uva 11178 Morley's Theorem (2D Geometry)

http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=2119
　　在uva跪了一个下午后提交这题，AC了。这题更简单，就是套入几何模板，求出交点就可以了。
　　这题测试通过了几何模板中的相交判断并求出交点等几个函数。
代码如下：
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  1  #include <cstdio>
  2  #include <cstring>
  3  #include <cmath>
  4  #include <vector>
  5  #include <iostream>
  6  #include <algorithm>
  7  
  8  using namespace std;
  9  
 10  #define REP(i, n) for (int i = 0; i < (n); i++)
 11  
 12  struct Point {
 13      double x, y;
 14      Point() {}
 15      Point(double x, double y) : x(x), y(y) {}
 16  } ;
 17  template<class T> T sqr(T x) { return x * x;}
 18  
 19  // basic calculations
 20  typedef Point Vec;
 21  Vec operator + (Vec a, Vec b) { return Vec(a.x + b.x, a.y + b.y);}
 22  Vec operator - (Vec a, Vec b) { return Vec(a.x - b.x, a.y - b.y);}
 23  Vec operator * (Vec a, double p) { return Vec(a.x * p, a.y * p);}
 24  Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}
 25  
 26  const double eps = 1e-8;
 27  int sgn(double x) { return fabs(x) < eps ? 0 : (x < 0 ? -1 : 1);}
 28  bool operator < (Point a, Point b) { return a.x < b.x || (a.x == b.x && a.y < b.y);}
 29  bool operator == (Point a, Point b) { return sgn(a.x - b.x) == 0 && sgn(a.y - b.y) == 0;}
 30  
 31  double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}
 32  double vecLen(Vec x) { return sqrt(sqr(x.x) + sqr(x.y));}
 33  double angle(Vec a, Vec b) { return acos(dotDet(a, b) / vecLen(a) / vecLen(b));}
 34  double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}
 35  double triArea(Point a, Point b, Point c) { return fabs(crossDet(b - a, c - a));}
 36  Vec rotate(Vec x, double rad) { return Vec(x.x * cos(rad) - x.y * sin(rad), x.x * sin(rad) + x.y * cos(rad));}
 37  Vec normal(Vec x) {
 38      double len = vecLen(x);
 39      return Vec(- x.y / len, x.x / len);
 40  }
 41  
 42  struct Line {
 43      Point s, t;
 44      Line() {}
 45      Line(Point s, Point t) : s(s), t(t) {}
 46  } ;
 47  typedef Line Seg;
 48  
 49  bool onSeg(Point x, Point a, Point b) { return sgn(crossDet(a - x, b - x)) == 0 && sgn(dotDet(a - x, b - x)) < 0;}
 50  bool onSeg(Point x, Seg s) { return onSeg(x, s.s, s.t);}
 51  // 0 : not intersect
 52  // 1 : proper intersect
 53  // 2 : improper intersect
 54  int segIntersect(Point a, Point c, Point b, Point d) {
 55      Vec v1 = b - a, v2 = c - b, v3 = d - c, v4 = a - d;
 56      int a_bc = sgn(crossDet(v1, v2));
 57      int b_cd = sgn(crossDet(v2, v3));
 58      int c_da = sgn(crossDet(v3, v4));
 59      int d_ab = sgn(crossDet(v4, v1));
 60      if (a_bc * c_da > 0 && b_cd * d_ab > 0) return 1;
 61      if (onSeg(b, a, c) && c_da) return 2;
 62      if (onSeg(c, b, d) && d_ab) return 2;
 63      if (onSeg(d, c, a) && a_bc) return 2;
 64      if (onSeg(a, d, b) && b_cd) return 2;
 65      return 0;
 66  }
 67  int segIntersect(Seg a, Seg b) { return segIntersect(a.s, a.t, b.s, b.t);}
 68  
 69  // point of the intersection of 2 lines
 70  Point lineIntersect(Point P, Vec v, Point Q, Vec w) {
 71      Vec u = P - Q;
 72      double t = crossDet(w, u) / crossDet(v, w);
 73      return P + v * t;
 74  }
 75  Point lineIntersect(Line a, Line b) { return lineIntersect(a.s, a.t - a.s, b.s, b.t - b.s);}
 76  
 77  // directed distance
 78  double pt2Line(Point x, Point a, Point b) {
 79      Vec v1 = b - a, v2 = x - a;
 80      return crossDet(v1, v2) / vecLen(v1);
 81  }
 82  double pt2Line(Point x, Line L) { return pt2Line(x, L.s, L.t);}
 83  
 84  double pt2Seg(Point x, Point a, Point b) {
 85      if (a == b) return vecLen(x - a);
 86      Vec v1 = b - a, v2 = x - a, v3 = x - b;
 87      if (sgn(dotDet(v1, v2)) < 0) return vecLen(v2);
 88      if (sgn(dotDet(v1, v3)) > 0) return vecLen(v3);
 89      return fabs(crossDet(v1, v2)) / vecLen(v1);
 90  }
 91  double pt2Seg(Point x, Seg s) { return pt2Seg(x, s.s, s.t);}
 92  
 93  struct Poly {
 94      vector<Point> pt;
 95      Poly() {}
 96      Poly(vector<Point> pt) : pt(pt) {}
 97      double area() {
 98          double ret = 0.0;
 99          int sz = pt.size();
100          for (int i = 1; i < sz; i++) {
101              ret += crossDet(pt[i], pt[i - 1]);
102          }
103          return fabs(ret / 2.0);
104      }
105  } ;
106  
107  /****************** template above *******************/
108  
109   Point p[3];
110   
111   Point cal(Point a, Point b, Point c) {
112       double angB = fabs(angle(c - b, a - b) / 3.0);
113       double angC = fabs(angle(b - c, a - c) / 3.0);
114       Vec v1, v2;
115       v1 = rotate(c - b, angB);
116       v2 = rotate(b - c, -angC);
117   //    return lineIntersect(Line(b, b + v1), Line(c, c + v2));
118       return lineIntersect(b, v1, c, v2);
119   }
120   
121   int main() {
122   //    freopen("in", "r", stdin);
123       int n;
124       cin >> n;
125       while (n--) {
126           for (int i = 0; i < 3; i++) {
127               cin >> p[i].x >> p[i].y;
128           }
129           for (int i = 0; i < 3; i++) {
130               Point tmp = cal(p[i % 3], p[(i + 1) % 3], p[(i + 2) % 3]);
131               if (i) putchar(' ');
132               printf("%.10f %.10f", tmp.x, tmp.y);
133           }
134           cout << endl;
135       }
136       return 0;
137   }
——written by Lyon