几何模板总结——算法竞赛入门经典（第二版）

 1 #include <iostream>

 2 #include <string>

 3 #include <cstdio>

 4 #include <cstring>

 5 #include <cmath>

 6 #include <vector>

 7 #include <algorithm>

 8 

 9 using namespace std;  10 

 11 const double PI = acos(-1);  12 

 13 struct Point {  14     double x, y;  15     Point(double x = 0, double y = 0) : x(x), y(y) {}  16 };  17 

 18 typedef Point Vector;  19 Vector operator + (const Vector &A, const Vector &B) { return Vector(A.x + B.x, A.y + B.y); }  20 Vector operator - (const Point &A, const Point &B) { return Vector(A.x - B.x, A.y - B.y); }  21 Vector operator * (const Vector &A, const double &p) { return Vector(A.x * p, A.y * p); }  22 Vector operator / (const Vector &A, const double &p) { return Vector(A.x / p, A.y / p); }  23 bool operator < (const Point &a, const Point &b) { return a.x < b.x || (a.x == b.x && a.y < b.y); }  24 

 25 const double eps = 1e-10;  26 int dcmp(double x) {  27     if(fabs(x) < eps) return 0;  28     else return x < 0 ? -1 : 1;  29 }  30 

 31 bool operator == (const Point &a, const Point &b) { return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0; }  32 

 33 double Dot(const Vector &A, const Vector &B) { return A.x * B.x + A.y * B.y; }  34 double Length(const Vector &A) { return sqrt(Dot(A, A)); }  35 double Angle(const Vector &A, const Vector &B) { return acos(Dot(A, B) / Length(A) / Length(B)); }  36 

 37 double Cross(const Vector &A, const Vector B) { return A.x * B.y - A.y * B.x; }  38 double Area2(const Point &A, const Point &B, const Point &C) { return Cross(B - A, C - A); }  39 

 40 Vector Rotate(const Vector &A, double rad) { return Vector(A.x * cos(rad) - A.y * sin(rad), A.x * sin(rad) + A.y * cos(rad)); }  41 

 42 Vector Normal(const Vector &A) {  43     double L = Length(A);  44     return Vector(-A.y / L, A.x / L);  45 }  46 

 47 Point GetLineIntersection(const Point &P, const Vector &v, const Point &Q, const Vector &w) {  48     Vector u = P - Q;  49     double t = Cross(w, u) / Cross(v, w);  50     return P + v * t;  51 }  52 

 53 double DistanceToLine(const Point &P, const Point &A, const Point &B) {  54     Vector v1 = B - A, v2 = P - A;  55     return fabs(Cross(v1, v2)) / Length(v1);  56 }  57 double DistanceToLine_(const Point &P, const Point &A, const Point &B) {  58     Vector v1 = B - A, v2 = P - A;  59     return Cross(v1, v2) / Length(v1);  60 }  61 double DistanceToSegment(const Point &P, const Point &A, const Point &B) {  62     if(A == B) return Length(P - A);  63     Vector v1 = B - A, v2 = P - A, v3 = P - B;  64     if(dcmp(Dot(v1, v2)) < 0) return Length(v2);  65     else if(dcmp(Dot(v1, v3)) > 0) return Length(v3);  66     else return fabs(Cross(v1, v2)) / Length(v1);  67 }  68 

 69 Point GetLineProjection(const Point &P, const Point &A, const Point &B) {  70     Vector v = B - A;  71     return A + v * (Dot(v, P - A) / Dot(v, v));  72 }  73 

 74 bool SegmentProperIntersection(const Point &a1, const Point &a2, const Point &b1, const Point &b2) {  75     double c1 = Cross(a2 - a1, b1 - a1), c2 = Cross(a2 - a1, b2 - a1), c3 = Cross(b2 - b1, a1 - b1), c4 = Cross(b2 - b1, a2 - b1);  76     return dcmp(c1) * dcmp(c2) < 0 && dcmp(c3) * dcmp(c4) < 0;  77 }  78 

 79 bool OnSegment(const Point &p, const Point &a1, const Point &a2) {  80     return dcmp(Cross(a1 - p, a2 - p)) == 0 && dcmp(Dot(a1 - p, a2 - p)) < 0;  81 }  82 

 83 double ConvexPolygonArea(Point *p, int n) {  84     double area = 0;  85     for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]);  86     return area / 2;  87 }  88 

 89 double PolygonArea(Point *p, int n) {  90     double area = 0;  91 

 92     for(int i = 1; i < n - 1; ++i) area += Cross(p[i] - p[0], p[i + 1] - p[0]);  93     return area / 2;  94 }  95 

 96 struct Line {  97  Point p;  98  Vector v;  99  Line(Point p, Vector v):p(p),v(v) { } 100   Point point(double t) { 101     return p + v*t; 102  } 103   Line move(double d) { 104     return Line(p + Normal(v)*d, v); 105  } 106 }; 107 

108 Line getLine(double x1, double y1, double x2, double y2) { 109  Point p1(x1,y1); 110  Point p2(x2,y2); 111   return Line(p1, p2-p1); 112 } 113 

114 struct Circle { 115  Point c; 116     double r; 117 

118     Circle(Point c, double r) : c(c), r(r) {} 119 

120     Point point(const double &a) const { 121         return Point(c.x + cos(a) * r, c.y + sin(a) * r); 122  } 123 }; 124 

125 int getLineCircleIntersection(Line L, Circle C, double &t1, double &t2, vector<Point> &sol) { 126     double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y - C.c.y; 127     double e = a * a + c * c, f = 2 * (a * b + c * d), g = b * b + d * d - C.r * C.r; 128     double delta = f * f - 4 * e * g; 129     if(dcmp(delta) < 0) return 0; 130     if(dcmp(delta) == 0) { 131         t1 = t2 = -f / (2 * e); 132  sol.push_back(L.point(t1)); 133         return 1; 134  } 135     t1 = (-f - sqrt(delta)) / (2 * e); 136  sol.push_back(L.point(t1)); 137     t2 = (-f + sqrt(delta)) / (2 * e); 138  sol.push_back(L.point(t2)); 139     return 2; 140 } 141 

142 double angle(const Vector &v) { return atan2(v.y, v.x); } 143 

144 int getCircleCircleIntersection(Circle C1, Circle C2, vector<Point> &sol) { 145     double d = Length(C1.c - C2.c); 146     if(dcmp(d) == 0) { 147         if(dcmp(C1.r - C2.r) == 0) return -1; 148         return 0; 149  } 150     if(dcmp(C1.r + C2.r - d) < 0) return 0; 151     if(dcmp(fabs(C1.r - C2.r) - d) > 0) return 0; 152 

153     double a = angle(C2.c - C1.c); 154     double da = acos((C1.r * C1.r + d * d - C2.r * C2.r) / (2 * C1.r * d)); 155 

156     Point p1 = C1.point(a - da), p2 = C1.point(a + da); 157 

158  sol.push_back(p1); 159     if(p1 == p2) return 1; 160  sol.push_back(p2); 161     return 2; 162 } 163 

164 int getTangents(Point p, Circle C, Vector *v) { 165     Vector u = C.c - p; 166     double dist = Length(u); 167     if(dist < C.r) return 0; 168     else if(dcmp(dist - C.r) == 0) { 169 // v[0] = Rotate(u, PI / 2);

170         return 1; 171  } 172     else { 173         double ang = asin(C.r / dist); 174         v[0] = Rotate(u, -ang); 175         v[1] = Rotate(u, +ang); 176         return 2; 177  } 178 } 179 

180 int getTangents(Circle A, Circle B, Point *a, Point *b) { 181     int cnt = 0; 182     if(A.r < B.r) { swap(A, B); swap(a, b); } 183     int d2 = (A.c.x - B.c.x) * (A.c.x - B.c.x) + (A.c.y - B.c.y) * (A.c.y - B.c.y); 184     int rdiff = A.r - B.r; 185     int rsum = A.r + B.r; 186     if(d2 < rdiff * rdiff) return 0; 187 

188     double base = atan2(B.c.y - A.c.y, B.c.x - A.c.x); 189     if(d2 == 0 && A.r == B.r) return -1; 190     if(d2 == rdiff * rdiff) { 191         a[cnt] = A.point(base); 192         b[cnt] = B.point(base); 193         ++cnt; 194         return 1; 195  } 196     double ang = acos((A.r - B.r) / sqrt(d2)); 197     a[cnt] = A.point(base + ang); 198     b[cnt] = B.point(base + ang); 199     ++cnt; 200     a[cnt] = A.point(base - ang); 201     b[cnt] = B.point(base - ang); 202     ++cnt; 203     if(d2 == rsum * rsum) { 204         a[cnt] = A.point(base); 205         b[cnt] = B.point(PI + base); 206         ++cnt; 207  } 208     else if(d2 > rsum * rsum) { 209         double ang = acos((A.r + B.r) / sqrt(d2)); 210         a[cnt] = A.point(base + ang); 211         b[cnt] = B.point(PI + base + ang); 212         ++cnt; 213         a[cnt] = A.point(base - ang); 214         b[cnt] = B.point(PI + base - ang); 215         ++cnt; 216  } 217     return cnt; 218 } 219 

220 double torad(const double &deg) { 221     return deg / 180 * PI; 222 } 223 

224 void get_coord(const double &R, double lat, double lng, double &x, double &y, double &z) { 225     lat = torad(lat); 226     lng = torad(lng); 227     x = R * cos(lat) * cos(lng); 228     y = R * cos(lat) * sin(lng); 229     z = R * sin(lat); 230 } 231 

232 int ConvexHull(Point *p, int n, Point *ch) { 233     sort(p, p + n); 234     int m = 0; 235     for(int i = 0; i < n; ++i) { 236         while(m > 1 && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m; 237         ch[m++] = p[i]; 238  } 239     int k = m; 240     for(int i = n - 2; i >= 0; --i) { 241         while(m > k && Cross(ch[m - 1] - ch[m - 2], p[i] - ch[m - 2]) <= 0) --m; 242         ch[m++] = p[i]; 243  } 244     if(n > 1) --m; 245     return m; 246 } 247 

248 int  isPointInPolygon(Point p, Point *poly, int n) { 249     int wn = 0; 250     for(int i = 0;i < n; ++i) { 251         if(OnSegment(p, poly[i], poly[(i+1)%n])) return -1; 252         int k=dcmp(Cross(poly[(i+1)%n]-poly[i], p-poly[i])); 253         int d1=dcmp(poly[i].y-p.y); 254         int d2=dcmp(poly[(i+1)%n].y-p.y); 255         if(k>0&&d1<=0&&d2>0) wn++; 256         if(k<0&&d2<=0&&d1>0) wn--; 257  } 258     if(wn!=0)  return 1; 259     else return 0; 260 } 261 

262 Point read_point() { 263  Point P; 264     scanf("%lf%lf",&P.x,&P.y); 265     return P; 266 } 267 

268 int main() { 269 

270 }