计算几何模板（点+线段）1.0

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<algorithm>
  4 #include<cmath>
  5 using namespace std;
  6 const int INF = 0x3f3f3f3f;
  7 const int maxn = 100;
  8 const double eps = 1e-6;
  9 
 10 struct point
 11 {
 12     double x,y;
 13     point(double _x=0,double _y=0)
 14     {
 15         x = _x; y = _y;
 16     }
 17 };
 18 
 19 int sgn(double x)
 20 {
 21     if(fabs(x)<eps) return 0;
 22     if(x<0) return -1;
 23     else return 1;
 24 }
 25 
 26 //向量-向量
 27 point operator -(const point &a, const point &b) {return point(a.x-b.x, a.y-b.y);}
 28 //向量+向量
 29 point operator +(const point &a, const point &b) {return point(a.x+b.x, a.y+b.y);}
 30 //向量*向量
 31 point operator *(const double &a, const point &b) {return point(a*b.x, a*b.y);}
 32 //向量*常数 Dot
 33 double operator *(const point &a, const point &b) {return a.x*b.x+a.y*b.y;}
 34 //向量X向量
 35 double operator ^(const point &a, const point &b) {return a.x*b.y-a.y*b.x;}
 36 //向量==向量
 37 bool operator == (const point &a,const point &b) {return sgn(a.x-b.x)==0&&sgn(a.y-b.y)==0;}
 38 
 39 double Length(point a) {return sqrt(a*a);}
 40 //AB夹角
 41 double Angle(point a,point b) {return acos( a*b/Length(a)/Length(b) );}
 42 //AB、AC组成的平行四边形面积
 43 double Area(point a,point b,point c) {return (b-a)^(c-a);}
 44 //A逆时针旋转弧度rad后的向量
 45 point Rotate(point a,double rad) {return point(a.x*cos(rad)-a.y*sin(rad),a.x*sin(rad)+a.y*cos(rad));}
 46 //计算A的单位法线，保证A不为0向量
 47 point Normal(point a)
 48 {
 49     double L = Length(a);
 50     return point(-a.y/L,a.x/L);
 51 }
 52 
 53 struct line
 54 {
 55     point s,e;
 56     line(){}
 57     line(point _s,point _e)
 58     {
 59         s = _s; e = _e;
 60     }
 61 };
 62 
 63 //线段是否相交、端点算相交
 64 bool inter(line l1,line l2)
 65 {
 66     return
 67     min(l1.s.x,l1.e.x)<=max(l2.s.x,l2.e.x) &&
 68     min(l2.s.x,l2.e.x)<=max(l1.s.x,l1.e.x) &&
 69     min(l1.s.y,l1.e.y)<=max(l2.s.y,l2.e.y) &&
 70     min(l2.s.y,l2.e.y)<=max(l1.s.y,l1.e.y) &&
 71     sgn((l2.s-l1.e)^(l1.s-l1.e)) * sgn((l2.e-l1.e)^(l1.s-l1.e))<=0 &&
 72     sgn((l1.s-l2.e)^(l2.s-l2.e)) * sgn((l1.e-l2.e)^(l2.s-l2.e))<=0;
 73 }
 74 
 75 //线段是否相交、端点不算相交
 76 bool inter2(line l1,line l2)
 77 {
 78     point a1=l1.s,a2=l1.e;
 79     point b1=l2.s,b2=l2.e;
 80     double c1 = (a2-a1)^(b1-a1), c2 = (a2-a1)^(b2-a1);
 81     double c3 = (b2-b1)^(a1-b1), c4 = (b2-b1)^(a2-b1);
 82     return sgn(c1)*sgn(c2)<0 && sgn(c3)*sgn(c4)<0;
 83 }
 84 //求p边形的面积、res[0~n-1]顺序存顶点、n为顶点数,res[n]=res[0]
 85 double area()
 86 {
 87     double ret = 0;
 88     for(int i=0;i<n;i++)
 89     {
 90         int sgn = dcmp(cross(res[i],res[i+1]));
 91         ret += sgn*calc(res[i],res[i+1]);
 92     }
 93     return fabs(ret);
 94 }
 95 
 96 point p[maxn];
 97 line Line[maxn];
 98 
 99 
100 int main()
101 {
102     double a,b,c,d;
103     while(scanf("%lf %lf %lf %lf",&a,&b,&c,&d)!=EOF)
104     {
105         Line[1] = line(point(a,b),point(c,d));
106         scanf("%lf %lf %lf %lf",&a,&b,&c,&d);
107         Line[2] = line(point(a,b),point(c,d));
108         if(inter(Line[1],Line[2]))
109         {
110             printf("Yes-inter1\n");
111         }
112         else
113         {
114             printf("No-inter1\n");
115         }
116         if(inter2(Line[1],Line[2]))
117         {
118             printf("Yes-inter2\n");
119         }
120         else
121         {
122             printf("No-inter2\n");
123         }
124     }
125 }