# pointSetDistMap

Below is a basic demonstration of the features of the pointSetDistMap function.

## Contents

```clear; close all; clc;

% PLOT SETTINGS
markerSize1=5;
markerSize2=5;
lineWidth=2;
fontSize=10;
faceAlpha=0.8;
```

## DEFORMING A 2D MESH

SIMULATING A 2D EXAMPLE

```interpMethod='pchip';
closeLoopOpt=1;
n=200;

%P1
t=linspace(0,2*pi,n);
t=t(1:end-1);
r=ones(size(t));
[x,y] = pol2cart(t,r);
P1=[x(:) y(:)];
[P1]=evenlySampleCurve(P1,n,interpMethod,closeLoopOpt);

%P2
t=linspace(0,2*pi,n);
t=t(1:end-1);
r=1+0.3*sin(3*t);
[x,y] = pol2cart(t,r);
P2=[x(:) y(:)];
[P2]=evenlySampleCurve(P2,n,interpMethod,closeLoopOpt);

%P1i
np=50;
[x,y]=meshgrid(linspace(-1,1,np));
P1i=zeros(numel(x(:)),2);
P1i(:,1)=x(:);
P1i(:,2)=y(:);
[IN,~] = inpolygon(P1i(:,1),P1i(:,2),P1(:,1),P1(:,2));
P1i=P1i(IN(:),:);
P1i=[P1i; P1];
P1i=unique(P1i,'rows');
DT = delaunayTriangulation(P1i(:,[1 2]));

%P2i
Fw=5;
[P2i]=pointSetDistMap(P1,P1i,P2,Fw);
```

PLOTTING RESULTS: Circles are boundary points which should be mapped exactly. Blue points are the initial and mapped points. Tesselation shows connectivity (which may become distorted)

```hf1=cFigure;;
subplot(1,2,1); hold on;
title('Initial','FontSize',fontSize);
patch('faces',DT.ConnectivityList,'Vertices',P1i,'FaceColor','g','FaceAlpha',faceAlpha);
plot(P1(:,1),P1(:,2),'ko-','MarkerSize',markerSize1);
plot(P1i(:,1),P1i(:,2),'b.','MarkerSize',markerSize2);
set(gca,'FontSize',fontSize);
view(2); grid on; axis equal; axis tight;

subplot(1,2,2); hold on;
title('Deformed','FontSize',fontSize);
patch('faces',DT.ConnectivityList,'Vertices',P2i,'FaceColor','r','FaceAlpha',faceAlpha);
plot(P2(:,1),P2(:,2),'ko-','MarkerSize',markerSize1);
plot(P2i(:,1),P2i(:,2),'b.','MarkerSize',markerSize2);
set(gca,'FontSize',fontSize);
view(2); grid on; axis equal; axis tight;
drawnow;
```

## DEFORMING A 3D MESH

SIMULATING A 3D EXAMPLE

```%P1
[F,P1,~]=geoSphere(3,1);

%P1i
np=15;
[x,y,z]=meshgrid(linspace(-1,1,np));
P1i=[x(:) y(:) z(:)];
DT = delaunayTriangulation(P1);
LI = ~isnan(pointLocation(DT,P1i));
P1i=[P1; P1i(LI,:)];
P1i=unique(P1i,'rows');
DT = delaunayTriangulation(P1i(:,[1 2]));

%P2
[PHI,THETA,R] = cart2sph(P1(:,1),P1(:,2),P1(:,3));
R=1+0.3*sin(3*PHI);
P2=P1;
[P2(:,1),P2(:,2),~]=sph2cart(PHI,THETA,R);

%P2i
Fw=5;
[P2i]=pointSetDistMap(P1,P1i,P2,Fw);
```
```Warning: Duplicate data points
have been detected and removed.
The Triangulation indices are
defined with respect to the
unique set of points in
delaunayTriangulation.
```

PLOTTING RESULTS: Circles are boundary points which should be mapped exactly. Blue points are the initial and mapped points. Tesselation shows connectivity (which may become distorted)

```hf2=cFigure;;
subplot(1,2,1); hold on;
title('Initial','FontSize',fontSize);
patch('faces',F,'Vertices',P1,'FaceColor','g','FaceAlpha',faceAlpha);
plot3(P1(:,1),P1(:,2),P1(:,3),'ko','MarkerSize',markerSize1);
plot3(P1i(:,1),P1i(:,2),P1i(:,3),'b.','MarkerSize',markerSize2);
set(gca,'FontSize',fontSize);
view(3); grid on; axis equal; axis tight;

subplot(1,2,2); hold on;
title('Deformed','FontSize',fontSize);
patch('faces',F,'Vertices',P2,'FaceColor','r','FaceAlpha',faceAlpha);
plot3(P2(:,1),P2(:,2),P2(:,3),'ko','MarkerSize',markerSize1);
plot3(P2i(:,1),P2i(:,2),P2i(:,3),'b.','MarkerSize',markerSize2);
set(gca,'FontSize',fontSize);
view(3); grid on; axis equal; axis tight;
drawnow;

%Create tesselations for vizualisation
V1=[P1; P1i]; V2=[P2; P2i];
[~,ind1,ind2]=unique(V1,'rows'); %remove double points
V1=V1(ind1,:);
V2=V2(ind1,:);
DT1 = delaunayTriangulation(V1);
TET=DT1.ConnectivityList;

%Create cut
Z=V1(:,3);
Ztet=mean(Z(TET),2);
Ltet=(Ztet<0);

%Convert elements of interest to patchable faces
[Ft,~]=element2patch(TET(Ltet,:),1:size(TET(Ltet,:),1));

%Only plot outer faces

%Get face counts
Fs=sort(Ft,2); %Sort so faces with same nodes have the same rows
[~,IND_F,IND_F_2]=unique(Fs,'rows');
F_uni=Ft(IND_F,:);
numF=size(Fs,1);
numFuni=size(F_uni,1);
logicColourMatrixEntry=sparse(IND_F_2,1:numF,1,numFuni,numF,numF);
F_count=full(sum(logicColourMatrixEntry,2));
Ftu=F_uni(F_count==1,:); %Get outer surfaces

hf3=cFigure;;
subplot(1,2,1); hold on;
title('Initial','FontSize',fontSize);
patch('faces',Ftu,'Vertices',V1,'FaceColor','g');
set(gca,'FontSize',fontSize);
view(3); grid on; axis equal; axis tight;

subplot(1,2,2); hold on;
title('Deformed','FontSize',fontSize);
patch('faces',Ftu,'Vertices',V2,'FaceColor','r');
set(gca,'FontSize',fontSize);
view(3); grid on; axis equal; axis tight;
drawnow;
```

GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

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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

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