# gramSchmidtOrtho

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

## Contents

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

## Syntax

`[E]=gramSchmidtOrtho(Q);`

## Description

This function uses the Gram-Schmidt method to convert the input basis Q to an orthonormal basis E.

## Examples

Create example non-orthonormal base vector set

rz=euler2DCM([0 0 0.25*pi]); %Rotation around z rx=euler2DCM([-0.25*pi 0 0]); %Rotation around x Q=eye(3,3); %Identify matrix (orthonormal) Q(:,1)=rz*Q(:,1); % Rotate the 1st axis towards 2nd Q(:,3)=rx*Q(:,3); % Rotate the 3rd towards 1-2-plane %Rotate all R=euler2DCM([0.25*pi 0.25*pi 0.25*pi]); Q=R*Q; %Scale all (so not normal) Q=Q*2;

Use Gram-Schmidt method to obtain an orthonormal basis

[E]=gramSchmidtOrtho(Q)

E = 0.000000000000000 -0.707106781186548 0.707106781186547 0.707106781186548 -0.500000000000000 -0.500000000000000 0.707106781186547 0.500000000000000 0.500000000000000

Visualization

cFigure; subplot(1,2,1); hold on; title('A non-orthonormal set'); hp1=quiverTriad(zeros(1,3),Q,2); axisGeom; camlight headlight; subplot(1,2,2); hold on; title('An orthonormal set'); hp2=quiverTriad(zeros(1,3),E,1); axisGeom; camlight headlight; gdrawnow;

* 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.

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