Line Segment intersection line intersection Template

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Const int maxn = 100000;
Const double eps = 1e-8;
Const double pi = acos (-1.0 );
# Define sgn (x) (fabs (x) <eps? 0 :( x> 0? 1:-1 ))
Struct Point {
Double x, y;
Point (double a = 0, double B = 0) {x = a; y = B ;}
Point operator-(const Point & t) const {
Point tmp;
Tmp. x = x-t. x;
Tmp. y = y-t. y;
Return tmp;
}
Bool operator <(const Point & p) const {
Return sgn (x-p.x) <0 | sgn (x-p.x) = 0 & sgn (y-p.y) <0;
}
Bool operator = (const Point & t) const {
Return sgn (x-t.x) = 0 & sgn (y-t.y) = 0;
}
} GP;
Struct Line {
Double a, B, c;
};
Struct Seg {
Point s, e;
Seg (Point a, Point B) {s = a; e = B ;}
};
Inline double Cross (Point a, Point B, Point c ){
Return (B. x-a.x) * (c. y-a.y)-(c. x-a.x) * (B. y-a.y );
};
Line Turn (Point s, Point e ){
Line ln;
Ln. a = s. y-e. y;
Ln. B = e. x-s. x;
Ln. c = s. x * e. y-e. x * s. y;
Return ln;
}
Bool dotOnSeg (Point p, Point s, Point e ){
If (p = s | p = e)
Return true;
Return sgn (Cross (s, e, p) = 0 &&
Sgn (p. x-s.x) * (p. x-e.x) <= 0 & sgn (p. y-s.y) * (p. y-e.y) <= 0; // sgn may be equal to 0, such as line vertical axis
}
Bool Intersect (Point p1, Point p2, Point p3, Point p4, Point & p) {// line intersection
Double a1, b1, c1, a2, b2, c2, d;
A1 = p1.y-p2.y; b1 = p2.x-p1.x; c1 = p1.x * p2.y-p2.x * p1.y;
A2 = p3.y-p4.y; b2 = p4.x-p3.x; c2 = p3.x * p4.y-p4.x * p3.y;
D = a1 * b2-a2 * b1;
If (! Sgn (d) return false;
P. x = (-c1 * b2 + c2 * b1)/d;
P. y = (-a1 * c2 + a2 * c1)/d;
Return true;
}
Bool Line_Inst (Line l1, Line l2, Point & p) {// Line intersection
Double d = l1.a * l2. B-l2.a * l1. B;
If (! Sgn (d) return false;
P. x = (-l1.c * l2. B + l2.c * l1. B)/d;
P. y = (-l1.a * l2.c + l2.a * l1.c)/d;
Return true;
}
Bool Seg_Inst (Seg s1, Seg s2, Point & p) {// determines the intersection of a line segment. Special Judgment is required when the line is collocated. First, the intersection of a line is determined, and then the judgment Point is on a straight line.
Line l1 = Turn (s1.s, s1.e), l2 = Turn (s2.s, s2.e );
Double d = l1.a * l2. B-l2.a * l1. B;
If (sgn (d) = 0) return false;
P. x = (-l1.c * l2. B + l2.c * l1. B)/d;
P. y = (-l1.a * l2.c + l2.a * l1.c)/d;
Return dotOnSeg (p, s1.s, s1.e) & dotOnSeg (p, s2.s, s2.e );
}
Bool check (Seg s1, Seg s2, Point & pp) {// collinearity, Special Judgment
If (s1.s = s2.s | s1.s = s2.e) {pp = s1.s; return true ;}
If (s1.e = s2.s | s1.e = s2.e) {pp = s1.e; return true ;}
Return false;
}