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 }