把点集凸包化Granham-Scan算法(使用水平序)概要

把点集凸包化Granham-Scan算法（使用水平序）#include<stdio.h>#include<string.h>#include<math.h>#include<algorithm>using nameaace std;const int M=100000+5;struct Point{double x,y;} p[M];double dis(Point A,Point B){return sqrt((B.x-A.x)*(B.x-A.x)+(B.y-A.y)*(B.y-A.y));}bool cmp(Point a,Point b){if (a.x<b.x) return true;if (a.x>b.x) return false;if (a.y<b.y) return true;return false;}double Xdet(Point A,Point B,Point C){double x1,x2,y1,y2;x1=B.x-A.x; y1=B.y-A.y; x2=C.x-A.x; y2=C.y-A.y;return x1*y2-x2*y1; //大于0在左手边，逆时针}bool bo[M];Point pp[M];int stack[M]; //from 1 to tvoid Gram_Scan(Point *p,int &n) //p从1-n,把点集土包化 n*log(n); {int i,t;sort(p+1,p+1+n,cmp);for(t=0,i=1;i<=n;i++){ //合并排序if (i>1 && p[i].x==p[i-1].x && p[i].y==p[i-1].y) continue;p[++t]=p[i];}n=t; t=0;memset(bo+1,true,n*sizeof(bo[0]));if (n>0){stack[++t]=1;bo[stack[t]]=false;}if (n>1){stack[++t]=2;bo[stack[t]]=false;}if (n>2){for(i=3;i<n;i++)if(bo[i] && Xdet(p[stack[t-1]],p[stack[t]],p[i])>=0) stack[++t]=i,bo[i]=false;else{while(t>=2&& Xdet(p[stack[t-1]],p[stack[t]],p[i])<0) bo[stack[t]]=true,t--;stack[++t]=i;bo[stack[t]]=false;}for(i=n;i>=1;i--)if (bo[i] && Xdet(p[stack[t-1]],p[stack[t]],p[i])>=0) stack[++t]=i,bo[i]=false;else{while(t>=2&&Xdet(p[stack[t-1]],p[stack[t]],p[i])<0) bo[stack[t]]=true,t--;stack[++t]=i;bo[stack[t]]=false;}t--;}for(i=1;i<=t;i++) pp[i]=p[stack[i]];memcpy(p+1,pp+1,t*sizeof(Point));n=t;}求凸点集的面积double area(Point *p,int n){double sum=0;int i;p[n+1]=p[1];for(i=1;i<=n;i++)sum+=p[i].x*p[i+1].y-p[i].y*p[i+1].x;return sum/2.0;}const double EPS=1e-9;const double maxn=1e6-1;const double PI=acos(-1.);const int M=100+5;const double offset=11213;#define zero(x) (((x)>0?(x):-(x))<EPS)struct Point{double x,y;} p[M];struct LINESEG{Point st,ed;};struct LINE{double a,b,c;};double dist(Point a,Point b){return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}double multiply(Point a,Point b,Point c){return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);}double dotmultiply(Point a,Point b,Point c){return (a.x-c.x)*(b.x-c.x)+(a.y-c.y)*(b.y-c.y);}bool online(LINESEG L,Point q){return fabs(multiply(L.ed,q,L.st))<EPS && (q.x-L.st.x)*(q.x-L.ed.x)<EPS && (q.y-L.st.y)*(q.y-L.ed.y)<EPS; }LINE makeline(Point p1,Point p2){LINE tl;tl.a=p2.y-p1.y; tl.b=p1.x-p2.x;tl.c=p1.y*p2.x-p1.x*p2.y;if (tl.a<EPS) tl.a=-tl.a,tl.b=-tl.b,tl.c=-tl.c;return tl;}inline double MAX(double x,double y){return x>y?x:y;}inline double MIN(double x,double y){return x<y?x:y;}bool intersect(LINESEG u,LINESEG v){return MAX(u.st.x,u.ed.x)>=MIN(v.st.x,v.ed.x)&& MAX(v.st.x,v.ed.x)>=MIN(u.st.x,u.ed.x)&& MAX(u.st.y,u.ed.y)>=MIN(v.st.y,v.ed.y)&& MAX(v.st.y,v.ed.y)>=MIN(u.st.y,u.ed.y)&& multiply(v.st,u.ed,u.st)*multiply(u.ed,v.ed,u.st)>=0&& multiply(u.st,v.ed,v.st)*multiply(v.ed,u.ed,v.st)>=0;}bool intersect_A(LINESEG u,LINESEG v){return intersect(u,v) && !online(u,v.st) && !online(u,v.ed)&& !online(v,u.st) && !online(u,v.ed);}bool intersect_L(LINESEG u,LINESEG v){return multiply(u.st,v.ed,v.st)*multiply(v.ed,u.ed,v.st)>=0;}bool intersection_line(LINE L1,LINE L2,Point &inter){ double det=L1.a*L2.b-L2.a*L1.b;if (fabs(det)<EPS) return false;inter.x=(L2.c*L1.b-L1.c*L2.b)/det;inter.y=(L2.a*L1.c-L1.a*L2.c)/det;return true;}bool intersection_lineseg(LINESEG u,LINESEG v,Point &inter){ LINE L1,L2;L1=makeline(u.st,u.ed);L2=makeline(v.st,v.ed);if (intersection_line(L1,L2,inter)) return online(u,inter) && online(v,inter);else return false;}bool intersection_LLS(LINE L1,LINESEG u,Point &inter){ LINE L2;L2=makeline(u.st,u.ed);if (intersection_line(L1,L2,inter))return online(u,inter);else return false;}int Inside(Point q,int n){Point q2;const int on_edge=0;int i=0,count;p[n]=p[0];while (i<n)for(count=0,i=0,q2.x=rand()+offset,q2.y=rand()+offset;i<n;i++)if (zero(multiply(q,p[i],p[i+1])) && (p[i].x-q.x)*(p[i+1].x-q.x)<EPS && (p[i].y-q.y)*(p[i+1].y-q.y)<EPS) return on_edge;else if (zero(multiply(q,q2,p[i]))) break;else if (multiply(q,p[i],q2)*multiply(q,p[i+1],q2)<-EPS &&multiply(p[i],q,p[i+1])*multiply(p[i],q2,p[i+1])<-EPS) count++;return count&1;}bool cmp(Point p,Point q){if (p.x<q.x) return true;if (p.x>q.x) return false;if (p.y<q.y) return true;return false;}//线段与多边形相交定义为至少有1个点在多边形内，返回true; bool LINESEG_intersect_Polygon(LINESEG LS1,int n) {LINESEG LS2;Point mid;int i;int j,top;Point stack[M];p[n]=p[000];for(i=0;i<n;i++){LS2.st=p[i]; LS2.ed=p[i+1];if (intersect_A(LS1,LS2)) return true;}top=0;stack[top++]=LS1.st;stack[top++]=LS1.ed;for(i=0;i<n;i++)if (online(LS1,p[i])) stack[top++]=p[i];sort(stack,stack+top,cmp);stack[top]=stack[0];for(j=0;j<top;j++) {mid.x=(stack[j].x+stack[j+1].x)/2;mid.y=(stack[j].y+stack[j+1].y)/2;if (Inside(mid,n)) return true;}return false;}const int M=15000;struct Line{double a,b,c;}L[M];struct Point{double x,y;} p[M],pp[M];//由两点化一般式Line LineChange(Point P1,Point P2){Line K;K.a=P2.y-P1.y;//(y2-y1)*x+(x1-x2)*y-(x1-x2)*y1-x1*(y2-y1)=0; counterclockK.b=P1.x-P2.x;K.c=-P1.x*K.a-K.b*P1.y;return k;}//求两直线交点bool GetSegcross(Line K1,Line K2,Point &pp){double det=K1.a*K2.b-K2.a*K1.b;if (fabs(det)<1e-8) return 0;pp.x=(K1.b*K2.c-K2.b*K1.c)/det;pp.y=-(K1.a*K2.c-K2.a*K1.c)/det;return 1;}//p在直线上返回0.00double p_on_line(Line K,Point p){return K.a*p.x+K.b*p.y+K.c;}//求两点的垂直平分线void MidLine(Point P1,Point P2,Line &K){K.a=2*(P1.x-P2.x);K.b=2*(P1.y-P2.y);K.c=(-K.a*(P1.x+P2.x)-K.b*(P1.y+P2.y))/2;}//求任意点对的最小距离，分治nlogn.double nearest(Point *p, int n) //p should already be sorted by x{if(n==2) return dist(p[0], p[1]);if(n==1) return INF;int m=p[n/2].x,i,j;double left,right,tmp,ret,t;left=nearest(p,n/2); right=nearest(&p[n/2],n-n/2);ret=tmp =left<right?left:right;for(i=n/2-1; i>=0 && p[i].x>m-tmp_nearest;i--)for(j=n/2; j<n && p[j].x<m+tmp_nearest;j++) {t=dist(p[i],p[j]);if(t<tmp_nearest) ret=t;}return ret;}Euler的任意四面体体积公式（已知边长求体积）已知4点坐标求体积（其中四个点的坐标分别为（x1,y1,z1）,（x2,y2,z2）,（x3,y3,z3）,（x4,y4,z4））11111234(1/6)*.12341234x x x xVy y y yz z z z=22222222222222222222222236.2222p q n p r mpp q n q r lV qp r m q r lr+-+-+-+-=+-+-。