# affineTransformationMatrixDirect

Below is a demonstration of the features of the affineTransformationMatrixDirect function

## Contents

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

## Syntax

[M]=affineTransformationMatrixDirect(V1,V2);

## Description

This function computes the affine transformation matrix (translation, rotation, and scaling). For the two point matches input sets V1 and V2.

## Examples

Plot settings

```fontSize=15;
faceAlpha=1;
edgeColor='k';
```

## Determine the affine transformation to overlay two surfaces

Below is a demonstration of the features of the affineTransformationMatrixDirect function

```% Load example patch data
[F,Vd]=parasaurolophus;

%Translation
OR=[-1 2 -3]; %Translations
T  = [1 0 0 OR(1);...
0 1 0 OR(2);...
0 0 1 OR(3);...
0 0 0 1];
%Rotation
a=[-0.25*pi 0.75*pi 0.1*pi]; %Euler angles
R  = eye(4,4); R(1:3,1:3)=euler2DCM(a);

%Scaling
v=[2 3 1]; %Scaling factors
S  = [v(1) 0    0    0;...
0    v(2) 0    0;...
0    0    v(3) 0;...
0    0    0    1];

M_true  = T * R * S; %The true transformation matrix

%Point set 1
V1=Vd+0.5;

%Point set 2
V2=tform(M_true,V1);
```

Plotting input data

```hf=cFigure;
title('The untransformed surfaces','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp=patch('Faces',F,'Vertices',V1,'FaceColor','g','FaceAlpha',faceAlpha);

hp=patch('Faces',F,'Vertices',V2,'FaceColor','r','FaceAlpha',faceAlpha,'edgeColor',edgeColor);

set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal; box on;
drawnow;
```

Get the transformation matrix for the point matched data using affineTransformationMatrixDirect

```[M_fit]=affineTransformationMatrixDirect(V1,V2);

V1f=tform(M_fit,V1);
```

Plotting results

```hf=cFigure;
title('The green surfaces transformed towards the red','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp=patch('Faces',F,'Vertices',V2,'FaceColor','r','FaceAlpha',0.5,'edgeColor',edgeColor);

hp=patch('Faces',F,'Vertices',V1f,'FaceColor','none','FaceAlpha',0.5,'edgeColor','g');
% hp=patch('Faces',F,'Vertices',V2ff,'FaceColor','none','FaceAlpha',0.5*2,'edgeColor','b');

set(gca,'FontSize',fontSize);
view(3); axis tight;  axis equal; box on;
drawnow;
```

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.

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.

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