Spline.java

//This applet implements interpolation using relaxed cubic splines
//The user can click on six points and move them around and the
//spline will be redrawn in real time
import java.awt.*;
import java.applet.Applet;
public class Spline extends Applet {

Point[] points;

//points to be interpolated

Point[] control;

//control points

int numpoints;

Image offscreenImg;

//used in double buffering

Graphics offscreenG;

double t;

//time variable

static final double k = .05; //partition length

int moveflag;

//point movement

Button polygon;

boolean poly = false;

//this method initializes the applet

public void init() {

//start off with 6 points

points = new Point[6];

control = new Point[6];

numpoints = 6;

moveflag = numpoints;

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

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

points[i] = new Point((i*increment)+30,(int)(size().height/2));

//create offscreen buffer

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

offscreenG = offscreenImg.getGraphics();

//put "Polygon" button on screen

polygon = new Button("Polygon");

add(polygon);

}

//this method is called by the repaint() method

public void update(Graphics g) {

paint(g);

}

public void paint(Graphics g) {

//points to be plotted

int x1,y1,x2,y2;

//Clear screen and set colors

setBackground(Color.white);

offscreenG.setColor(Color.white);

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

offscreenG.setColor(Color.black);

//check if user wants control polygon and points drawn

1

---

Spline.java
if(poly) {
//draw control polygon and control points
for(int i=0;i<numpoints-1;i++) {
offscreenG.fillOval(points[i].x-2,points[i].y-2,4,4);
offscreenG.fillOval((int)(.6667*control[i].x+.3333*control[i+1].x)
-2,

(int)(.6667*control[i].y+.3333*control[i+1].y)
-2,4,4);
offscreenG.fillOval((int)(.3333*control[i].x+.6667*control[i+1].x)
-2,

(int)(.3333*control[i].y+.6667*control[i+1].y)
-2,4,4);
offscreenG.fillOval(points[i+1].x-2,points[i+1].y-2,4,4);
offscreenG.drawLine(points[i].x,points[i].y,(int)(.6667*control[i]
.x+

.3333*control[i+1].x),(int)(.6667*control[i].y
+
.3333*control[i+1].y));
offscreenG.drawLine((int)(.6667*control[i].x+.3333*control[i+1].x)
,

(int)(.6667*control[i].y+.3333*control[i+1].y)
,

(int)(.3333*control[i].x+.6667*control[i+1].x)
,

(int)(.3333*control[i].y+.6667*control[i+1].y)
);
offscreenG.drawLine((int)(.3333*control[i].x+.6667*control[i+1].x)
,

(int)(.3333*control[i].y+.6667*control[i+1].y)
,
points[i+1].x,points[i+1].y);
}
}
//Change interpolating points into control points
control[0] = new Point(points[0].x,points[0].y);
control[numpoints-1] = new Point(points[numpoints-1].x,
points[numpoints-1].y);
x1=(int)(1.6077*(double)points[1].x-.26794*(double)points[0].x-
.43062*(double)points[2].x+.11483*(double)points[3].x-
.028708*(double)points[4].x+.004785*(double)points[5].x);
y1=(int)(1.6077*(double)points[1].y-.26794*(double)points[0].y-
.43062*(double)points[2].y+.11483*(double)points[3].y-
2

---

Spline.java

.028708*(double)points[4].y+.004785*(double)points[5].y);

control[1] = new Point(x1,y1);
x1=(int)(-.43062*(double)points[1].x+.07177*(double)points[0].x+

1.7225*(double)points[2].x-.45933*(double)points[3].x+

.11483*(double)points[4].x-.019139*(double)points[3].x);

y1=(int)(-.43062*(double)points[1].y+.07177*(double)points[0].y+

1.7225*(double)points[2].y-.45933*(double)points[3].y+

.11483*(double)points[4].y-.019139*(double)points[3].y);

control[2] = new Point(x1,y1);
x1=(int)(.11483*(double)points[1].x-.019139*(double)points[0].x-

.45933*(double)points[2].x+1.7225*(double)points[3].x-

.43062*(double)points[4].x+.07177*(double)points[5].x);

y1=(int)(.11483*(double)points[1].y-.019139*(double)points[0].y-

.45933*(double)points[2].y+1.7225*(double)points[3].y-

.43062*(double)points[4].y+.07177*(double)points[5].y);

control[3] = new Point(x1,y1);
x1=(int)(-.028708*(double)points[1].x+.004785*(double)points[0].x+

.114835*(double)points[2].x-.43062*(double)points[3].x+

1.6077*(double)points[4].x-.26794*(double)points[5].x);

y1=(int)(-.028708*(double)points[1].y+.004785*(double)points[0].y+

.114835*(double)points[2].y-.43062*(double)points[3].y+

1.6077*(double)points[4].y-.26794*points[5].y);

control[4] = new Point(x1,y1);
//Plot points
for(int i=0;i<numpoints;i++)

offscreenG.fillOval(points[i].x-2,points[i].y-2,4,4);

//draw n bezier curves using Bernstein Polynomials
x1=points[0].x;
y1=points[0].y;
for(int i=1;i<numpoints;i++) {

for(t=i-1;t<=i;t+=k) {

x2=(int)((double)points[i-1].x+(t-(i-1))*(-3*(double)points[i-1].x

+

3*(.6667*(double)control[i-1].x+.3333*(double)control[i].x)+

(t-(i-1))*(3*(double)points[i-1].x-6*(.6667*(double)control[i-1

].x+

.3333*(double)control[i].x)+3*(.3333*(double)control[i-1].x+

.6667*(double)control[i].x)+(-(double)points[i-1].x+

3*(.6667*(double)control[i-1].x+.3333*(double)control[i].x)-

3*(.3333*(double)control[i-1].x+.6667*(double)control[i].x)+

(double)points[i].x)*(t-(i-1)))));

y2=(int)((double)points[i-1].y+(t-(i-1))*(-3*(double)points[i-1].y

+

3*(.6667*(double)control[i-1].y+.3333*(double)control[i].y)+

(t-(i-1))*(3*(double)points[i-1].y-6*(.6667*(double)control[i-1

].y+

.3333*(double)control[i].y)+3*(.3333*(double)control[i-1].y+

.6667*(double)control[i].y)+(-(double)points[i-1].y+

3*(.6667*(double)control[i-1].y+.3333*(double)control[i].y)-

3

---

Spline.java

3*(.3333*(double)control[i-1].y+.6667*(double)control[i].y)+

(double)points[i].y)*(t-(i-1)))));

offscreenG.drawLine(x1,y1,x2,y2);

x1=x2;

y1=y2;

}

}

//draw buffered image to screen

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

}

//check if user has pushed polygon button

public boolean action(Event e, Object o) {

if (e.target == polygon) {

if(poly)

poly = false;

else

poly = true;

repaint();

return true;

}

return false;

}

//Check if user has clicked on point

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

Point p = new Point(x,y);

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

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

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

if(p.equals(new Point(points[i].x+j,

points[i].y+l)))

//set moveflag to the ith point

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) {

//move the point and redraw screen

points[moveflag].move(x,y);

repaint();

}

return true;

}

//if user unclicks mouse, reset moveflag

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

moveflag = 6;

return true;

}

}

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