Coordinate Geometry.txt

#define PI 3.14159265

double rad2Deg(double rad) {
	return (180 * rad) / PI;
}
double deg2Rad(double deg) {
	return (PI*deg) / 180;
}

struct Point {
	double x, y;
	Point() { x = y = 0.0; }
	Point(double _x, double _y) : x(_x), y(_y) {}
	bool operator < (Point other) const { // override less than operator
		if (fabs(x - other.x) > eps) // useful for sorting
			return x < other.x; // first criteria , by x-coordinate
		return y < other.y;
	}
	bool operator == (Point other) const {
		return (fabs(x - other.x) < eps && (fabs(y - other.y) < eps));
	}
	double dist(Point p1, Point p2) { // Euclidean distance
									  // hypot(dx, dy) returns sqrt(dx * dx + dy * dy)
		return hypot(p1.x - p2.x, p1.y - p2.y);
	} // return double
	  // rotate p by theta degrees CCW w.r.t origin (0, 0)
	point rotate(Point p, double theta) {
		double rad = deg2Rad(theta); // multiply theta with PI / 180.0
		return Point(p.x * cos(rad) - p.y * sin(rad),
			p.x * sin(rad) + p.y * cos(rad));
	}
}; // second criteria, by y-coordinate

struct Line { double a, b, c; }; // a way to represent a line								 
void pointsToLine(point p1, point p2, line &l) {
	// the answer is stored in the third parameter (pass by reference)
	if (fabs(p1.x - p2.x) < eps) { // vertical line is fine
		l.a = 1.0; l.b = 0.0; l.c = -p1.x; // default values
	}
	else {
		l.a = -(double)(p1.y - p2.y) / (p1.x - p2.x);
		l.b = 1.0; // IMPORTANT: we fix the value of b to 1.0
		l.c = -(double)(l.a * p1.x) - p1.y;
	}
}
bool areParallel(line l1, line l2) { // check coefficients a & b
	return (fabs(l1.a - l2.a) < eps) && (fabs(l1.b - l2.b) < eps);
}
bool areSame(line l1, line l2) { // also check coefficient c
	return areParallel(l1, l2) && (fabs(l1.c - l2.c) < eps);
}
// returns true (+ intersection point) if two lines are intersect
bool areIntersect(line l1, line l2, point &p) {
	if (areParallel(l1, l2)) return false; // no intersection
										   // solve system of 2 linear algebraic equations with 2 unknowns
	p.x = (l2.b * l1.c - l1.b * l2.c) / (l2.a * l1.b - l1.a * l2.b);
	// special case: test for vertical line to avoid division by zero
	if (fabs(l1.b) > eps) p.y = -(l1.a * p.x + l1.c);
	else p.y = -(l2.a * p.x + l2.c);
	return true;
}