判断线段相交，凸包

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判断线段相交

#include<cstdio>#include<algorithm>using namespace std;typedef struct dotnode{double x;double y;}dot;double Direction(dot pi,dot pj,dot pk){    return (pk.x-pi.x)*(pj.y-pi.y)-(pj.x-pi.x)*(pk.y-pi.y);}bool OnSegment(dot pi,dot pj,dot pk){if ((min(pi.x,pj.x)<=pk.x)&&(pk.x<=max(pi.x,pj.x))&&(min(pi.y,pj.y)<=pk.y)&&(pk.y<=max(pi.y,pj.y)))    return true;else return false;}bool SegmentIntersect(dot p1,dot p2,dot p3,dot p4){int d1,d2,d3,d4;d1=Direction(p3,p4,p1);d2=Direction(p3,p4,p2);d3=Direction(p1,p2,p3);d4=Direction(p1,p2,p4);if(((d1>0&&d2<0)||(d1<0&&d2>0))&&((d3>0&&d4<0)||(d3<0&&d4>0))) return true;else if(d1==0&&OnSegment(p3,p4,p1))    return true;else if(d2==0&&OnSegment(p3,p4,p2))    return true;else if(d3==0&&OnSegment(p1,p2,p3))    return true;else if(d4==0&&OnSegment(p1,p2,p4))    return true;else return false;}int main(){dot p1,p2,p3,p4;p1.x=1,p1.y=1;p2.x=3,p2.y=4;p3.x=0,p3.y=3;p4.x=4,p4.y=-1;printf("%d\n",SegmentIntersect(p1,p2,p3,p4));printf("%d\n",SegmentIntersect(p1,p3,p2,p4));}

凸包

#include<cstdio>#include<algorithm> using namespace std;#define MAX 10000typedef struct DotNode{double x;double y;}dot;dot Stack[MAX];int top;dot p[MAX];int FindMin(int n){int k=0;    for(int i=1;i<n;i++){      if(p[i].y<p[k].y||((p[i].y==p[k].y)&&(p[i].x<p[k].x)))           k=i;    }    return k;}double Direction(dot pi,dot pj,dot pk){    return (pk.x-pi.x)*(pj.y-pi.y)-(pj.x-pi.x)*(pk.y-pi.y);}double Distance(dot p1,dot p2){return ((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));}bool cmp(const dot a,const dot b){if(Direction(a,b,p[0])<0)return true;if(Direction(a,b,p[0])==0&&Distance(a,p[0])>=Distance(b,p[0]))return true;return false;}void Graham(int n){int tmp=FindMin(n);top=2;swap(p[0],p[tmp]);sort(p+1,p+n,cmp);Stack[0]=p[0],Stack[1]=p[1],Stack[2]=p[2];for(int i=3;i<n;i++){while(top>1&&Direction(Stack[top-1],Stack[top],p[i])>=0){top--;}Stack[++top]=p[i];}}int main(){p[0].x=2.3,p[0].y=2.3;p[1].x=9.2,p[1].y=1.2;p[2].x=3.2,p[2].y=8;p[3].x=12.1,p[3].y=10;p[4].x=6.5,p[4].y=4;p[5].x=4,p[5].y=7.2;p[6].x=2,p[6].y=6;p[7].x=8.9,p[7].y=6;p[8].x=2,p[8].y=1.2;p[9].x=7.4,p[9].y=5.4;Graham(10); for(int i=0;i<=top;i++){printf("（%lf,%lf）\n",Stack[i].x,Stack[i].y);}}

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