# filletCurve

Below is a demonstration of the features of the filletCurve function

## Syntax

[VN]=filletCurve(Vt,r,np,closedLoopOption);

## Description

This function fillets a curve based on the input radius r using np points per fillet arc. If closedLoopOpt==1 then closed end conditions are used such that the end and start regions are also filleted.

## Examples

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

Plot settings

```fontSize=15;
markerSize1=45;
lineWidth1=2;
lineWidth2=5;
lineWidth3=2;
faceAlpha=0.5;
```

## Example 1: Filleting a non-closed curve in 2D

Simulating a curve with sharp features

```Vt=2*[-1 -1; -1 1 ; 1 1; 1 -1]; %A square
```
```%Setting control parameters
np=25; %Number of points used to construct each fillet edge
closedLoopOption=0; %Use 1 if curve represents a closed loop but containes unique points
VN=filletCurve(Vt,r,np,closedLoopOption);
```

Plotting results

```cFigure; hold on;
title('A filleted curve','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp1=plotV(Vt,'k.-.','lineWidth',lineWidth1,'MarkerSize',markerSize1);
hp2=plotV(VN,'r.-','lineWidth',lineWidth2);
legend([hp1 hp2],{'Input','Filleted'});
axisGeom(gca,fontSize);
drawnow;
```

## Example 2: Filleting a closed curve in 2D

```%Setting control parameters
np=25; %Number of points used to construct each fillet edge
closedLoopOption=1; %Use 1 if curve represents a closed loop but containes unique points
VN=filletCurve(Vt,r,np,closedLoopOption);
```

Plotting results

```cFigure; hold on;
title('A filleted curve','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp1=plotV(Vt,'k.-.','lineWidth',lineWidth1,'MarkerSize',markerSize1);
hp2=plotV(VN,'r.-','lineWidth',lineWidth2);
legend([hp1 hp2],{'Input','Filleted'});
axisGeom(gca,fontSize);
drawnow;
```

```%Setting control parameters
r=[0.5 1.5 0 0.75]; %Fillet radii for each point
np=25; %Number of points used to construct each fillet edge
closedLoopOption=1; %Use 1 if curve represents a closed loop but containes unique points
VN=filletCurve(Vt,r,np,closedLoopOption);
```

Plotting results

```cFigure; hold on;
title('A filleted curve','FontSize',fontSize);
xlabel('X','FontSize',fontSize); ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp1=plotV(Vt,'k.-.','lineWidth',lineWidth1,'MarkerSize',markerSize1);
hp2=plotV(VN,'r.-','lineWidth',lineWidth2);
legend([hp1 hp2],{'Input','Filleted'});
axisGeom(gca,fontSize); view(2);
drawnow;
```

## Example 4: Filleting a curve in 3D

Simulating a curve with sharp features

```Vt=[0 0 0; 10 0 0; 0 10 0; 10 10 10; 10 10 0; ];

%
%Setting control parameters
np=25; %Number of points used to construct each fillet edge
closedLoopOption=0; %Use 1 if curve represents a closed loop but containes unique points
VN=filletCurve(Vt,r,np,closedLoopOption);

%
% Plotting results
cFigure; hold on;
title('A filleted curve','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp1=plotV(Vt,'k.-.','lineWidth',lineWidth1,'MarkerSize',markerSize1);
hp2=plotV(VN,'r.-','lineWidth',lineWidth2);
legend([hp1 hp2],{'Input','Filleted'});
axisGeom(gca,fontSize);
drawnow;
```

## Example 5: Extruding a filleted curve for CAD like model building

```%Sketching side profile
Vt=[0 0 0; 10 0 0; 10 10 0; 20 15 0];

%Fillet sketch
r=[0 2 4 0]; %Fillet radius
np=25; %Number of points used to construct each fillet edge
closedLoopOption=0; %Use 1 if curve represents a closed loop but containes unique points
[Vc]=filletCurve(Vt,r,np,closedLoopOption);

pointSpacing=1;
Vc=evenlySpaceCurve(Vc,pointSpacing,'pchip',0);
```

Plotting sketch

```cFigure; hold on;
title('The side profile sketch','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);

hp1=plotV(Vt,'k.-.','lineWidth',lineWidth1,'MarkerSize',markerSize1);
hp2=plotV(Vc,'r.-','lineWidth',lineWidth2);
legend([hp1 hp2],{'Input','Filleted'});
axisGeom(gca,fontSize); view(2);
drawnow;
```

Extruding model

```cPar.depth=20;
cPar.patchType='tri';
cPar.dir=0;
cPar.n=[0 0 1];
cPar.closeLoopOpt=0;
numSteps=round(cPar.depth./pointSpacing);
numSteps=numSteps+double(iseven(numSteps)); %Force uneven
cPar.numSteps=numSteps;
[F_tri,V_tri]=polyExtrude(Vc,cPar);
```

Plotting meshed model

```hf2=cFigure;
title('The extruded surface mesh','FontSize',fontSize);
xlabel('X','FontSize',fontSize);ylabel('Y','FontSize',fontSize); zlabel('Z','FontSize',fontSize);
hold on;

hp1=plotV(Vc,'r.-','lineWidth',lineWidth2);
hp2=gpatch(F_tri,V_tri,'gw');
legend([hp1 hp2],{'Input curve','Extruded surface'});
axis equal; view(3); axis tight;  grid on;  set(gca,'FontSize',fontSize);
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.

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