POJ1375 Intervals（直线与圆切线、线段合并）

  1 #include <iostream>
  2 #include <cstdio>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <cmath>
  6 #include <vector>
  7 using namespace std;
  8 
  9 const double EPS = 1e-10;        //精度系数
 10 const double PI = acos(-1.0);    //π
 11 const int N = 510;
 12 
 13 struct Point {
 14     double x, y;
 15     Point(double x = 0, double y = 0) :x(x), y(y) {}
 16 };    //点的定义
 17 
 18 typedef Point Vector;    //向量的定义
 19 
 20 Vector operator - (Vector A, Vector B) { return Vector(A.x - B.x, A.y - B.y); }    //向量减法
 21 
 22 int dcmp(double x) {
 23     if (fabs(x) < EPS)return 0; else return x < 0 ? -1 : 1;
 24 }    //与0的关系
 25 
 26 double Dot(Vector A, Vector B) { return A.x*B.x + A.y*B.y; }    //向量点乘
 27 double Length(Vector A) { return sqrt(Dot(A, A)); }    //向量长度
 28 
 29 Vector Rotate(Vector A, double rad) {
 30     return Vector(A.x*cos(rad) - A.y*sin(rad), A.x*sin(rad) + A.y*cos(rad));
 31 }    //逆时针旋转rad度
 32 
 33 struct Circle {
 34     Point c;
 35     double r;
 36     Circle() :c(Point(0, 0)), r(0) {}
 37     Circle(Point c, double r = 0) :c(c), r(r) {}
 38     Point point(double a) { return Point(c.x + cos(a)*r, c.y + sin(a)*r); }    //输入极角返回点坐标
 39 }C[N];    //圆
 40 
 41 int getTangents(Point p, Circle C, Vector* v) {
 42     Vector u = C.c - p;
 43     double dist = Length(u);
 44     if (dist < C.r)return 0;
 45     else if (dcmp(dist - C.r) == 0) {    //p在圆上，只有一条切线
 46         v[0] = Rotate(u, PI / 2);
 47         return 1;
 48     } else {
 49         double ang = asin(C.r / dist);
 50         v[0] = Rotate(u, -ang);
 51         v[1] = Rotate(u, +ang);
 52         return 2;
 53     }
 54 }    //过点p到圆C的切线。v[i]是第i条切线的向量。返回切线条数
 55 
 56 double LineInterX_axisPoint(Point p, Vector v) {
 57     double t = -1 * p.y / v.y;
 58     return p.x + t*v.x;
 59 }    //直线与x轴交点横坐标
 60 
 61 struct Interval {
 62     double l, r;
 63     Interval(double l = 0, double r = 0) :l(l), r(r) {}
 64     const bool operator < (Interval A) const {
 65         return l < A.l;
 66     }
 67 };
 68 
 69 void CombineIntervals(vector<Interval>& itvls) {
 70     int n = itvls.size();
 71     if (!n)return;
 72     sort(itvls.begin(), itvls.end());
 73     vector<Interval> ans;
 74     double nl = itvls[0].l, nr = itvls[0].r;
 75     for (int i = 1; i < n; ++i) {
 76         double tl = itvls[i].l, tr = itvls[i].r;
 77         if (dcmp(tl - nr) > 0) {
 78             ans.push_back(Interval(nl, nr));
 79             nl = tl, nr = tr;
 80         } else nr = max(tr, nr);
 81     }
 82     ans.push_back(Interval(nl, nr));
 83     itvls.clear();
 84     for (int i = 0; i < (int)ans.size(); ++i)
 85         itvls.push_back(ans[i]);
 86 }    //合并线段
 87 
 88 int n;
 89 
 90 int main() {
 91     while (cin >> n && n) {
 92         int bx, by, a, b, R;
 93         scanf("%d%d", &bx, &by);
 94         for (int i = 0; i < n; ++i) {
 95             scanf("%d%d%d", &a, &b, &R);
 96             C[i].c.x = a, C[i].c.y = b, C[i].r = R;
 97         }
 98         Point B(bx, by);
 99         Vector v[2];
100         vector<Interval> itvls;
101         double l, r;
102         for (int i = 0; i < n; ++i) {
103             getTangents(B, C[i], v);
104             l = LineInterX_axisPoint(B, v[0]), r = LineInterX_axisPoint(B, v[1]);
105             if (l > r)swap(l, r);
106             itvls.push_back(Interval(l, r));
107         }
108         CombineIntervals(itvls);
109         for (int i = 0; i < (int)itvls.size(); ++i)
110             printf("%.2lf %.2lf\n", itvls[i].l, itvls[i].r);
111         printf("\n");
112     }
113 }