5.1 半平面交模板(from UESTC)
const double eps = 1e-8;
const double PI = acos(-1.0);
int sgn(double x)
{
if(fabs(x) < eps) return 0;
if(x < 0) return -1;
else return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x = _x; y = _y;
}
Point operator -(const Point &b)const
{
return Point(x - b.x, y - b.y);
}
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
};
struct Line
{
Point s,e;
double k;
Line(){}
Line(Point _s,Point _e)
{
s = _s; e = _e;
k = atan2(e.y - s.y,e.x - s.x);
}
Point operator &(const Line &b)const
{
Point res = s;
double t = ((s - b.s)^(b.s - b.e))/((s - e)^(b.s - b.e));
res.x += (e.x - s.x)*t;
res.y += (e.y - s.y)*t;
return res;
}
};
//半平面交，直线的左边代表有效区域
bool HPIcmp(Line a,Line b)
{
if(fabs(a.k - b.k) > eps)return a.k < b.k;
return ((a.s - b.s)^(b.e - b.s)) < 0;
}
Line Q[110];
void HPI(Line line[], int n, Point res[], int &resn)
{
int tot = n;
sort(line,line+n,HPIcmp);
tot = 1;
for(int i = 1;i < n;i++)
if(fabs(line[i].k - line[i-1].k) > eps)
line[tot++] = line[i];
int head = 0, tail = 1;
Q[0] = line[0];
Q[1] = line[1];
resn = 0;
for(int i = 2; i < tot; i++)
{
if(fabs((Q[tail].e-Q[tail].s)^(Q[tail-1].e-Q[tail-1].s)) < eps ||
fabs((Q[head].e-Q[head].s)^(Q[head+1].e-Q[head+1].s)) < eps)
return;
while(head < tail && (((Q[tail]&Q[tail-1]) -
line[i].s)^(line[i].e-line[i].s)) > eps)
tail--;
while(head < tail && (((Q[head]&Q[head+1]) -
line[i].s)^(line[i].e-line[i].s)) > eps)
head++;
Q[++tail] = line[i];
}
while(head < tail && (((Q[tail]&Q[tail-1]) -
Q[head].s)^(Q[head].e-Q[head].s)) > eps)
tail--;
while(head < tail && (((Q[head]&Q[head-1]) -
Q[tail].s)^(Q[tail].e-Q[tail].e)) > eps)
head++;
if(tail <= head + 1)return;
for(int i = head; i < tail; i++)
res[resn++] = Q[i]&Q[i+1];
if(head < tail - 1)
res[resn++] = Q[head]&Q[tail];
}
5.2 普通半平面交写法
POJ 1750
const double eps = 1e-18;
int sgn(double x)
{
if(fabs(x) < eps)return 0;
if(x < 0)return -1;
else return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x = _x; y = _y;
}
Point operator -(const Point &b)const
{
return Point(x - b.x, y - b.y);
}
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
};
//计算多边形面积
double CalcArea(Point p[],int n)
{
double res = 0;
for(int i = 0;i < n;i++)
res += (p[i]^p[(i+1)%n]);
return fabs(res/2);
}
//通过两点，确定直线方程
void Get_equation(Point p1,Point p2,double &a,double &b,double &c)
{
a = p2.y - p1.y;
b = p1.x - p2.x;
c = p2.x*p1.y - p1.x*p2.y;
}
//求交点
Point Intersection(Point p1,Point p2,double a,double b,double c)
{
double u = fabs(a*p1.x + b*p1.y + c);
double v = fabs(a*p2.x + b*p2.y + c);
Point t;
t.x = (p1.x*v + p2.x*u)/(u+v);
t.y = (p1.y*v + p2.y*u)/(u+v);
return t;
}
Point tp[110];
void Cut(double a,double b,double c,Point p[],int &cnt)
{
int tmp = 0;
for(int i = 1;i <= cnt;i++)
{
//当前点在左侧，逆时针的点
if(a*p[i].x + b*p[i].y + c < eps)tp[++tmp] = p[i];
else
{
if(a*p[i-1].x + b*p[i-1].y + c < -eps)
tp[++tmp] = Intersection(p[i-1],p[i],a,b,c);
if(a*p[i+1].x + b*p[i+1].y + c < -eps)
tp[++tmp] = Intersection(p[i],p[i+1],a,b,c);
}
}
for(int i = 1;i <= tmp;i++)
p[i] = tp[i];
p[0] = p[tmp];
p[tmp+1] = p[1];
cnt = tmp;
}
double V[110],U[110],W[110];
int n;
const double INF = 100000000000.0;
Point p[110];
bool solve(int id)
{
p[1] = Point(0,0);
p[2] = Point(INF,0);
p[3] = Point(INF,INF);
p[4] = Point(0,INF);
p[0] = p[4];
p[5] = p[1];
int cnt = 4;
for(int i = 0;i < n;i++)
if(i != id)
{
double a = (V[i] - V[id])/(V[i]*V[id]);
double b = (U[i] - U[id])/(U[i]*U[id]);
double c = (W[i] - W[id])/(W[i]*W[id]);
if(sgn(a) == 0 && sgn(b) == 0)
{
if(sgn(c) >= 0)return false;
else continue;
}
Cut(a,b,c,p,cnt);
}
if(sgn(CalcArea(p,cnt)) == 0)return false;
else return true;
}
int main()
{
while(scanf("%d",&n) == 1)
{
for(int i = 0;i < n;i++)
scanf("%lf%lf%lf",&V[i],&U[i],&W[i]);
for(int i = 0;i < n;i++)
{
if(solve(i))printf("Yes
");
else printf("No
");
}
}
return 0;
}