Lagrangesrc.txt

//This applet implements interpolation of a certain number of
//points using Lagrange polynomials
import java.awt.*;
import java.applet.Applet;
import Matrix;
import java.lang.Math;
public class Lagrange extends Applet {

Matrix points;

//interpolating points

int numpoints;

Matrix mat;

//used to precompute basis functions

Image offscreenImg;

//used in double buffering

Graphics offscreenG;

double[] t;

//time values

static final int k = 100; //number of partitions

int moveflag;

//the point being moved, if any

Button restart;

Button addpoint;

Button subpoint;

boolean go = false;

//for restart button

boolean addpt = false; //flag for add point button

boolean subpt = false; //flag for subtracting point button

//used to initialize the applet

public void init() {

//start off with 5 points

numpoints = 5;

startagain();

//create time interval [0,1] with k partitions

t = new double[k+1];

for(int i=0;i<=k;i++)

t[i] = (double)i/(double)k;

//create matrix with current info

create();

//create offscreen buffer

offscreenImg = createImage(size().width,size().height);

offscreenG = offscreenImg.getGraphics();

restart = new Button("Restart");

add(restart);

addpoint = new Button("Add Point");

add(addpoint);

subpoint = new Button("Subtract Point");

add(subpoint);

}

//precompute the basis functions for Lagrange polynomials and evaluate

//over the time interval, store in matrix

public void create() {

mat = new Matrix(numpoints,k+1);

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Lagrangesrc.txt

double c;

for(int i=0;i<mat.rowsize();i++)

for(int j=0;j<mat.colsize();j++) {

c=1;

for(int h=0;h<numpoints;h++)

if(h!=i)

//calculate i,j position of matrix

c *= (t[j]-(double)h/(double)(numpoints-1))/

((double)i/(double)(numpoints-1)-

(double)h/(double)(numpoints-1));

mat.set(i,j,c);

}

//transpose matrix for later calculations

mat.trans();

}
//called internally by repaint()
public void update(Graphics g) {

paint(g);

}
//check if any of the buttons have been pressed
public boolean action(Event e, Object o) {

if (e.target == restart) {

go = true;

repaint();

return true;

}

else if(e.target == addpoint) {

addpt = true;

repaint();

return true;

}

else if(e.target == subpoint) {

if(numpoints>2) {

subpt = true;

repaint();

}

return true;

}

return false;

}
//Initialize all necessary data: points, moveflag
public void startagain() {

moveflag = numpoints;

points = new Matrix(numpoints,2);

double increment = (double)(size().width-60)/(double)(numpoints-1);

for(int i=0;i<numpoints;i++){

points.set(i,0,(i*increment)+30.0);

points.set(i,1,(double)size().height/2.0);

}

}
public void paint(Graphics g) {

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Lagrangesrc.txt

//prepare buffered screen for plot

setBackground(Color.white);

offscreenG.setColor(Color.white);

offscreenG.fillRect(0,0,size().width,size().height);

offscreenG.setColor(Color.black);

//if adding a point, create a new matrix and new set of points

if(addpt) {

numpoints++;

startagain();

create();

addpt = false;

}

//if subtracting a point, create new matrix and new set of points

if(subpt) {

numpoints--;

startagain();

create();

subpt = false;

}

//if restart button, start all over

if(go) {

startagain();

go = false;

}

//Display number of points

offscreenG.drawString("Points = "+String.valueOf(numpoints),20,20);

//plot points

for(int i=0;i<numpoints;i++)

offscreenG.fillOval((int)points.get(i,0)-2,

(int)points.get(i,1)-2,4,4);

//draw interpolating polynomial by multiplying precomputed basis

function

//matrix by the points, thus taking a linear combination, and plotting

output

Matrix plot = new Matrix(mat.mult(points));

for(int i=0;i<plot.rowsize()-1;i++)

//must round off the doubles in the matrix

offscreenG.drawLine((int)Math.round(plot.get(i,0)),

(int)Math.round(plot.get(i,1)),

(int)Math.round(plot.get(i+1,0)),

(int)Math.round(plot.get(i+1,1)));

//draw image from buffer to screen

g.drawImage(offscreenImg,0,0,this);

}
//check if user is clicking on any of the points
public boolean mouseDown(Event evt, int x, int y) {

Point p = new Point(x,y);

for(int i=0;i<numpoints;i++)

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Lagrangesrc.txt

for(int j=-2;j<3;j++)

for(int l=-2;l<3;l++)

if(p.equals(new Point((int)points.get(i,0)+j,

(int)points.get(i,1)+l)))

//set moveflag to the point being moved

moveflag=i;

return true;

}

public boolean mouseDrag(Event evt, int x, int y) {

//check if user is trying to drag an old point

if(moveflag < numpoints) {

//change the point being moved and redraw screen

points.set(moveflag,0,x);

points.set(moveflag,1,y);

repaint();

}

return true;

}

public boolean mouseUp(Event evt, int x, int y) {

moveflag = numpoints;

return true;

}

}

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