[poj 3130]How I Mathematician Wonder What You Are![半平面交][模板题]

题意:

判断多边形是否有核.

思路:

使用模板求多边形的核, 注意 input 中点的顺序.

#include <cstdio>
#define vector point
const double INF = 1e18;
struct point
{
double x,y;
point(double xx = 0,double yy = 0)
{
x = xx;
y = yy;
}
point operator - (const point& s)
{
return point(x - s.x, y - s.y);
}
point operator + (const point& s)
{
return point(x + s.x,y + s.y);
}
};
struct polygon
{
point p[55];
int size;
};
struct line
{
point first,second;
line(point p1 = point(),point p2 = point())
{
first = p1;
second = p2;
}
};

double cross_product(vector v1,vector v2)
{
return v1.x * v2.y - v1.y * v2.x;
}
//点积
double dot_product(vector v1,vector v2)
{
return v1.x * v2.x + v1.y * v2.y;
}

//求两直线交点
point line_intersection(line ln1,line ln2)
{
double a1,b1,c1,a2,b2,c2;
a1 = ln1.first.y - ln1.second.y;
b1 = ln1.second.x - ln1.first.x;
c1 = cross_product(ln1.first, ln1.second);
a2 = ln2.first.y - ln2.second.y;
b2 = ln2.second.x - ln2.first.x;
c2 = cross_product(ln2.first, ln2.second);
double d = a1 * b2 - a2 * b1;
return point((b1 * c2 - b2 * c1) / d,(c1 * a2 - c2 * a1) / d);
}

//一个多边形与一个半平面的交集
polygon half_plane_intersection(polygon& poly,line& ln)
{
int m = 0;
polygon hull;
point p1 = ln.first,p2 = ln.second;
//穷举多边形的所有点，判断是否在半平面上
//如果凸多边形hull与直线ln有交点就求交点
for(int i = 0;i < poly.size;i++)
{
double c = cross_product(p2 - p1,poly.p[i] - p1);
double d = cross_product(p2 - p1,poly.p[(i + 1) % poly.size] - p1);
//点poly.p[i]在半平面上
if(c >= 0)
hull.p[m++] = poly.p[i];
//有规范交点
if(c * d < 0)
{
hull.p[m++] = line_intersection(line(poly.p[(i + 1) % poly.size],poly.p[i]),ln);
//printf("intersect = ( %g, %g)\n",hull.p[m - 1].x,hull.p[m - 1].y);
}
}
//printf("\n\n");
hull.size = m;
return hull;
}

bool polygon_kernel(polygon& poly,polygon& knl)
{
//初始化核为无限大
knl.p[0] = point(-INF,-INF);
knl.p[1] = point(INF,-INF);
knl.p[2] = point(INF,INF);
knl.p[3] = point(-INF,INF);
knl.size = 4;
line ln;
// point pre = poly.p[0];
for(int i = 1;i <= poly.size;i++)
{
ln.first = poly.p[i - 1];//input is counterclockwise
ln.second = poly.p[i % poly.size];
knl = half_plane_intersection(knl,ln);
if(knl.size == 0)
return false;
}
return true;
}

int main()
{
int n;
polygon poly,knl;

while(scanf("%d",&n)==1 && n)
{
for(int i = 0;i < n;i++)
scanf("%lf%lf",&poly.p[i].x,&poly.p[i].y);
poly.size = n;
if(polygon_kernel(poly,knl))
printf("1\n");
else
printf("0\n");
}
return 0;
}