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common_tanline.cpp
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//
// 2 円の共通接線
//
// verified:
// AOJ Course CGL_7_G: Common Tangent
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=CGL_7_G&lang=ja
//
// AOJ 2201 Immortal Jewels
// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2201
//
#include <iostream>
#include <vector>
#include <cmath>
#include <iomanip>
#include <algorithm>
using namespace std;
//------------------------------//
// 基本要素 (点, 線分, 円)
//------------------------------//
using DD = double;
const DD INF = 1LL<<60; // to be set appropriately
const DD EPS = 1e-10; // to be set appropriately
const DD PI = acosl(-1.0);
DD torad(int deg) {return (DD)(deg) * PI / 180;}
DD todeg(DD ang) {return ang * 180 / PI;}
/* Point */
struct Point {
DD x, y;
Point(DD x = 0.0, DD y = 0.0) : x(x), y(y) {}
friend ostream& operator << (ostream &s, const Point &p) {return s << '(' << p.x << ", " << p.y << ')';}
};
inline Point operator + (const Point &p, const Point &q) {return Point(p.x + q.x, p.y + q.y);}
inline Point operator - (const Point &p, const Point &q) {return Point(p.x - q.x, p.y - q.y);}
inline Point operator * (const Point &p, DD a) {return Point(p.x * a, p.y * a);}
inline Point operator * (DD a, const Point &p) {return Point(a * p.x, a * p.y);}
inline Point operator * (const Point &p, const Point &q) {return Point(p.x * q.x - p.y * q.y, p.x * q.y + p.y * q.x);}
inline Point operator / (const Point &p, DD a) {return Point(p.x / a, p.y / a);}
inline Point conj(const Point &p) {return Point(p.x, -p.y);}
inline Point rot(const Point &p, DD ang) {return Point(cos(ang) * p.x - sin(ang) * p.y, sin(ang) * p.x + cos(ang) * p.y);}
inline Point rot90(const Point &p) {return Point(-p.y, p.x);}
inline DD cross(const Point &p, const Point &q) {return p.x * q.y - p.y * q.x;}
inline DD dot(const Point &p, const Point &q) {return p.x * q.x + p.y * q.y;}
inline DD norm(const Point &p) {return dot(p, p);}
inline DD abs(const Point &p) {return sqrt(dot(p, p));}
inline DD amp(const Point &p) {DD res = atan2(p.y, p.x); if (res < 0) res += PI*2; return res;}
inline bool eq(const Point &p, const Point &q) {return abs(p - q) < EPS;}
inline bool operator < (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x < q.x : p.y < q.y);}
inline bool operator > (const Point &p, const Point &q) {return (abs(p.x - q.x) > EPS ? p.x > q.x : p.y > q.y);}
inline Point operator / (const Point &p, const Point &q) {return p * conj(q) / norm(q);}
/* Line */
struct Line : vector<Point> {
Line(Point a = Point(0.0, 0.0), Point b = Point(0.0, 0.0)) {
this->push_back(a);
this->push_back(b);
}
friend ostream& operator << (ostream &s, const Line &l) {return s << '{' << l[0] << ", " << l[1] << '}';}
};
/* Circle */
struct Circle : Point {
DD r;
Circle(Point p = Point(0.0, 0.0), DD r = 0.0) : Point(p), r(r) {}
friend ostream& operator << (ostream &s, const Circle &c) {return s << '(' << c.x << ", " << c.y << ", " << c.r << ')';}
};
//------------------------------//
// 接線
//------------------------------//
// tanline
vector<Point> tanline(const Point &p, const Circle &c) {
vector<Point> res;
DD d = norm(p - c);
DD l = d - c.r * c.r;
if (l < -EPS) return res;
if (l <= 0.0) l = 0.0;
Point cq = (p - c) * (c.r * c.r / d);
Point qs = rot90((p - c) * (c.r * sqrt(l) / d));
Point s1 = c + cq + qs, s2 = c + cq - qs;
res.push_back(s1);
res.push_back(s2);
return res;
}
// common tanline, a and b must be different!
// Line[0] is tangent point in a
vector<Line> comtanline(Circle a, Circle b) {
vector<Line> res;
// intersect
if (abs(a - b) > abs(a.r - b.r) + EPS) {
if (abs(a.r - b.r) < EPS) {
Point dir = b - a;
dir = rot90(dir * (a.r / abs(dir)));
res.push_back(Line(a + dir, b + dir));
res.push_back(Line(a - dir, b - dir));
}
else {
Point p = a * -b.r + b * a.r;
p = p * (1.0 / (a.r - b.r));
vector<Point> bs = tanline(p, a);
vector<Point> as = tanline(p, b);
for (int i = 0; i < min(as.size(), bs.size()); ++i) {
res.push_back(Line(bs[i], as[i]));
}
}
}
// inscribed
else if (abs(abs(a - b) - abs(a.r - b.r)) <= EPS) {
Point dir = b - a;
if (a.r > b.r) dir = dir * (a.r / abs(dir));
else dir = dir * (-a.r / abs(dir));
Point p = a + dir;
res.push_back(Line(p, p + rot90(dir)));
}
// disjoint
if (abs(a - b) > a.r + b.r + EPS) {
Point p = a * b.r + b * a.r;
p = p * (1.0 / (a.r + b.r));
vector<Point> bs = tanline(p, a);
vector<Point> as = tanline(p, b);
for (int i = 0; i < min(as.size(), bs.size()); ++i) {
res.push_back(Line(bs[i], as[i]));
}
}
// circumscribed
else if (abs(abs(a - b) - (a.r + b.r)) <= EPS) {
Point dir = b - a;
dir = dir * (a.r / abs(dir));
Point p = a + dir;
res.push_back(Line(p, p + rot90(dir)));
}
return res;
}
//------------------------------//
// Examples
//------------------------------//
void AOJCourse() {
Circle p, q;
while (cin >> p.x >> p.y >> p.r >> q.x >> q.y >> q.r) {
auto l = comtanline(p, q);
vector<Point> res;
for (int i = 0; i < l.size(); ++i) res.push_back(l[i][0]);
sort(res.begin(), res.end());
for (int i = 0; i < res.size(); ++i) {
cout << fixed << setprecision(10) << res[i].x << " " << res[i].y << endl;
}
}
}
int main() {
AOJCourse();
}