1.多边形面积计算
1 double S(Point p[],int n) 2 { 3 double ans = 0; 4 p[n] = p[0]; 5 for(int i=1;i<n;i++) 6 ans += cross(p[0],p[i],p[i+1]); 7 if(ans < 0) ans = -ans; 8 return ans / 2.0; 9 }
2.求凸包
1 bool cmp(Point A,Point B) 2 { 3 double k = cross(MinA,A,B); 4 if(k<0) return 0; 5 if(k>0) return 1; 6 return dist(MinA,A)<dist(MinA,B); 7 } 8 9 void Graham(Point p[],int n) 10 { 11 for(int i=1;i<n;i++) 12 if(p[i].y<p[0].y || (p[i].y == p[0].y && p[i].x < p[0].x)) 13 swap(p[i],p[0]); 14 MinA = p[0]; 15 p[n] = p[0]; 16 sort(p+1,p+n,cmp); 17 stack[0] = p[0]; 18 stack[1] = p[1]; 19 top = 2; 20 for(int i=2;i<n;i++) 21 { 22 while(top >= 2 && cross(stack[top-2],stack[top-1],p[i])<=0) top--; 23 stack[top++] = p[i]; 24 } 25 }
3.任意多边形求重心
1 Point Gravity(Point p[],int n) 2 { 3 Point O,t; 4 O.x = O.y = 0; 5 t.x = t.y = 0; 6 p[n] = p[0]; 7 double A = 0; 8 for(int i=0; i<n; i++) 9 A += cross(O,p[i],p[i+1]); 10 A /= 2.0; 11 for(int i=0; i<n; i++) 12 { 13 t.x += (p[i].x + p[i+1].x) * cross(O,p[i],p[i+1]); 14 t.y += (p[i].y + p[i+1].y) * cross(O,p[i],p[i+1]); 15 } 16 t.x /= 6*A; 17 t.y /= 6*A; 18 return t; 19 }
4.求线段交点的坐标
1 bool Segment_crossing(Segment u,Segment v) /** 判断线段是否相交 */ 2 { 3 return((max(u.a.x,u.b.x)>=min(v.a.x,v.b.x))&& 4 (max(v.a.x,v.b.x)>=min(u.a.x,u.b.x))&& 5 (max(u.a.y,u.b.y)>=min(v.a.y,v.b.y))&& 6 (max(v.a.y,v.b.y)>=min(u.a.y,u.b.y))&& 7 (cross(v.a,u.b,u.a)*cross(u.b,v.b,u.a)>=0)&& 8 (cross(u.a,v.b,v.a)*cross(v.b,u.b,v.a)>=0)); 9 } 10 11 /**求直线交点的坐标，如果没有交点返回NULL，否则返回交点p的地址*/ 12 Point* CrossPoint(Segment u,Segment v) 13 { 14 Point p; 15 if(Segment_crossing(u,v)) 16 { 17 p.x=(cross(v.b,u.b,u.a)*v.a.x-cross(v.a,u.b,u.a)*v.b.x)/(cross(v.b,u.b,u.a)-cross(v.a,u.b,u.a)); 18 p.y=(cross(v.b,u.b,u.a)*v.a.y-cross(v.a,u.b,u.a)*v.b.y)/(cross(v.b,u.b,u.a)-cross(v.a,u.b,u.a)); 19 return &p; 20 } 21 return NULL; 22 }
5.三角形外接圆的半径与圆心
1 Point Circle_Point(Point A,Point B,Point C) 2 { 3 double a=dist(B,C); 4 double b=dist(A,C); 5 double c=dist(A,B); 6 double p=(a+b+c)/2.0; 7 double S=sqrt(p*(p-a)*(p-b)*(p-c)); 8 R=(a*b*c)/(4*S); //三角形外接圆的半径为R 9 10 double t1=(A.x*A.x+A.y*A.y-B.x*B.x-B.y*B.y)/2; 11 double t2=(A.x*A.x+A.y*A.y-C.x*C.x-C.y*C.y)/2; 12 Point center; 13 center.x=(t1*(A.y-C.y)-t2*(A.y-B.y))/((A.x-B.x)*(A.y-C.y)-(A.x-C.x)*(A.y-B.y)); 14 center.y=(t1*(A.x-C.x)-t2*(A.x-B.x))/((A.y-B.y)*(A.x-C.x)-(A.y-C.y)*(A.x-B.x)); 15 return center; 16 }
6.旋转卡壳求凸包的直径，也就是平面最远点对，p[]为凸包的点集
1 double rotating_calipers(Point p[],int n) 2 { 3 int k = 1; 4 double ans = 0; 5 p[n] = p[0]; 6 for(int i=0;i<n;i++) 7 { 8 while(fabs(cross(p[i],p[i+1],p[k])) < fabs(cross(p[i],p[i+1],p[k+1]))) 9 k = (k+1) % n; 10 ans = max(ans, max(dist(p[i],p[k]),dist(p[i+1],p[k]))); 11 } 12 return ans; 13 }
7.求凸包的宽度
1 double rotating_calipers(Point p[],int n) 2 { 3 int k = 1; 4 double ans = 0x7FFFFFFF; 5 p[n] = p[0]; 6 for(int i=0;i<n;i++) 7 { 8 while(fabs(cross(p[i],p[i+1],p[k])) < fabs(cross(p[i],p[i+1],p[k+1]))) 9 k = (k+1) % n; 10 double tmp = fabs(cross(p[i],p[i+1],p[k])); 11 double d = dist(p[i],p[i+1]); 12 ans = min(ans,tmp/d); 13 } 14 return ans; 15 }
点的向量，叉乘，点乘
1 const double eps = 1e-8; 2 int sgn(double x) 3 { 4 if(fabs(x) < eps)return 0; 5 if(x < 0) return -1; 6 else return 1; 7 } 8 struct Point 9 { 10 double x,y; 11 Point(){} 12 Point(double _x,double _y) 13 { 14 x = _x;y = _y; 15 } 16 Point operator -(const Point &b)const 17 { 18 return Point(x - b.x,y - b.y); 19 } 20 double operator ^(const Point &b)const 21 { 22 return x*b.y - y*b.x; 23 } 24 double operator *(const Point &b)const 25 { 26 return x*b.x + y*b.y; 27 } 28 }; 29 struct Line 30 { 31 Point s,e; 32 Line(){} 33 Line(Point _s,Point _e) 34 { 35 s = _s;e = _e; 36 } 37 }; 38 //判断线段相交 39 bool inter(Line l1,Line l2) 40 { 41 return 42 max(l1.s.x,l1.e.x) >= min(l2.s.x,l2.e.x) && 43 max(l2.s.x,l2.e.x) >= min(l1.s.x,l1.e.x) && 44 max(l1.s.y,l1.e.y) >= min(l2.s.y,l2.e.y) && 45 max(l2.s.y,l2.e.y) >= min(l1.s.y,l1.e.y) && 46 sgn((l2.s-l1.s)^(l1.e-l1.s))*sgn((l2.e-l1.s)^(l1.e-l1.s)) <= 0 && 47 sgn((l1.s-l2.s)^(l2.e-l2.s))*sgn((l1.e-l2.s)^(l2.e-l2.s)) <= 0; 48 } 49 double dist(Point a,Point b) 50 { 51 return sqrt((b-a)*(b-a)); 52 }