import java.util.$*$;

import javax.swing.$*$;

import java.awt.image.$*$;

import java.awt.$*$;

class Bezier extends JApplet $\{$

BufferedImage image $=$ new BufferedImage$(600,600,$ BufferedImage.TYPE$\_$INT$\_$ARGB$)$;

WritableRaster raster $=$ image.getRaster$()$;

private final double controlPoints$[][]$;

private final double steps;

Bezier$($double controPoints$[][],$ int steps$)\{$

this.controlPoints $=$ controPoints;

this.steps $=$ steps;

$\}$

public void init$()\{$

setSize$(1280,720)$;

repaint$()$;

$\}$

int$[]$ computePoint$($float u$)\{$

float c$0,$c$1,$c$2,$c$3$;

c$0=1-3*$u $+3*$u$*$u $-$ u$*$u$*$u;

c$1=3*$u $-6*$u$*$u $+3*$u$*$u$*$u;

c$2=3*$u$*$u $-3*$u$*$u$*$u;

c$3=$ u$*$u$*$u;

int ptx $=($int$)($c$0*$ controlPoints$[0][0]+$ c$1*$ controlPoints$[1][0]+$ c$2*$ controlPoints$[2][0]+$ c$3*$ controlPoints$[3][0])$;

int pty $=($int$)($c$0*$ controlPoints$[0][1]+$ c$1*$ controlPoints$[1][1]+$ c$2*$ controlPoints$[2][1]+$ c$3*$ controlPoints$[3][1])$;

int pts$[]=\{$ptx$,$ pty$\}$;

return pts;

$\}$

public void paint$($Graphics g$)\{$

int prevPointx $=0$;

int prevPointy $=0$;

int color$[]=\{255,0,0,255\}$;

for$($int i $=0$; i $$ steps; i$++)\{$

int$[]$ pts $=$ computePoint$($i$/($float$)$steps$)$;

int x $=$ pts$[0]$;

int y $=$ pts$[1]$;

if$($i $!=0)$

g$.$drawLine$($prevPointx$,$ prevPointy, x$,$ y$)$;

prevPointx $=$ x;

prevPointy $=$ y;

raster.setPixel$($x$,$ y$,$color$)$;

$\}$

g$.$drawImage$($image$,0,0,$ null$)$;

$\}$

$\}$

public class Main $\{$

public static void main$($String$[]$ args$)\{$

Scanner input $=$ new java.util.Scanner$($System$.$in$)$;

double points$[][]=$ new double$[4][2]$;

System.out.println$("$Enter p$1,$ p$1\text{'},$ p$2,$ p$2\text{'}$ x and y coordinates respectively"$)$;

for$($int i $=0$; i $$ points.length; i$++)\{$

points$[$i$][0]=$ input.nextInt$()$;

points$[$i$][1]=$ input.nextInt$()$;

$\}$

System.out.print$("$Enter how many steps to do: $")$;

int steps $=$ input.nextInt$()$;

JFrame frame $=$ new JFrame$("$Bezier Cubic Spline"$)$;

frame.setDefaultCloseOperation$($JFrame$.$EXIT$\_$ON$\_$CLOSE$)$;

Bezier curve $=$ new Bezier$($points$,$ steps$)$;

curve.setPreferredSize$($new Dimension$(600,600))$;

frame.add$($curve$)$;

frame.pack$()$;

frame.setVisible$($true$)$;

$\}$

$\}$

based on the prev code we need to do this:

$1.$Write a program to draw curves sing Beizer curve for P$1(200250),$ P$1`(300350)$ control points and P$2(550600),$ P$2`(500450)$ tangent vectors $.$

$2.$Modify the above program $,$along with the curve add an object shape of the ball at the end of the point P$2$ using $2$D graphics.