POJ 2986 A Triangle and a Circle 圆与三角形的公共面积
计算几何模板
1 #include<stdio.h> 2 #include<string.h> 3 #include<stdlib.h> 4 #include<math.h> 5 #include<algorithm> 6 7 const double eps = 1e-8; 8 const double pi = acos(-1.0); 9 10 int dcmp(double x) 11 { 12 if(x > eps) return 1; 13 return x < -eps ? -1 : 0; 14 } 15 16 struct Point 17 { 18 double x, y; 19 Point() 20 { 21 x = y = 0; 22 } 23 Point(double a, double b) 24 { 25 x = a, y = b; 26 } 27 inline void read() 28 { 29 scanf("%lf%lf", &x, &y); 30 } 31 inline Point operator-(const Point &b)const 32 { 33 return Point(x - b.x, y - b.y); 34 } 35 inline Point operator+(const Point &b)const 36 { 37 return Point(x + b.x, y + b.y); 38 } 39 inline Point operator*(const double &b)const 40 { 41 return Point(x * b, y * b); 42 } 43 inline double dot(const Point &b)const 44 { 45 return x * b.x + y * b.y; 46 } 47 inline double cross(const Point &b, const Point &c)const 48 { 49 return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y); 50 } 51 inline double Dis(const Point &b)const 52 { 53 return sqrt((*this - b).dot(*this - b)); 54 } 55 inline bool InLine(const Point &b, const Point &c)const//三点共线 56 { 57 return !dcmp(cross(b, c)); 58 } 59 inline bool OnSeg(const Point &b, const Point &c)const//点在线段上，包括端点 60 { 61 return InLine(b, c) && (*this - c).dot(*this - b) < eps; 62 } 63 }; 64 65 inline double min(double a, double b) 66 { 67 return a < b ? a : b; 68 } 69 inline double max(double a, double b) 70 { 71 return a > b ? a : b; 72 } 73 inline double Sqr(double x) 74 { 75 return x * x; 76 } 77 inline double Sqr(const Point &p) 78 { 79 return p.dot(p); 80 } 81 82 Point LineCross(const Point &a, const Point &b, const Point &c, const Point &d) 83 { 84 double u = a.cross(b, c), v = b.cross(a, d); 85 return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v)); 86 } 87 88 double LineCrossCircle(const Point &a, const Point &b, const Point &r, 89 double R, Point &p1, Point &p2) 90 { 91 Point fp = LineCross(r, Point(r.x + a.y - b.y, r.y + b.x - a.x), a, b); 92 double rtol = r.Dis(fp); 93 double rtos = fp.OnSeg(a, b) ? rtol : min(r.Dis(a), r.Dis(b)); 94 double atob = a.Dis(b); 95 double fptoe = sqrt(R * R - rtol * rtol) / atob; 96 if(rtos > R - eps) return rtos; 97 p1 = fp + (a - b) * fptoe; 98 p2 = fp + (b - a) * fptoe; 99 return rtos; 100 } 101 102 double SectorArea(const Point &r, const Point &a, const Point &b, double R) 103 //不大于180度扇形面积，r->a->b逆时针 104 { 105 double A2 = Sqr(r - a), B2 = Sqr(r - b), C2 = Sqr(a - b); 106 return R * R * acos((A2 + B2 - C2) * 0.5 / sqrt(A2) / sqrt(B2)) * 0.5; 107 } 108 109 double TACIA(const Point &r, const Point &a, const Point &b, double R) 110 //TriangleAndCircleIntersectArea，逆时针，r为圆心 111 { 112 double adis = r.Dis(a), bdis = r.Dis(b); 113 if(adis < R + eps && bdis < R + eps) return r.cross(a, b) * 0.5; 114 Point ta, tb; 115 if(r.InLine(a, b)) return 0.0; 116 double rtos = LineCrossCircle(a, b, r, R, ta, tb); 117 if(rtos > R - eps) return SectorArea(r, a, b, R); 118 if(adis < R + eps) return r.cross(a, tb) * 0.5 + SectorArea(r, tb, b, R); 119 if(bdis < R + eps) return r.cross(ta, b) * 0.5 + SectorArea(r, a, ta, R); 120 return r.cross(ta, tb) * 0.5 + 121 SectorArea(r, a, ta, R) + SectorArea(r, tb, b, R); 122 } 123 124 const int N = 505; 125 126 Point p[N]; 127 128 double SPICA(int n, Point r, double R)//SimplePolygonIntersectCircleArea 129 { 130 int i; 131 double res = 0, if_clock_t; 132 for(i = 0; i < n; ++ i) 133 { 134 if_clock_t = dcmp(r.cross(p[i], p[(i + 1) % n])); 135 if(if_clock_t < 0) res -= TACIA(r, p[(i + 1) % n], p[i], R); 136 else res += TACIA(r, p[i], p[(i + 1) % n], R); 137 } 138 return fabs(res); 139 } 140 141 double r; 142 143 int main() 144 { 145 while (~scanf("%lf%lf", &p[0].x, &p[0].y)) 146 { 147 for (int i = 1; i < 4; i++) 148 p[i].read(); 149 scanf("%lf", &r); 150 printf("%.2f\n", SPICA(3, p[3], r)); 151 } 152 return 0; 153 }
