UVA-10674 Tangents(求圆和圆的切线)(计算几何)

题意:求圆和圆的切线，并将每根直线按在第一个圆的切点排序。

分析:排序可以使用冒泡，记住比较大小的时候要处理精度问题。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
#include <cmath>
#include <algorithm>

using namespace std;

const double eps = 1e-8;
const double PI = acos(-1.0);
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-(Point A, Point B) { return Vector(A.x - B.x, A.y - B.x); }
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); }

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

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

Vector Normal(Vector A)
{
	double L = Length(A);
	return Vector(-A.y / L, A.x / L);
}

double dist(Point a, Point b)
{
	return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}

int dcmp(double x)
{
	if (fabs(x) < eps) return 0;
	else return x < 0 ? -1 : 1;
}

bool operator<(const Point& a, const Point& b)
{
	return dcmp(a.x - b.x) < 0 || dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) < 0;
}

struct Circle
{
	Point c;
	double r;
	Circle(Point c, double r):c(c), r(r){}
	Point point(double a)
	{
		return Point(c.x + cos(a) * r, c.y + sin(a) * r);
	}
};

struct Line
{
	Point p;
	Vector v;
	Line(Point p, Vector v):p(p),v(v){}
	Point point(double t)
	{
		return p + v * t;
	}
	Line move(double d)
	{
		return Line(p + Normal(v) * d, v);
	}
};

int getTangents(Circle A, Circle B, Point* a, Point* b)
{
	//存储切点
	int cnt = 0;
	if (dcmp(A.r - B.r) < 0) { swap(A, B); swap(a, b); }
	double d2 = (A.c.x - B.c.x) * (A.c.x - B.c.x) + (A.c.y - B.c.y) * (A.c.y - B.c.y);

	double rdiff = A.r - B.r;
	double rsum = A.r + B.r;
	if (dcmp(d2 - rdiff * rdiff) < 0) return 0;

	//两个圆心之间的向量的极角
	double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x);
	//无限多条切线
	if (dcmp(d2) == 0 && dcmp(A.r - B.r) == 0) return -1;
	//内切，一条切线
	if (dcmp(d2 - rdiff * rdiff) == 0)
	{
		a[cnt] = A.point(base); b[cnt] = B.point(base); ++cnt;
		return 1;
	}
	//有外公切线
	double ang = acos((A.r - B.r) / sqrt(d2));
	a[cnt] = A.point(base + ang); b[cnt] = B.point(base + ang); ++cnt;
	a[cnt] = A.point(base - ang); b[cnt] = B.point(base - ang); ++cnt;
	if (dcmp(d2 - rsum * rsum) == 0)
	{
		a[cnt] = A.point(base); b[cnt] = B.point(PI + base); ++cnt;
	}
	else if (dcmp(d2 - rsum * rsum) > 0)
	{
		double ang = acos((A.r + B.r) / sqrt(d2));
		a[cnt] = A.point(base + ang); b[cnt] = B.point(PI + base + ang); ++cnt;
		a[cnt] = A.point(base - ang); b[cnt] = B.point(PI + base - ang); ++cnt;
	}
	return cnt;
}

bool check(Circle A)
{
	if (A.c.x == 0 && A.c.y == 0 && A.r == 0)
		return 1;
	return 0;
}

int main()
{
	double x1, y1, r1, x2, y2, r2;
	while (scanf("%lf%lf%lf%lf%lf%lf", &x1, &y1, &r1, &x2, &y2, &r2) != EOF)
	{
		Circle A(Point(x1, y1), r1);
		Circle B(Point(x2, y2), r2);

		if (check(A) && check(B)) break;

		Point a[10], b[10];

		int res = getTangents(A, B, a, b);
		if (res == -1)
		{
			puts("-1");
			continue;
		}

		printf("%d
", res);

		//冒泡
		for (int i = 0; i < res; ++i)
		{
			for (int j = res - 1; j > i; --j)
			{
				if (a[j] < a[j - 1])
				{
					swap(a[j - 1], a[j]);
					swap(b[j - 1], b[j]);
				}
			}
		}

		for (int i = 0; i < res; ++i)
		{
			printf("%.5lf %.5lf %.5lf %.5lf %.5lf
", a[i].x, a[i].y, b[i].x, b[i].y, dist(a[i], b[i]));
		}
	}



	return 0;
}