Program 5

Program to implement Cohen-Suderland Line

Clipping Algorithm. Make provision to specify

the input line, window for clipping and view

port for displaying the clipped image.

Cohen-Sutherland Line-Clipping:

• It is a very good algorithm for clipping pictures that are

larger than the screen.

• This algorithm divides a 2D space into 9 parts, of which

only the middle part (view port) is visible.

• The 9 regions can be uniquely identified using a 4 bit

code. This 4 bit code is called outcode.

Cohen-Sutherland Line-Clipping

Outcode

9 8 10

1 0 2

5 4 6

We use the order Left,

Right, Bottom, Top for

these 4 bits.

Cohen-Sutherland Line-Clipping

Outcodes

1001 1000 1010

0001 0000 0010

0101 0100 0110

We use the order Left,

Right, Bottom, Top for

these 4 bits.

Cohen-Sutherland Line-Clipping

Region Outcodes

1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

XminXmax

Ymin

Ymax

Cohen-Sutherland Line-Clipping

Region Outcodes

Bit Number 1 0

Fourth (LSB) Left of left edge X<Xmin Right of left edge X>Xmin

Third Right of right edge X>Xmax Left of right edge X<Xmax

Second Below bottom edge Y<Ymin Above bottom edge Y>Ymin

First (MSB) Above top edge Y>Ymax Below top edge Y<Ymax

1001 1000 1010

0001 0000 0010

0101 0100 0110

XminXmax

Ymin

Ymax

Line-Clipping Algorithm

Assume two endpoints are p0 and p1

1. If code(p0) OR code(p1) is 0000,• the line can be trivially accepted.• the line is drawn.

2. If code(p0) AND code(p1) is NOT 0000,• the line can be trivially rejected.• the line is not drawn at all.

3. Otherwise, compute the intersection points of theline segment and window boundary lines (makesure to check all the boundary lines)

Line-Clipping

1001 1000 1010

0001 0000 0010

0101 0100 0110

XminXmax

Ymin

Ymax

L1

L2

L3

Line L1

code1 = 0000, code2 = 0000Is code1|code2==0? Trivial accept

Is code1 & code2!=0? Trivial reject

Else clip the line until one code becomes 0

code1 | code2 = 0000 | 0000 = 0000Trivial accept completely – no need to clip.

Line-Clipping

1001 1000 1010

0001 0000 0010

0101 0100 0110

XminXmax

Ymin

Ymax

L1

L2

L5

Line L2code1 = 0101, code2 = 0100

Is code1|code2==0? Trivial accept

Is code1 & code2!=0? Trivial reject

Else clip the line until one code becomes 0

code1 | code2 = 0101 | 0100 = 0101 (NOT 0000) : No Trivial acceptCode1 & code2 = 0101 & 0100 = 0100 (NOT 0000) : Trivial reject

Line-Clipping

1001 1000 1010

0001 0000 0010

0101 0100 0110

XminXmax

Ymin

Ymax

L1

L2

L5

Line L5

code1 = 0000, code2 = 1010Is code1|code2==0? Trivial accept

Is code1 & code2!=0? Trivial reject

Else clip the line until one code becomes 0

code1 | code2 = 0000 | 1010 = 1010 (NOT 0000) : No Trivial acceptcode1 & code2 = 0000 & 1010 = 0000 : No Trivial reject Clip the line

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

a

c

f

e

d

b

x0,y0

x1,y1Intersection computationLine equationy = y0 + m(x - x0)wherem = y1 - y0

x1 - x0

x=x min x=x max

y=y max

y=y min

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

a

c

f

e

d

b

x0,y0

x1,y1

Line intersection with the left vertical boundary

Assume the intersection is cx = xmin

y = y0 +m(xmin – x0)

Line ab is clipped w.r.t. x= xmin

now ab becomes cb

Intersection computationLine equationy = y0 +m(x – x0)wherem = y1 – y0

x1 – x0

x=x max

y=y max

y=y min

x=x min x=x max

y=y max

y=y min

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

c

f

e

d

b

x0,y0

x1,y1

Line intersection with the bottom boundary

Assume the intersection is fy = ymin

x = (1/m) (ymin – y0) + x0Line cb is clipped w.r.t. y= ymax

Line cb becomes fb

Intersection computationLine equationy = y0 +m(x – x0)wherem = y1 – y0

x1 – x0

x=x min x=x max

y=y max

y=y min

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

f

e

x0,y0

Line intersection with the top boundary

Assume the intersection is dy = ymax

x = 1/m (ymax – y0) + x0Line fb is clipped w.r.t. y=ymax

line fb becomes fd

Intersection computationLine equationy = y0 +m(x – x0)wherem = y1 – y0

x1 – x0

x=x min x=x max

y=y max

y=y minf

e

dx1,y1

b

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

f

e

x0,y0

Line intersection with the right boundary

Assume the intersection is ex = xmax

y = y0 + m(xmax – x0)Line fd is clipped w.r.t. x=xmax

line fd becomes fe

Intersection computationLine equationy = y0 +m(x – x0)wherem = y1 – y0

x1 – x0

x=x min x=x max

y=y max

y=y min

d

Line-Clipping Example1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

f

e

x0,y0

x1,y1

FINALLY…………….

ab -----> cbcb -----> fbfb -----> fdfd -----> fe

x=x min x=x max

y=y max

y=y min

#include<GL/glut.h>

#define outcode int

double xmin=50,ymin=50, xmax=100,ymax=100;

// Window boundaries

double xvmin=200,yvmin=200,xvmax=300,yvmax=300;

// Viewport boundaries

double m;

//bit codes for the right, left, top, & bottom

const int LEFT = 1;

const int RIGHT = 2;

const int BOTTOM = 4;

const int TOP = 8;

//used to compute bit codes of a point

outcode ComputeOutCode (double x, double y);

//Cohen-Sutherland clipping algorithm clips a line from

//P0 = (x0, y0) to P1 = (x1, y1) against a rectangle with

//diagonal from (xmin, ymin) to (xmax, ymax).

void CohenSutherlandLineClipAndDraw(double x0, double y0,double x1, double y1){

//Outcodes for P0, P1, and whatever point lies outside the clip rectangleoutcode outcode0, outcode1, outcodeOut;bool accept = false, done = false;

outcode0 = ComputeOutCode (x0, y0);outcode1 = ComputeOutCode (x1, y1);m= (y1-y0)/(x1-x0);do{

if (!(outcode0 | outcode1)) //logical or is 0 Trivially accept & exit{

accept = true;done = true;

}else if (outcode0 & outcode1)//logical and is not 0.Trivially reject &exitdone = true;

else { /* failed both tests, so calculate the line segment to clip from an outside point to an intersection with clip edge */

double x, y; outcodeOut = outcode0? outcode0: outcode1;

if (outcodeOut& TOP) //point is above the clip rectangle {

x = x0 + (1/m) * (ymax – y0);y = ymax;

}

else if (outcodeOut& BOTTOM) //point is below the clip rectangle {

x = x0 + (1/m) * (ymin – y0);y = ymin;

}

else if(outcodeOut& RIGHT) //point is to right of clip rectangle {

y = y0 +m*(xmax – x0);x = xmax;

}

else // Left //point is to the left of clip rectangle {

y = y0 +m*(xmin – x0);x = xmin;

}

//Now we move outside point to intersection point to clip //and get ready for next pass.

if (outcodeOut == outcode0) {

x0 = x; y0 = y; outcode0 = ComputeOutCode (x0, y0);

} else {

x1 = x; y1 = y; outcode1= ComputeOutCode (x1, y1);

}}

}while (!done);

if (accept){ double sx=(xvmax-xvmin)/(xmax-xmin);

double sy=(yvmax-yvmin)/(ymax-ymin);double vx0=xvmin+(x0-xmin)*sx;double vy0=yvmin+(y0-ymin)*sy;double vx1=xvmin+(x1-xmin)*sx;double vy1=yvmin+(y1-ymin)*sy;glColor3f(1.0, 0.0, 0.0); // new view port in red colorglBegin(GL_LINE_LOOP);

glVertex2f(xvmin, yvmin);glVertex2f(xvmax, yvmin);glVertex2f(xvmax, yvmax);glVertex2f(xvmin, yvmax);

glEnd();glColor3f(0.0,0.0,1.0); // clipped line in blue colorglBegin(GL_LINES);

glVertex2d (vx0, vy0);glVertex2d (vx1, vy1);

glEnd();}

}

outcode ComputeOutCode (double x, double y){

outcode code = 0;if (y >ymax) //above the clip windowcode |= TOP;else if (y <ymin) //below the clip windowcode |= BOTTOM;if (x >xmax) //to the right of clip windowcode |= RIGHT;else if (x <xmin) //to the left of clip windowcode |= LEFT;return code;

}

Bit Number 1 0

Fourth (LSB) Left of left edge X<Xmin Right of left edge X>Xmin

Third Right of right edge X>Xmax Left of right edge X<Xmax

Second Below bottom edge Y<Ymin Above bottom edge Y>Ymin

First (MSB) Above top edge Y>Ymax Below top edge Y<Ymax

void display(){

double x0=60,y0=20,x1=80,y1=120;glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0,0.0,0.0); //draw the line with red colorglBegin(GL_LINES);

glVertex2d (x0, y0);glVertex2d (x1, y1);

glEnd();glColor3f(0.0, 0.0, 1.0); //draw a blue colored windowglBegin(GL_LINE_LOOP);

glVertex2f(xmin, ymin);glVertex2f(xmax, ymin);glVertex2f(xmax, ymax);glVertex2f(xmin, ymax);

glEnd();CohenSutherlandLineClipAndDraw(x0,y0,x1,y1);glFlush();

}

void myinit(){

glClearColor(1.0,1.0,1.0,1.0);glColor3f(1.0,0.0,0.0);glMatrixMode(GL_PROJECTION);glLoadIdentity();gluOrtho2D(0.0,499.0,0.0,499.0);

}

void main(int argc, char** argv){

glutInit(&argc,argv);glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);glutInitWindowSize(500,500);glutCreateWindow("Cohen Suderland Line Clipping Algorithm");glutDisplayFunc(display);myinit();glutMainLoop();

}

Cohen-Sutherland Line-Clipping

1001 1000 1010

0001 0000 0010

0101 0100 0110

XminXmax

Ymin

Ymax

AlgorithmIs code1|code2==0? Trivial acceptIs code1 & code2!=0? Trivial rejectElse clip the line until one code becomes 0

Intersection computationLine equationy = y0 +m(x – x0)wherem = y1 – y0

x1 – x0

Line intersection with the left boundaryx = xmin

y = y0 +m(xmin – x0)

Line intersection with the right boundaryx = xmax

y = y0 + m(xmax – x0)

Line intersection with the bottom boundaryy = ymin

x = (1/m) (ymin – y0) + x0

Line intersection with the top boundaryy = ymax

x = 1/m (ymax – y0) + x0

1001 1000 1010

0001 0000 0010

0101 0100 0110

Xmin Xmax

Ymin

Ymax

Bit Number 1 0

Fourth (LSB) Left of left edge X<Xmin Right of left edge X>Xmin

Third Right of right edge X>Xmax Left of right edge X<Xmax

Second Below bottom edge Y<Ymin Above bottom edge Y>Ymin

First (MSB) Above top edge Y>Ymax Below top edge Y<Ymax

Checking the Edges