we a java program that draw the prophet dome, and draw a leaf, by using hermite: package org.example;

import javax.swing.$*$;

import java.util.$*$;

import java.awt.$*$;

import java.awt.image.$*$;

class Hermite extends JApplet $\{$

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

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

private double controlPoints$[][]$;

private double steps;

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

this.controlPoints $=$ controPoints;

this.steps $=$ steps;

$\}$

@Override

public void init$()\{$

$//$ TODO start asynchronous download of heavy resources

setBackground$($Color$.$YELLOW$)$;

setSize$(800,600)$;

repaint$()$;

$\}$

$//$ TODO overwrite start$(),$ stop$()$ and destroy$()$ methods

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

$//$hermite blending functions

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

h$0=2*$ u $*$ u $*$ u $-3*$ u $*$ u $+1$;

h$1=-2*$ u $*$ u $*$ u $+3*$ u $*$ u;

h$2=$ u $*$ u $*$ u $-2*$ u $*$ u $+$ u;

h$3=$ u $*$ u $*$ u $-$ u $*$ u;

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

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

$//$ Draw the line from previous end point to the current end point

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$2,$ p$1\text{'},$ p$2\text{'}$ 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$("$Hermite splines"$)$;

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

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

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

frame.add$($curve$)$;

frame.pack$()$;

frame.setVisible$($true$)$;

$\}$

$\}$