# evenlySampleCurve

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

## Contents

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

## Syntax

[Vg] = evenlySampleCurve(V,n,interpPar,closeLoopOpt,spacingFlag);

## Description

The evenlySampleCurve function samples a curve evenly in n points. The curve is parameterized using curve distance and can be closed loop if closeLoopOpt==1 (default=0). The resampling is performed using interpolation based on the method specified by interpPar. Available methods are those associated with interp1 i.e.: 'linear', 'nearest', 'next', 'previous', 'spline', 'pchip' (default), 'cubic', and also the custom 'biharmonic' method. Alternatively interpPar my be set as a scalar in the range 0-1 to use the csaps method for cubic spline based smoothening. The 5th input is spacingFlag and defines wether n should be interpretet as number of desired points (0) or as a desired point spacing (1).

The default values for the optional parameters are: n -> size(V,1) interpPar -> 'pchip' closeLoopOpt -> 0 spacingFlag -> 0

## Examples

Plot settings

```markerSize1=25;
lineWidth=2;
```

## EXAMPLE 1: Evenly sampling a curve

```%Simulating the case of an unevenly sampled curve
ns=11;
x=linspace(0,2*pi,ns);
y=4*sin(x);
V=[x(:) y(:)];
```

Resampling a curve evenly (point spacing based on number of points)

Below the original and resampled curves are shown. Note that the original curve is sampled evenly allong the x-axis but is not evenly sampled allong the curve (point spacing not even) For instance the spacing is smallest in flat regions and lowest in steep regions.Various interpolation methods are shown.

```interpMethods={'linear','pchip','spline','biharmonic'};
closeLoopOpt=0; %Option for closed curve
n=50; %New number of points

cFigure;
subplot(2,3,1); hold on;
title('Input data');
plotV(V,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;
drawnow;

for q=1:1:numel(interpMethods)

[Vg]=evenlySampleCurve(V,n,interpMethods{q},closeLoopOpt);

subplot(2,3,q+1); hold on;
title(['Resampled, ',interpMethods{q},' interpolation']);
plotV(Vg,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(Vg,'g.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;
end
drawnow;
``` ## EXAMPLE 2: Upsample a closed polygon

```%Simulating the case of an unevenly sampled curve
ns=4;
t=linspace(0,2*pi,ns+1)';
t=t(1:end-1);%+0.25*pi;
V=[cos(t) sin(t)];
```

Resampling a curve evenly (point spacing based on number of points)

Below the original and resampled curves are shown. Note that the original curve is sampled evenly allong the x-axis but is not evenly sampled allong the curve (point spacing not even) For instance the spacing is smallest in flat regions and lowest in steep regions.Various interpolation methods are shown.

```interpMethods={'linear','pchip','spline','biharmonic'};
closeLoopOpt=1; %Option for closed curve
n=ns*20; %New number of points

cFigure;
subplot(2,3,1); hold on;
title('Input data');
plotV(V,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;
drawnow;

for q=1:1:numel(interpMethods)

[Vg]=evenlySampleCurve(V,n,interpMethods{q},closeLoopOpt);

subplot(2,3,q+1); hold on;
title(['Resampled, ',interpMethods{q},' interpolation']);
plotV(Vg,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(Vg,'g.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;
end
drawnow;
``` ## EXAMPLE 3: Evenly sampling a closed curve

```%Simulating the case of an unevenly sampled loop curve
ns=75;
t=sort(linspace(0,2*pi,ns)+pi/10*rand(1,ns));
t=unique(t); %removing double points
t=t(t<2*pi);%Removing 2*pi points since they are the same as the 0 point
r=3+2.*cos(6*t);
[x,y] = pol2cart(t,r);
z=y;
V=[x(:) y(:) z(:)];

interpMethod='pchip';
closeLoopOpt=1;
n=200;
[Vg]=evenlySampleCurve(V,n,interpMethod,closeLoopOpt);
```

Resampling a curve evenly (point spacing based on number of points)

Below the original and resampled curves are shown. Note that the original curve is sampled evenly allong the x-axis but is not evenly sampled allong the curve (point spacing not even) For instance the spacing is smallest in flat regions and lowest in steep regions.Various interpolation methods are shown.

```interpMethods={'linear','pchip','spline','biharmonic'};
closeLoopOpt=1; %Option for closed curve
n=ns*2; %New number of points

cFigure;
subplot(2,3,1); hold on;
title('Input data');
plotV(V,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(3); grid on; axis equal; axis tight; box on;
drawnow;

for q=1:1:numel(interpMethods)

[Vg]=evenlySampleCurve(V,n,interpMethods{q},closeLoopOpt);

subplot(2,3,q+1); hold on;
title(['Resampled, ',interpMethods{q},' interpolation']);
plotV(Vg,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(Vg,'g.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(3); grid on; axis equal; axis tight; box on;
end
drawnow;
``` ## EXAMPLE 4: Resampling and smoothening a curve based on CSAPS

By setting interpMethod as a scalar between 0 and 1 it is interpreted as a smoothening parameter for csaps based cubic smoothening.

```ns=125;
t=sort(linspace(0,2*pi,ns)+pi/10*rand(1,ns));
t=unique(t); %removing double points
t=t(t<2*pi);%Removing 2*pi points since they are the same as the 0 point
r=3+2.*cos(6*t);
[x,y] = pol2cart(t,r);
z=y;
V=[x(:) y(:) z(:)];

V=V+0.2.*randn(size(V));

interpMethod=0.25; %Setting a scaler triggers csaps based smoothening
closeLoopOpt=1;
[Vg]=evenlySampleCurve(V,n,interpMethod,closeLoopOpt);

cFigure;
subplot(1,2,1); hold on;
title('Unevenly sampled and noisy');
plotV(V,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(3); grid on; axis equal; axis tight;  box on;
subplot(1,2,2); hold on;
title('Evenly sampled and smoothened');
plotV(Vg,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(Vg,'g.','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1);
view(3); grid on; axis equal; axis tight;  box on;
drawnow;
``` ## EXAMPLE 5: Using point spacing instead of number of points

If the spacingFlag value is set to true (or 1) then the second input is instead interpretet as the desired point spacing.

```ns=75;
t=sort(linspace(0,2*pi,ns)+pi/10*rand(1,ns));
t=unique(t); %removing double points
t=t(t<2*pi);%Removing 2*pi points since they are the same as the 0 point
r=3+2.*cos(6*t);
[x,y] = pol2cart(t,r);
z=y;
V=[x(:) y(:) z(:)];

interpMethod='pchip';
closeLoopOpt=1;
spacingFlag=1;
pointSpacing=0.5;
[Vg]=evenlySampleCurve(V,pointSpacing,interpMethod,closeLoopOpt,spacingFlag);

cFigure;
subplot(1,2,1); hold on;
title('Input data');
plotV(V,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(V,'r.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;
drawnow;

subplot(1,2,2); hold on;
title('Resampled with a desired point spacing');
plotV(Vg,'k-','MarkerSize',markerSize1,'lineWidth',lineWidth);
plotV(Vg,'g.','MarkerSize',markerSize1,'lineWidth',lineWidth);
view(2); grid on; axis equal; axis tight; box on;

drawnow;
```  GIBBON www.gibboncode.org

Kevin Mattheus Moerman, gibbon.toolbox@gmail.com

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Copyright (C) 2019 Kevin Mattheus Moerman

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