1); quiverVec(P,d,1,'g','none',1,1); % quiverVec(P,d,1,'k','none',1,1); axisGeom; camlight headlight; drawnow;

* 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) 2019 Kevin Mattheus Moerman

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.

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