# cohen sutherland implementation using OpenGL

## Cohen Sutherland line clipping - snapshot

In computer graphics, the **Cohen–Sutherland** algorithm is a line clipping algorithm. The algorithm divides a 2D space into 9 regions, of which only the middle part (viewport) is visible.

In 1967, flight simulation work by Danny Cohen (engineer) lead to the development of the Cohen–Sutherland computer graphics two and three dimensional line clipping algorithms, created with Ivan Sutherland. For more, read p. 124 and p. 252 of *Principles of Interactive Computer Graphics.*

## The algorithm

The algorithm includes, excludes or partially includes the line based on where:

- Both endpoints are in the viewport region (bitwise OR of endpoints == 0): trivial accept.
- Both endpoints are on the same non-visible region (bitwise AND of endpoints != 0): trivial reject.
- Both endpoints are in different regions: In case of this non trivial situation the algorithm finds one of the two points that are outside the viewport region (there will be at least one point outside). The intersection of the outpoint and extended viewport border is then calculated (i.e. with the parametric equation for the line) and this new point replaces the outpoint. The algorithm repeats until a trivial accept or reject occurs.

The numbers in the figure below are called outcodes. An outcode is computed for each of the two points in the line. The first bit is set to 1 if the point is above the viewport. The bits in the outcode represent: Top, Bottom, Right, Left. For example the outcode 1010 represents a point that is top-right of the viewport. Note that the outcodes for endpoints **must** be recalculated on each iteration after the clipping occurs.

## Cohen sutherland line clipping using OpenGL source code

/* Refer to the Cohen_Sutherland algorithm in the textbook. */ #include <GL/glut.h> #include <stdio.h> #include <stdlib.h> #define X_COORDINATE 0 #define Y_COORDINATE 1 #define Z_COORDINATE 2 #define b0 0 #define b1 1 #define b2 2 #define b3 3 float xBoundaryRight, xBoundaryLeft, yBoundaryUpper, yBoundaryLower; float p1[3], p2[3], p3[3], p4[3]; /* corners of the clipping rectangle, clock-wise from top left */ float givenLineSegmentP1[3], givenLineSegmentP2[3]; float clippedLineP1[3], clippedLineP2[3]; void display (); void myInit (); int main (int argc, char **argv) { char outP1[4], outP2[4], outTemp[4]; /* b0, b1, b2 and b3 as described in the textbook. */ int i; float m, c, tempPoint[3]; printf ("Enter X-Boundary (right): "); scanf ("%f", &xBoundaryRight); printf ("Enter X-Boundary (left): "); scanf ("%f", &xBoundaryLeft); printf ("Enter Y-Boundary (upper): "); scanf ("%f", &yBoundaryUpper); printf ("Enter Y-Boundary (lower): "); scanf ("%f", &yBoundaryLower); printf ("Enter the first point of the the line segment to be clipped (x, y): "); scanf ("%f %f", &givenLineSegmentP1[X_COORDINATE], &givenLineSegmentP1[Y_COORDINATE]); printf ("Enter the second point of the the line segment to be clipped (x, y): "); scanf ("%f %f", &givenLineSegmentP2[X_COORDINATE], &givenLineSegmentP2[Y_COORDINATE]); givenLineSegmentP2[Z_COORDINATE] = givenLineSegmentP1[Z_COORDINATE] = 0; /* Now calcluate the corners of the clipping rectangle */ p1[X_COORDINATE] = xBoundaryLeft; p1[Y_COORDINATE] = yBoundaryUpper; p1[Z_COORDINATE] = 0; p2[X_COORDINATE] = xBoundaryRight; p2[Y_COORDINATE] = yBoundaryUpper; p2[Z_COORDINATE] = 0; p3[X_COORDINATE] = xBoundaryRight; p3[Y_COORDINATE] = yBoundaryLower; p3[Z_COORDINATE] = 0; p4[X_COORDINATE] = xBoundaryLeft; p4[Y_COORDINATE] = yBoundaryLower; p4[Z_COORDINATE] = 0; /* Do the required calculations. */ /* b0 is 1 if point is outside of yBoundaryUpper b1 is 1 if point is outside of yBoundaryLower b2 is 1 if point is outside of xBoundaryLeft and b3 is 1 if point is outside of xBoundaryRight. */ outP1[b0] = (givenLineSegmentP1[Y_COORDINATE] > yBoundaryUpper) ? 1 : 0; outP1[b1] = (givenLineSegmentP1[Y_COORDINATE] < yBoundaryLower) ? 1 : 0; outP1[b2] = (givenLineSegmentP1[X_COORDINATE] < xBoundaryLeft) ? 1 : 0; outP1[b3] = (givenLineSegmentP1[X_COORDINATE] > xBoundaryRight) ? 1 : 0; outP2[b0] = (givenLineSegmentP2[Y_COORDINATE] > yBoundaryUpper) ? 1 : 0; outP2[b1] = (givenLineSegmentP2[Y_COORDINATE] < yBoundaryLower) ? 1 : 0; outP2[b2] = (givenLineSegmentP2[X_COORDINATE] < xBoundaryLeft) ? 1 : 0; outP2[b3] = (givenLineSegmentP2[X_COORDINATE] > xBoundaryRight) ? 1 : 0; /* We now have four cases to consider according to the Cohen-Sutherland Algorithm. */ /* The point may be out of more than one side. In which case, we first clip w.r.t one side and continue the loop (updating the outP[] and clippedLine[] arrays */ for (i = 0; i < 3; i++) clippedLineP1[i] = givenLineSegmentP1[i]; for (i = 0; i < 3; i++) clippedLineP2[i] = givenLineSegmentP2[i]; /* Henceforth, only clippedLineP[] will be used. */ while (1) { /* case 1 */ if (outP1[b0] == 0 && outP1[b1] == 0 && outP1[b2] == 0 && outP1[b3] == 0 && outP2[b0] == 0 && outP2[b1] == 0 && outP2[b2] == 0 && outP2[b3] == 0) { break; } /* case 2. One point inside and the other outside the rect. Split into two cases. */ /* case 2a: outP1 != 0 && outP2 == 0: First point is outside and second inside. */ else if ((outP1[b0] != 0 || outP1[b1] != 0 || outP1[b2] != 0 || outP1[b3] != 0) && (outP2[b0] == 0 && outP2[b1] == 0 && outP2[b2] == 0 && outP2[b3] == 0)) { if (clippedLineP1[X_COORDINATE] == clippedLineP2[X_COORDINATE]) { /* then m = (y2-y1)/(x2-x1) would be infinity. */ if (outP1[b0] == 1) { clippedLineP1[Y_COORDINATE] = yBoundaryUpper; outP1[b0] = 0; } else { clippedLineP1[Y_COORDINATE] = yBoundaryLower; outP1[b2] = 0; } continue; } m = clippedLineP1[Y_COORDINATE]-clippedLineP2[Y_COORDINATE]; m /= clippedLineP1[X_COORDINATE]-clippedLineP2[X_COORDINATE]; if (m == 0) { if (outP1[b2] == 1) { clippedLineP1[X_COORDINATE] = xBoundaryLeft; outP1[b2] = 0; } else { clippedLineP1[X_COORDINATE] = xBoundaryRight; outP1[b3] = 0; } continue; } /* Line is neither horizontal nor vertical at this point */ /* We try to clip whichever bound exceeds that we see first. After clipping at that point, we immediately check if the other (if any) has been clipped too. */ c = clippedLineP1[Y_COORDINATE]-(m*clippedLineP1[X_COORDINATE]); if (outP1[b0] == 1) { clippedLineP1[Y_COORDINATE] = yBoundaryUpper; clippedLineP1[X_COORDINATE] = (yBoundaryUpper-c)/m; outP1[b0] = 0; if (clippedLineP1[X_COORDINATE] <= xBoundaryRight && clippedLineP1[X_COORDINATE] >= xBoundaryLeft) { outP1[b2] = outP1[b3] = 0; break; } continue; } if (outP1[b1] == 1) { clippedLineP1[Y_COORDINATE] = yBoundaryLower; clippedLineP1[X_COORDINATE] = (yBoundaryLower-c)/m; outP1[b1] = 0; if (clippedLineP1[X_COORDINATE] <= xBoundaryRight && clippedLineP1[X_COORDINATE] >= xBoundaryLeft) { outP1[b2] = outP1[b3] = 0; break; } continue; } if (outP1[b2] == 1) { clippedLineP1[X_COORDINATE] = xBoundaryLeft; clippedLineP1[Y_COORDINATE] = (m*xBoundaryLeft)+c; outP1[b2] = 0; if (clippedLineP1[Y_COORDINATE] <= yBoundaryUpper && clippedLineP1[Y_COORDINATE] >= yBoundaryLower) { outP1[b0] = outP1[b1] = 0; break; } continue; } if (outP1[b3] == 1) { clippedLineP1[X_COORDINATE] = xBoundaryRight; clippedLineP1[Y_COORDINATE] = (m*xBoundaryRight)+c; outP1[b3] = 0; if (clippedLineP1[Y_COORDINATE] <= yBoundaryUpper && clippedLineP1[Y_COORDINATE] >= yBoundaryLower) { outP1[b0] = outP1[b1] = 0; break; } continue; } } /* Case2b: If first point is inside and second point is outside. */ else if ((outP2[b0] != 0 || outP2[b1] != 0 || outP2[b2] != 0 || outP2[b3] != 0) && (outP1[b0] == 0 && outP1[b1] == 0 && outP1[b2] == 0 && outP1[b3] == 0)) { /* Exchange first and second points completely including outP[] and continue. */ for (i = 0; i < 3; i++) tempPoint[i] = clippedLineP1[i]; for (i = 0; i < 3; i++) clippedLineP1[i] = clippedLineP2[i]; for (i = 0; i < 3; i++) clippedLineP2[i] = tempPoint[i]; for (i = 0; i < 4; i++) outTemp[i] = outP1[i]; for (i = 0; i < 4; i++) outP1[i] = outP2[i]; for (i = 0; i < 4; i++) outP2[i] = outTemp[i]; continue; } /* Case 3. if (outP1 & outP2 != 0): Both points exceed the same boundary. */ else if ((outP1[b0] && outP2[b0] == 1) || (outP1[b1] && outP2[b1] == 1) || (outP1[b2] && outP2[b2] == 1) || (outP1[b3] && outP2[b3] == 1)) { /* set clippedLineP1 and clippedLineP2 both to 0,0,0 */ for (i = 0; i < 3; i++) clippedLineP2[i] = clippedLineP1[i] = 0; break; } /* case 4. Both endpoints are outside, but of different edges. */ else { /* Determine the points of intersection of the line with the four boundaries and determine the outcode for each of these intersection points. We can then estimate if the line is entirely out of the boundary or not. */ float intersectionP1[3], intersectionP2[3], intersectionP3[3], intersectionP4[3]; int validIntersections = 0; /* check for special cases where line is horizontal or vertical. */ if (clippedLineP1[X_COORDINATE] == clippedLineP2[X_COORDINATE]) { /* The line starts from above yBoundaryUpper and ends below yBoundaryLower. */ clippedLineP1[Y_COORDINATE] = yBoundaryUpper; clippedLineP2[Y_COORDINATE] = yBoundaryLower; break; } if (clippedLineP1[Y_COORDINATE] == clippedLineP2[Y_COORDINATE]) { /* The line starts from left of xBoundaryLeft and ends after xBoundaryRight. */ clippedLineP1[X_COORDINATE] = xBoundaryLeft; clippedLineP2[X_COORDINATE] = xBoundaryRight; break; } /* Line is neither vertical nor horizontal. Do all four intersections. */ m = clippedLineP1[Y_COORDINATE] - clippedLineP2[Y_COORDINATE]; m /= clippedLineP1[X_COORDINATE] - clippedLineP2[X_COORDINATE]; c = clippedLineP1[Y_COORDINATE] - (m*clippedLineP1[X_COORDINATE]); /* Intersection with yBoundaryUpper */ intersectionP1[Y_COORDINATE] = yBoundaryUpper; intersectionP1[X_COORDINATE] = (yBoundaryUpper-c)/m; intersectionP1[Z_COORDINATE] = 0; /* Intersection with yBoundaryLower */ intersectionP2[Y_COORDINATE] = yBoundaryLower; intersectionP2[X_COORDINATE] = (yBoundaryLower-c)/m; intersectionP2[Z_COORDINATE] = 0; /* Intersection with xBoundaryLeft */ intersectionP3[X_COORDINATE] = xBoundaryLeft; intersectionP3[Y_COORDINATE] = (m*xBoundaryLeft)+c; intersectionP3[Z_COORDINATE] = 0; /* Intersection with xBoundaryRight */ intersectionP4[X_COORDINATE] = xBoundaryRight; intersectionP4[Y_COORDINATE] = (m*xBoundaryRight)+c; intersectionP4[Z_COORDINATE] = 0; /* If all these intersections are "outside", line is outside. If at least one intersection is inside, there is one more intersection that is inside. These two intersections form the clipped line. (unless the line passes through a corner). */ /* The line cannot pass through the viewing rectange at more than two points. If there are more than two points (among the above intersection points) that are inside the viewing rectangle, some are identical. We need to set clippedLineP1 and clippedLineP2 to these two points (if any). */ /* When we find the 2nd valid intersection, we verify that it is not the same as the first and then only use it. At the end, if we have only one valid intersection, we reset both end points to 0,0,0 so that the line is not displayed as clipped. */ /* WE NEED TO FIND UNIQUE INTERSECTION POINTS THAT ARE INSIDE (if any). */ /* intersectionP1 (intersection with yBoundaryUpper). */ if (intersectionP1[X_COORDINATE] <= xBoundaryRight && intersectionP1[X_COORDINATE] >= xBoundaryLeft) { for (i = 0; i < 3; i++) clippedLineP1[i] = intersectionP1[i]; validIntersections++; } /* intersectionP2 (intersection with yBoundaryLower). */ if (intersectionP2[X_COORDINATE] <= xBoundaryRight && intersectionP2[X_COORDINATE] >= xBoundaryLeft) { if (validIntersections == 1) { /* we need to verify if its the same point as the first one. */ if (intersectionP2[X_COORDINATE] == clippedLineP1[X_COORDINATE] && intersectionP2[Y_COORDINATE] == clippedLineP1[Y_COORDINATE] && intersectionP2[Z_COORDINATE] == clippedLineP1[Z_COORDINATE]) /* do nothing. */ ; else { for (i = 0; i < 3; i++) clippedLineP2[i] = intersectionP2[i]; validIntersections++; break; } } else { for (i = 0; i < 3; i++) clippedLineP1[i] = intersectionP2[i]; validIntersections++; } } /* intersectionP3 (intersection with xBoundaryLeft). */ if (intersectionP3[Y_COORDINATE] <= yBoundaryUpper && intersectionP3[Y_COORDINATE] >= yBoundaryLower) { if (validIntersections == 1) { /* we need to verify if its the same point as the first one. */ if (intersectionP3[X_COORDINATE] == clippedLineP1[X_COORDINATE] && intersectionP3[Y_COORDINATE] == clippedLineP1[Y_COORDINATE] && intersectionP3[Z_COORDINATE] == clippedLineP1[Z_COORDINATE]) /* do nothing. */ ; else { for (i = 0; i < 3; i++) clippedLineP2[i] = intersectionP3[i]; validIntersections++; break; } } else { for (i = 0; i < 3; i++) clippedLineP1[i] = intersectionP3[i]; validIntersections++; } } /* intersectionP4 (intersection with xBoundaryRight */ if (intersectionP4[Y_COORDINATE] <= yBoundaryUpper && intersectionP4[Y_COORDINATE] >= yBoundaryLower) { if (validIntersections == 1) { /* we need to verify if its the same point as the first one. */ if (intersectionP4[X_COORDINATE] == clippedLineP1[X_COORDINATE] && intersectionP4[Y_COORDINATE] == clippedLineP1[Y_COORDINATE] && intersectionP4[Z_COORDINATE] == clippedLineP1[Z_COORDINATE]) /* do nothing. */ ; else { for (i = 0; i < 3; i++) clippedLineP2[i] = intersectionP4[i]; validIntersections++; break; } } else { for (i = 0; i < 3; i++) clippedLineP1[i] = intersectionP4[i]; validIntersections++; } } /* If validIntersections <= 1 at this point, we set both clippedLineP1 and clippedLineP2 to 0,0,0. Only one validIntersection means that the line just passes through a corner of the viewing rectangle. */ if (validIntersections <= 1) for (i = 0; i < 3; i++) clippedLineP2[i] = clippedLineP1[i] = 0; break; } } glutInit (&argc, argv); glutCreateWindow ("Cohen-Sutherland Line Clipping"); glutInitWindowPosition (400, 400); glutInitWindowSize (640, 480); glutDisplayFunc (display); myInit(); glutMainLoop(); } void myInit () { glClearColor (1.0, 1.0, 1.0, 1.0); glPointSize (1); glColor3f (0.0, 0.0, 0.0); glMatrixMode (GL_PROJECTION); glLoadIdentity(); glOrtho (-50.0, 50.0, -50.0, 50.0, -50.0, 50.0); glMatrixMode (GL_MODELVIEW); } void display () { /* Clipped line is displayed in red, and unclipped in black. */ glClear (GL_COLOR_BUFFER_BIT); glColor3f (0.0, 0.0, 0.0); glBegin (GL_LINE_LOOP); glVertex3fv (p1); glVertex3fv (p2); glVertex3fv (p3); glVertex3fv (p4); glEnd (); glBegin (GL_LINES); glVertex3fv (givenLineSegmentP1); glVertex3fv (givenLineSegmentP2); glColor3f (1.0, 0.0, 0.0); glLineWidth (2); glVertex3fv (clippedLineP1); glVertex3fv (clippedLineP2); glEnd(); glFlush(); }

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