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:
![](https://images.cnblogs.com/OutliningIndicators/ContractedBlock.gif)
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