计算几何基础

struct Point {
	double x, y;
	Point(double x = 0, double y = 0):x(x), y(y) { } 
};

typedef Point Vector;

Vector operator + (Vector A, Vector B) {
	return Vector(A.x + B.x, A.y + B.y);
}

Vector operator - (Vector A, Vector B) {
	return Vector(A.x - B.x, A.y - B.y);
}

Vector operator * (Vector A, double p) {
	return Vector(A.x * p, A.y * p);
}

Vector operator / (Vector A, double p) {
	return Vector(A.x / p, A.y / p);
}

const double EPS = 1e-10;
int dcmp(double x) {
	if (fabs(x) < EPS) return 0; else return x < 0 ? -1 : 1;
}

bool operator == (Vector A, Vector B) {
	return dcmp(A.x - B.x) == 0 && dcmp(A.y - B.y) == 0;
}

double Cross(Vector A, Vector B) {
	return A.x * B.y - A.y * B.x;
}

double Dot(Vector A, Vector B) {
	return A.x * B.x + A.y * B.y;
}

double Length(Vector A) {
	return sqrt(Dot(A, A));
}

Point GetLineIntersection(Point P, Vector v, Point Q, Vector w) {
	Vector u = P - Q;
	double t = Cross(w, u) / Cross(v, w);
	return P + v * t;
}

double Angle(Vector A, Vector B) {
	return acos(Dot(A, B) / Length(A) / Length(B));
}

Vector Rotate(Vector A, double rad) {
	return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad));
}

double DistanceToSegment(Point P, Point A, Point B) {
    if (A == B) return Length(P - A);
    Vector v1 = B - A, v2 = P - A, v3 = P - B;
    if (dcmp(Dot(v1, v2)) < 0) return length(v2);
    else if (demp(Dot(v1, v3)) < 0) return length(v3);
    else return fabs(Cross(v1, v2)) / Length(v1);
}