/* lines_intersect: AUTHOR: Mukesh Prasad * * This function computes whether two line segments, * respectively joining the input points (x1,y1) -- (x2,y2) * and the input points (x3,y3) -- (x4,y4) intersect. * If the lines intersect, the output variables x, y are * set to coordinates of the point of intersection. * * All values are in integers. The returned value is rounded * to the nearest integer point. * * If non-integral grid points are relevant, the function * can easily be transformed by substituting floating point * calculations instead of integer calculations. * * Entry * x1, y1, x2, y2 Coordinates of endpoints of one segment. * x3, y3, x4, y4 Coordinates of endpoints of other segment. * * Exit * x, y Coordinates of intersection point. * * The value returned by the function is one of: * * DONT_INTERSECT 0 * DO_INTERSECT 1 * COLLINEAR 2 * * Error conditions: * * Depending upon the possible ranges, and particularly on 16-bit * computers, care should be taken to protect from overflow. * * In the following code, 'long' values have been used for this * purpose, instead of 'int'. * */ #define DONT_INTERSECT 0 #define DO_INTERSECT 1 #define COLLINEAR 2 /************************************************************** * * * NOTE: The following macro to determine if two numbers * * have the same sign, is for 2's complement number * * representation. It will need to be modified for other * * number systems. * * * **************************************************************/ #define SAME_SIGNS( a, b ) \ (((long) ((unsigned long) a ^ (unsigned long) b)) >= 0 ) int lines_intersect( x1, y1, /* First line segment */ x2, y2, x3, y3, /* Second line segment */ x4, y4, x, y /* Output value: * point of intersection */ ) long x1, y1, x2, y2, x3, y3, x4, y4, *x, *y; { long a1, a2, b1, b2, c1, c2; /* Coefficients of line eqns. */ long r1, r2, r3, r4; /* 'Sign' values */ long denom, offset, num; /* Intermediate values */ /* Compute a1, b1, c1, where line joining points 1 and 2 * is "a1 x + b1 y + c1 = 0". */ a1 = y2 - y1; b1 = x1 - x2; c1 = x2 * y1 - x1 * y2; /* Compute r3 and r4. */ r3 = a1 * x3 + b1 * y3 + c1; r4 = a1 * x4 + b1 * y4 + c1; /* Check signs of r3 and r4. If both point 3 and point 4 lie on * same side of line 1, the line segments do not intersect. */ if ( r3 != 0 && r4 != 0 && SAME_SIGNS( r3, r4 )) return ( DONT_INTERSECT ); /* Compute a2, b2, c2 */ a2 = y4 - y3; b2 = x3 - x4; c2 = x4 * y3 - x3 * y4; /* Compute r1 and r2 */ r1 = a2 * x1 + b2 * y1 + c2; r2 = a2 * x2 + b2 * y2 + c2; /* Check signs of r1 and r2. If both point 1 and point 2 lie * on same side of second line segment, the line segments do * not intersect. */ if ( r1 != 0 && r2 != 0 && SAME_SIGNS( r1, r2 )) return ( DONT_INTERSECT ); /* Line segments intersect: compute intersection point. */ denom = a1 * b2 - a2 * b1; if ( denom == 0 ) return ( COLLINEAR ); offset = denom < 0 ? - denom / 2 : denom / 2; /* The denom/2 is to get rounding instead of truncating. It * is added or subtracted to the numerator, depending upon the * sign of the numerator. */ num = b1 * c2 - b2 * c1; *x = ( num < 0 ? num - offset : num + offset ) / denom; num = a2 * c1 - a1 * c2; *y = ( num < 0 ? num - offset : num + offset ) / denom; return ( DO_INTERSECT ); } /* lines_intersect */ /* A main program to test the function. */ main() { long x1, x2, x3, x4, y1, y2, y3, y4; long x, y; for (;;) { printf( "X1, Y1: " ); scanf( "%ld %ld", &x1, &y1 ); printf( "X2, Y2: " ); scanf( "%ld %ld", &x2, &y2 ); printf( "X3, Y3: " ); scanf( "%ld %ld", &x3, &y3 ); printf( "X4, Y4: " ); scanf( "%ld %ld", &x4, &y4 ); switch ( lines_intersect( x1, y1, x2, y2, x3, y3, x4, y4, &x, &y )) { case DONT_INTERSECT: printf( "Lines don't intersect\n" ); break; case COLLINEAR: printf( "Lines are collinear\n" ); break; case DO_INTERSECT: printf( "Lines intersect at %ld,%ld\n", x, y ); break; } } } /* main */