// The main function that returns true if line segment 'p1q1' // and 'p2q2' intersect. bool segmentsIntersect(Line2 l1, Line2 l2) { // Find the four orientations needed for general and // special cases int o1 = orientation(l1.getStart(), l1.getEnd(), l2.getStart()); int o2 = orientation(l1.getStart(), l1.getEnd(), l2.getEnd()); int o3 = orientation(l2.getStart(), l2.getEnd(), l1.getStart()); int o4 = orientation(l2.getStart(), l2.getEnd(), l1.getEnd()); // General case if (o1 != o2 && o3 != o4) return true; // Special Cases // p1, q1 and p2 are colinear and p2 lies on segment p1q1 if (o1 == 0 && onSegment(l1.getStart(), l2.getStart(), l1.getEnd())) return true; // p1, q1 and p2 are colinear and q2 lies on segment p1q1 if (o2 == 0 && onSegment(l1.getStart(), l2.getEnd(), l1.getEnd())) return true; // p2, q2 and p1 are colinear and p1 lies on segment p2q2 if (o3 == 0 && onSegment(l2.getStart(), l1.getStart(), l2.getEnd())) return true; // p2, q2 and q1 are colinear and q1 lies on segment p2q2 if (o4 == 0 && onSegment(l2.getStart(), l1.getEnd(), l2.getEnd())) return true; return false; // Doesn't fall in any of the above cases }
bool oppositeSide(Point2 p1, Point2 p2, Line2 ab)//returns whether or not p1 and p2 are on the same side of AB { double & ax = p1.x; double & ay = p1.y; double & bx = p2.x; double & by = p2.y; double & x1 = ab.x; double & y1 = ab.y; double x2 = ab.getEnd().x; double y2 = ab.getEnd().y; return ((y1 - y2)*(ax - x1)+(x2 - x1)*(ay - y1))*((y1 - y2)*(bx - x1)+(x2 - x1)*(by - y1))<0; }
bool operator==(Line2 const & lhs, Line2 const & rhs) { return (lhs.getStart() == rhs.getStart() && lhs.getEnd() == rhs.getEnd()) || (lhs.getStart() == rhs.getEnd() && lhs.getEnd() == rhs.getStart()); }
bool intersect(Line2 ab, Line2 cd) { return oppositeSide(ab, ab.getEnd(), cd) && oppositeSide(cd, cd.getEnd(), ab); }