hdu 4667 Building Fence < 计算几何模板>

  1 //大白p263

  2 #include <cmath>

  3 #include <cstdio>

  4 #include <cstring>

  5 #include <string>

  6 #include <queue>

  7 #include <functional>

  8 #include <set>

  9 #include <iostream>

 10 #include <vector>

 11 #include <algorithm>

 12 using namespace std;

 13 const double eps=1e-8;//精度

 14 const int INF=0x3f3f3f3f;

 15 const double PI=acos(-1.0);

 16 inline int dcmp(const double& x){//判断double等于0或。。。

 17     if(fabs(x)<eps)return 0;else return x<0?-1:1;

 18 }

 19 struct Point{

 20     double x,y;

 21     Point(){}

 22     Point(double x,double y):x(x),y(y){}

 23 };

 24 typedef Point Vector;

 25 typedef vector<Point> Polygon;

 26 inline Vector operator+(const Vector& a,const Vector& b){return Vector(a.x+b.x,a.y+b.y);}//向量+向量=向量

 27 inline Vector operator-(const Point& a,const Point& b){return Vector(a.x-b.x,a.y-b.y);}//点-点=向量

 28 inline Vector operator*(const Vector& a,const double& p){return Vector(a.x*p,a.y*p);}//向量*实数=向量

 29 inline Vector operator/(const Vector& a,const double& p){return Vector(a.x/p,a.y/p);}//向量/实数=向量

 30 inline bool operator<( const Point& A,const Point& B ){return dcmp(A.x-B.x)<0||(dcmp(A.x-B.x)==0&&dcmp(A.y-B.y)<0);}

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

 32 inline bool operator!=(const Point&a,const Point&b){return a==b?false:true;}

 33 struct Segment{

 34     Point a,b;

 35     Segment(){}

 36     Segment(Point _a,Point _b){a=_a,b=_b;}

 37     inline bool friend operator<(const Segment& p,const Segment& q){return p.a<q.a||(p.a==q.a&&p.b<q.b);}

 38     inline bool friend operator==(const Segment& p,const Segment& q){return (p.a==q.a&&p.b==q.b)||(p.a==q.b&&p.b==q.a);}

 39 };

 40 struct Circle{

 41     Point c;

 42     double r;

 43     Circle(){}

 44     Circle(Point _c, double _r):c(_c),r(_r) {}

 45     Point point(double a)const{return Point(c.x+cos(a)*r,c.y+sin(a)*r);}

 46     bool friend operator<(const Circle& a,const Circle& b){return a.r<b.r;}

 47 };

 48 struct Line{

 49     Point p;

 50     Vector v;

 51     double ang;

 52     Line() {}

 53     Line(const Point &_p, const Vector &_v):p(_p),v(_v){ang = atan2(v.y, v.x);}

 54     inline bool operator<(const Line &L)const{return  ang < L.ang;}

 55 };

 56 inline double Dot(const Vector& a,const Vector& b){return a.x*b.x+a.y*b.y;}//|a|*|b|*cosθ 点积

 57 inline double Length(const Vector& a){return sqrt(Dot(a,a));}//|a| 向量长度

 58 inline double Angle(const Vector& a,const Vector& b){return acos(Dot(a,b)/Length(a)/Length(b));}//向量夹角θ

 59 inline double Cross(const Vector& a,const Vector& b){return a.x*b.y-a.y*b.x;}//叉积 向量围成的平行四边形的面积

 60 inline double Area2(const Point& a,const Point& b,Point c){return Cross(b-a,c-a);}//同上 参数为三个点

 61 inline double DegreeToRadius(const double& deg){return deg/180*PI;}

 62 inline double GetRerotateAngle(const Vector& a,const Vector& b){//向量a顺时针旋转theta度得到向量b的方向

 63     double tempa=Angle(a,Vector(1,0));

 64     if(a.y<0) tempa=2*PI-tempa;

 65     double tempb=Angle(b,Vector(1,0));

 66     if(b.y<0) tempb=2*PI-tempb;

 67     if((tempa-tempb)>0) return tempa-tempb;

 68     else return tempa-tempb+2*PI;

 69 }

 70 inline double torad(const double& deg){return deg/180*PI;}//角度化为弧度

 71 inline Vector Rotate(const Vector& a,const double& rad){//向量逆时针旋转rad弧度

 72     return Vector(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));

 73 }

 74 inline Vector Normal(const Vector& a){//计算单位法线

 75     double L=Length(a);

 76     return Vector(-a.y/L,a.x/L);

 77 }

 78 inline Point GetLineProjection(const Point& p,const Point& a,const Point& b){//点在直线上的投影

 79     Vector v=b-a;

 80     return a+v*(Dot(v,p-a)/Dot(v,v));

 81 }

 82 inline Point GetLineIntersection(Point p,Vector v,Point q,Vector w){//求直线交点 有唯一交点时可用

 83     Vector u=p-q;

 84     double t=Cross(w,u)/Cross(v,w);

 85     return p+v*t;

 86 }

 87 int ConvexHull(Point* p,int n,Point* sol){//计算凸包

 88     sort(p,p+n);

 89     int m=0;

 90     for(int i=0;i<n;i++){

 91         while(m>1&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;

 92         sol[m++]=p[i];

 93     }

 94     int k=m;

 95     for(int i=n-2;i>=0;i--){

 96         while(m>k&&dcmp(Cross(sol[m-1]-sol[m-2],p[i]-sol[m-2]))<=0) m--;

 97         sol[m++]=p[i];

 98     }

 99     if(n>0) m--;

100     return m;

101 }

102 double Heron(double a,double b,double c){//海伦公式

103     double p=(a+b+c)/2;

104     return sqrt(p*(p-a)*(p-b)*(p-c));

105 }

106 bool SegmentProperIntersection(const Point& a1,const Point& a2,const Point& b1,const Point& b2){//线段规范相交判定

107     double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1);

108     double c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);

109     return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;

110 }

111 double CutConvex(const int& n,Point* poly,const Point& a,const Point& b, vector<Point> result[3]){//有向直线a b 切割凸多边形

112     vector<Point> points;

113     Point p;

114     Point p1=a,p2=b;

115     int cur,pre;

116     result[0].clear();

117     result[1].clear();

118     result[2].clear();

119     if(n==0) return 0;

120     double tempcross;

121     tempcross=Cross(p2-p1,poly[0]-p1);

122     if(dcmp(tempcross)==0) pre=cur=2;

123     else if(tempcross>0) pre=cur=0;

124     else pre=cur=1;

125     for(int i=0;i<n;i++){

126         tempcross=Cross(p2-p1,poly[(i+1)%n]-p1);

127         if(dcmp(tempcross)==0) cur=2;

128         else if(tempcross>0) cur=0;

129         else cur=1;

130         if(cur==pre){

131             result[cur].push_back(poly[(i+1)%n]);

132         }

133         else{

134             p1=poly[i];

135             p2=poly[(i+1)%n];

136             p=GetLineIntersection(p1,p2-p1,a,b-a);

137             points.push_back(p);

138             result[pre].push_back(p);

139             result[cur].push_back(p);

140             result[cur].push_back(poly[(i+1)%n]);

141             pre=cur;

142         }

143     }

144     sort(points.begin(),points.end());

145     if(points.size()<2){

146         return 0;

147     }

148     else{

149         return Length(points.front()-points.back());

150     }

151 }

152 double DistanceToSegment(Point p,Segment s){//点到线段的距离

153     if(s.a==s.b) return Length(p-s.a);

154     Vector v1=s.b-s.a,v2=p-s.a,v3=p-s.b;

155     if(dcmp(Dot(v1,v2))<0) return Length(v2);

156     else if(dcmp(Dot(v1,v3))>0) return Length(v3);

157     else return fabs(Cross(v1,v2))/Length(v1);

158 }

159 inline bool isPointOnSegment(const Point& p,const Segment& s){

160     return dcmp(Cross(s.a-p,s.b-p))==0&&dcmp(Dot(s.a-p,s.b-p))<0;

161 }

162 int isPointInPolygon(Point p, Point* poly,int n){//点与多边形的位置关系

163     int wn=0;

164     for(int i=0;i<n;i++){

165         Point& p2=poly[(i+1)%n];

166         if(isPointOnSegment(p,Segment(poly[i],p2))) return -1;//点在边界上

167         int k=dcmp(Cross(p2-poly[i],p-poly[i]));

168         int d1=dcmp(poly[i].y-p.y);

169         int d2=dcmp(p2.y-p.y);

170         if(k>0&&d1<=0&&d2>0)wn++;

171         if(k<0&&d2<=0&&d1>0)wn--;

172     }

173     if(wn) return 1;//点在内部

174     else return 0;//点在外部

175 }

176 double PolygonArea(Point* p,int n){//多边形有向面积

177     double area=0;

178     for(int i=1;i<n-1;i++)

179         area+=Cross(p[i]-p[0],p[i+1]-p[0]);

180     return area/2;

181 }

182 int GetLineCircleIntersection(Line L,Circle C,Point& p1,Point& p2){//圆与直线交点 返回交点个数

183     double a = L.v.x, b = L.p.x - C.c.x, c = L.v.y, d = L.p.y-C.c.y;

184     double e = a*a + c*c, f = 2*(a*b+c*d), g = b*b + d*d -C.r*C.r;

185     double delta = f*f - 4*e*g;

186     if(dcmp(delta) < 0)  return 0;//相离

187     if(dcmp(delta) == 0) {//相切

188         p1=p1=L.p+L.v*(-f/(2*e));

189         return 1;

190     }//相交

191     p1=(L.p+L.v*(-f-sqrt(delta))/(2*e));

192     p2=(L.p+L.v*(-f+sqrt(delta))/(2*e));

193     return 2;

194 }

195 double rotating_calipers(Point *ch,int n)//旋转卡壳

196 {

197     int q=1;

198     double ans=0;

199     ch[n]=ch[0];

200     for(int p=0;p<n;p++)

201     {

202         while(Cross(ch[q+1]-ch[p+1],ch[p]-ch[p+1])>Cross(ch[q]-ch[p+1],ch[p]-ch[p+1]))

203             q=(q+1)%n;

204         ans=max(ans,max(Length(ch[p]-ch[q]),Length(ch[p+1]-ch[q+1])));

205     }

206     return ans;

207 }

208 Polygon CutPolygon(Polygon poly,const Point& a,const Point& b){//用a->b切割多边形 返回左侧

209     Polygon newpoly;

210     int n=poly.size();

211     for(int i=0;i<n;i++){

212         Point c=poly[i];

213         Point d=poly[(i+1)%n];

214         if(dcmp(Cross(b-a,c-a))>=0) newpoly.push_back(c);

215         if(dcmp(Cross(b-a,c-d))!=0){

216             Point ip=GetLineIntersection(a,b-a,c,d-c);

217             if(isPointOnSegment(ip,Segment(c,d))) newpoly.push_back(ip);

218         }

219     }

220     return newpoly;

221 }

222 int GetCircleCircleIntersection(Circle c1,Circle c2,Point& p1,Point& p2){//求两圆相交

223     double d=Length(c1.c-c2.c);

224     if(dcmp(d)==0){

225         if(dcmp(c1.r-c2.r)==0) return -1;//两圆重合

226         return 0;

227     }

228     if(dcmp(c1.r+c2.r-d)<0) return 0;

229     if(dcmp(fabs(c1.r-c2.r)-d)>0) return 0;

230     double a=Angle(c2.c-c1.c,Vector(1,0));

231     double da=acos((c1.r*c1.r+d*d-c2.r*c2.r)/(2*c1.r*d));

232     p1=c1.point(a-da);p2=c1.point(a+da);

233     if(p1==p2) return 1;

234     return 2;

235 }

236 inline bool isPointOnleft(Point p,Line L){return dcmp(Cross(L.v,p-L.p))>0;}//点在直线左边 线上不算

237 int HalfplaneIntersection(Line *L,int n,Point* poly){//半平面交

238     sort(L,L+n);

239     int first,last;

240     Point* p=new Point[n];

241     Line* q=new Line[n];

242     q[first=last=0]=L[0];

243     for(int i=1;i<n;i++){

244         while(first<last&&!isPointOnleft(p[last-1],L[i])) last--;

245         while(first<last&&!isPointOnleft(p[first],L[i])) first++;

246         q[++last]=L[i];

247         if(dcmp(Cross(q[last].v,q[last-1].v))==0){

248             last--;

249             if(isPointOnleft(L[i].p,q[last])) q[last]=L[i];

250         }

251         if(first<last) p[last-1]=GetLineIntersection(q[last-1].p,q[last-1].v,q[last].p,q[last].v);

252     }

253     while(first<last&&!isPointOnleft(p[last-1],q[first])) last--;

254     if(last-first<=1) return 0;

255     p[last]=GetLineIntersection(q[last].p,q[last].v,q[first].p,q[first].v);

256     int m=0;

257     for(int i=first;i<=last;i++) poly[m++]=p[i];

258     return m;

259 }

260 //两点式化为一般式A = b.y-a.y, B = a.x-b.x, C = -a.y*(B)-a.x*(A);

261 //--------------------------------------

262 //--------------------------------------

263 //--------------------------------------

264 //--------------------------------------

265 //--------------------------------------

266 Point point[444444],ppoint[444444];

267 int main()

268 {

269     int n,m;

270     while(~scanf("%d%d",&n,&m))

271     {

272         int tot = 0;

273         double x,y,r;

274         for(int i = 0;i<n;i++)

275         {

276             scanf("%lf%lf%lf",&x,&y,&r);

277             for(double j = 0;j<2*PI;j += 0.0032)

278             {

279                 point[tot++] = Point(x+r*cos(j),y+r*sin(j));

280             }

281         }

282         for(int i = 0;i<m;i++)

283             for(int j = 0;j<3;j++)

284             {

285                 scanf("%lf%lf",&x,&y);

286                 point[tot++] = Point(x,y);

287             }

288         tot=ConvexHull(point,tot,ppoint);

289         double ans = 0;

290         Point pre = ppoint[0];

291         for(int i = 1;i<tot;i++)

292         {

293             ans += Length(ppoint[i]-pre);

294             pre = ppoint[i];

295         }

296         ans += Length(ppoint[0]-pre);

297         printf("%.5f\n",ans);

298     }

299     return 0;

300 }

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