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struct pt { //complex<double> does not work here, becuase we need to set pt.x and pt.y
double x, y;
pt() {};
pt(double x, double y) : x(x), y(y) {};
};
struct line {
double a, b, c; //a*x+b*y+c, b=0 <=> vertical line, b=1 <=> otherwise
};
line pointsToLine(pt p1, pt p2) {
line l;
if (fabs(p1.x - p2.x) < EPSILON) {
l.a = 1; l.b = 0.0; l.c = -p1.x;
} else {
l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x);
l.b = 1.0;
l.c = -(double)(l.a * p1.x) - p1.y;
}
return l;
}
bool areParallel(line l1, line l2) {
return (fabs(l1.a - l2.a) < EPSILON) && (fabs(l1.b - l2.b) < EPSILON);
}
bool areSame(line l1, line l2) {
return areParallel(l1, l2) && (fabs(l1.c - l2.c) < EPSILON);
}
bool areIntersect(line l1, line l2, pt &p) {
if (areParallel(l1, l2)) return false;
p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);
if (fabs(l1.b) > EPSILON) p.y = -(l1.a * p.x + l1.c);
else p.y = -(l2.a * p.x + l2.c);
return true;
}
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