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```// <applet code="Curve" width=512 height=512></applet>
// FB 201003265
// Create a curve that passes thru N randomly selected points.
import java.applet.Applet;
import java.awt.*;
import java.awt.image.*;
import java.util.Random;

public class Curve extends Applet
{
Image img;
int w,h,x,y,pix[],red,green,blue,alpha;
Random rng=new Random();

int n=rng.nextInt(10)+5; // n random points
int[] arx=new int[n];
int[] ary=new int[n];

public void init()
{
w=getSize().width;
h=getSize().height;
alpha=255;
pix=new int[w*h];
img = createImage(new MemoryImageSource(w, h, pix, 0, w));

// n random points
for(int i=0;i<n;i++)
{
arx[i]=rng.nextInt(w);
ary[i]=rng.nextInt(h);
}

double wgh;
int y;
double sum;
double sumw;
boolean flag;

for(x=0;x<w;x++)
{
flag=false;
sum=0.0;
sumw=0.0;
y=0;
for(int i=0;i<n;i++)
{
if(x!=arx[i])
{
//wgh=1.0/Math.pow(Math.abs((double)(x-arx[i])),1.0); // linear
wgh=1.0/Math.pow(Math.abs((double)(x-arx[i])),2.0); // quadratic
//wgh=1.0/Math.pow(Math.abs((double)(x-arx[i])),3.0); // cubic
sumw+=wgh;
sum+=(ary[i]*wgh);
}
else
{
flag=true;
y=ary[i];
break;
}
}
if(flag==false)
{
y=(int)(sum/sumw);
}

red=36;
green=76;
blue=16;
pix[w*y+x]=(alpha<<24)|(red<<16)|(green<<8)|blue;

}

img = createImage(new MemoryImageSource(w, h, pix, 0, w));
}

public void paint(Graphics g)
{
g.drawImage(img,0,0,this);

// show the n points on the curve
for(int i=0;i<n;i++)
{
g.drawOval(arx[i]-5,ary[i]-5,10,10);
}

long ctm=System.currentTimeMillis();
while((System.currentTimeMillis()-ctm)<3000) {;}
init();
}
}
```