Liang-Barsky Parametric Line Clipping

2) Write an OpenGL Program to implement Liang-Barsky line clipping algorithm.

This is a parametric line clipping algorithm.

The parameter t is a fraction between 0 and 1. So your lessons in ratios in school are useful in this program. The thing is if we know the parameter t on a line from (x1,y1) to (x2,y2) we can find any point(x,y) on the line by:

x=x1+t*dx;
y=y1+t*dy;

where dx and dy are x2-x1 and y2-y1 respectively. So starting from (x1,y1) t gives an idea of how much far have we gone towards (x2,y2).

For clipping we find t value of intersection points. There are four intersection points of a line with four edges of the window. If at an intersection point if line is going into the window it means it is a potentially entering point.

If intersection point is such that line is leaving the window then it is potentially leaving. We consider lines going from left to right and bottom to top.
Argument holds if line is in any other direction.



In this figure Line number 1 looks proper and its part is inside the window. It starts with line entering bottom edge then entering left edge then leaving top edge and then leaving right edge.
Something wrong with Line Number 2. It enters bottom edge then leaves top edge and then enters left edge and then leaves right edge(not shown). So since entering intersection point has crossed over after the leaving intersection point. Hence the line is rejected.
Lines no. 3 are horizontal and dy=0 so they go to third condition in cliptest function and are rejected.
Ditto with lines no 4. where dx=0;
*/







#include<stdio.h>
#include<GL/glut.h>

double xmin=50, ymin=50, xmax=100,ymax=100; //window boundaries
double xvmin=200,yvmin=200,xvmax=300, yvmax=300; //viewport boundaries
int x1,y1,x2,y2;
int cliptest(double p,double q,double *t1,double *t2)
{      // p is denominator in division and q is numerator                 
// t1 is t entering and t2 is t leaving
    double t=q/p;
    if(p<0.0)        //potentially entry point ,update te
    {    if(t>*t1) *t1=t;
        if(t>*t2) return(0); //line portion is outside as in line no 2 where t(entering)
                                       // has become more than t(leaving)
    }
    else if(p>0.0) //potentially leaving point ,update tl
        {
        if(t<*t2) *t2=t;
            if(t<*t1) return(0); //line portion is outside
        }
        else if(p==0.0)
            { if(q<0.0)
                 return(0);//line parallel to edge but outside
            }
            return(1);
}
void liangbaraskylineclipanddraw(double x0,double y0,double x1,double y1)
{
    double dx= x1-x0,dy=y1-y0, te=0.0,tl=1.0;


    if(cliptest(-dx,x0-xmin,&te,&tl))// inside test wrt left edge
// t for the left edge is t=(xmin-x0) /dx .... order of numerator is reversed and you get -dx
    if(cliptest(dx,xmax-x0,&te,&tl))// inside test wrt right edge
// t for the right edge is t=(xmax-x0)/dx.... first parameter becomes q and second p then t=q/p
    if(cliptest(-dy,y0-ymin,&te,&tl))// inside test wrt bottom edge
// same story numerator by demoninator to find t
    if(cliptest(dy,ymax-y0,&te,&tl))// inside test wrt top edge
// in one way cohen sutherland and liang barasky are similar
    {
        if(tl<1.0)
        {
            x1=x0+tl*dx;
            y1=y0+tl*dy;
        }
        if(te>0.0)
        {
            x0=x0+te*dx;
            y0=y0+te*dy;
        }
    }
    //window to viewport mappings
    double sx= (xvmax-xvmin)/(xmax-xmin);// scale parameters
            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;
// draw a red colored viewport
        glColor3f(1.0,0.0,0.0);
        glBegin(GL_LINE_LOOP);
        glVertex2f(xvmin,yvmin);
        glVertex2f(xvmax,yvmin);
        glVertex2f(xvmax,yvmax);
        glVertex2f(xvmin,yvmax);
        glEnd();
        glColor3f(0.0,0.0,1.0); //draw blue colored clip line
        glBegin(GL_LINES);
        glVertex2d(vx0,vy0);
        glVertex2f(vx1,vy1);
        glEnd();

}
void display()
{
    double x0=60,y0=20,x1=80,y1=120;
    glClear(GL_COLOR_BUFFER_BIT);
    glColor3f(1.0,0.0,0.0);          //draw a line with red color
    glBegin(GL_LINES);
    glVertex2d(x0,y0);
    glVertex2d(x1,y1);
    glEnd();
    glColor3f(0.0,0.0,1.0);     //draw a blue color window
    glBegin(GL_LINE_LOOP);
    glVertex2f(xmin,ymin);
    glVertex2f(xmax,ymin);
    glVertex2f(xmax,ymax);
    glVertex2f(xmin,ymax);
    glEnd();
    liangbaraskylineclipanddraw(x0,y0,x1,y1);
    glFlush();
}
void myinit()
{    glClearColor(1.0,1.0,1.0,1.0);
    glColor3f(1.0,0.0,0.0);
    glPointSize(1.0);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluOrtho2D(0.0,499.0,0.0,499.0);
}
int main(int argc, char** argv)
{
    glutInit(&argc,argv);
    glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);
    glutInitWindowSize(500,500);
    glutInitWindowPosition(0,0);
    glutCreateWindow("liang barsky line clipping algorithm");
    glutDisplayFunc(display);
    myinit();
    glutMainLoop();
    return 0;
}

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