Computational Geometry Template (二)
t(p2,l.b)))>eps;
}
//判两点在线段异侧,点在线段上返回0,不共面无意义
bool opposite_side(point3 p1,point3 p2,line3 l)
{
return dmult(xmult(subt(l.a,l.b),subt(p1,l.b)),xmult(subt(l.a,l.b),subt(p2,l.b)))<-eps;
}
//判两点在平面同侧,点在平面上返回0
bool same_side(point3 p1,point3 p2,plane3 s)
{
return dmult(pvec(s),subt(p1,s.a))*dmult(pvec(s),subt(p2,s.a))>eps;
}
bool same_side(point3 p1,point3 p2,point3 s1,point3 s2,point3 s3)
{
return dmult(pvec(s1,s2,s3),subt(p1,s1))*dmult(pvec(s1,s2,s3),subt(p2,s1))>eps;
}
//判两点在平面异侧,点在平面上返回0
bool opposite_side(point3 p1,point3 p2,plane3 s)
{
return dmult(pvec(s),subt(p1,s.a))*dmult(pvec(s),subt(p2,s.a))<-eps;
}
bool opposite_side(point3 p1,point3 p2,point3 s1,point3 s2,point3 s3)
{
return dmult(pvec(s1,s2,s3),subt(p1,s1))*dmult(pvec(s1,s2,s3),subt(p2,s1))<-eps;
}
//判两直线平行
bool parallel(line3 u,line3 v)
{
return vlen(xmult(subt(u.a,u.b),subt(v.a,v.b)))
#include
#define eps 1e-8
#define zero(x) (((x)>0 (x):-(x))
eps;
}
//判两点在线段异侧,点在线段上返回0
bool opposite_side(point p1,point p2,line l)
{
return xmult(l.a,p1,l.b)*xmult(l.a,p2,l.b)<-eps;
}
//判两直线平行
bool parallel(line u,line v)
{
return zero((u.a.x-u.b.x)*(v.a.y-v.b.y)-(v.a.x-v.b.x)*(u.a.y-u.b.y));
}
//判两直线垂直
bool perpendicular(line u,line v)
{
return zero((u.a.x-u.b.x)*(v.a.x-v.b.x)+(u.a.y-u.b.y)*(v.a.y-v.b.y));
}
//判两线段相交,包括端点和部分重合
bool intersect_in(line u,line v)
{
if (!dots_inline(u.a,u.b,v.a)||!dots_inline(u.a,u.b,v.b))
return !same_side(u.a,u.b,v)&&!same_side(v.a,v.b,u);
return dot_online_in(u.a,v)||dot_online_in(u.b,v)||dot_online_in(v.a,u)||dot_online_in(v.b,u);
}
//判两线段相交,不包括端点和部分重合
bool intersect_ex(line u,line v)
{
return opposite_side(u.a,u.b,v)&&opposite_side(v.a,v.b,u);
}
//计算两直线交点,注意事先判断直线是否平行!
//线段交点请另外判线段相交(同时还是要判断是否平行!)
point intersection(line u,line v)
{
point ret=u.a;
double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
/((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
ret.x+=(u.b.x-u.a.x)*t;
ret.y+=(u.b.y-u.a.y)*t;
return ret;
}
point intersection(point u1,point u2,point v1,point v2)
{
point ret=u1;
double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))
/((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
ret.x+=(u2.x-u1.x)*t;
ret.y+=(u2.y-u1.y)*t;
return ret;
}
//点到直线上的最近点
point ptoline(point p,line l)
{
point t=p;
t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;
return intersection(p,t,l.a,l.b);
}
//点到直线距离
double disptoline(point p,line l)
{
return fabs(xmult(p,l.a,l.b))/distance(l.a,l.b);
}
//点到线段上的最近点
point ptoseg(point p,line l)
{
point t=p;
t.x+=l.a.y-l.b.y,t.y+=l.b.x-l.a.x;
if (xmult(l.a,t,p)*xmult(l.b,t,p)>eps)
return distance(p,l.a)eps)
return distance(p,l.a)=pi+pi)
dlng-=pi+pi;
if (dlng>pi)
dlng=pi+pi-dlng;
lat1*=pi/180,lat2*=pi/180;
return acos(cos(lat1)*cos(lat2)*cos(dlng)+sin(lat1)*sin(lat2));
}
//计算距离,r 为球半径
double line_dist(double r,double lng1,double lat1,double lng2,double lat2)
{
double dlng=fabs(lng1-lng2)*pi/180;
while (dlng>=pi+pi)
dlng-=pi+pi;
if (dlng>pi)
dlng=pi+pi-dlng;
lat1*=pi/180,lat2*=pi/180;
return r*sqrt(2-2*(cos(lat1)*cos(lat2)*cos(dlng)+sin(lat1)*sin(lat2)));
}
//计算球面距离,r 为球半径
inline double sphere_dist(double r,double lng1,double lat1,double lng2,double lat2)
{
return r*angle(lng1,lat1,lng2,lat2);
}
//外心
point circumcenter(point a,point b,point c)
{
line u,v;
u.a.x=(a.x+b.x)/2;
u.a.y=(a.y+b.y)/2;
u.b.x=u.a.x-a.y+b.y;
u.b.y=u.a.y+a.x-b.x;
v.a.x=(a.x+c.x)/2;
v.a.y=(a.y+c.y)/2;
v.b.x=v.a.x-a.y+c.y;
v.b.y=v.a.y+a.x-c.x;
return intersection(u,v);
}
//内心
point incenter(point a,point b,point c)
{
line u,v;
double m,n;
u.a=a;
m=atan2(b.y-a.y,b.x-a.x);
n=atan2(c.y-a.y,c.x-a.x);
u.b.x=u.a.x+cos((m+n)/2);
u.b.y=u.a.y+sin((m+n)/2);
v.a=b;
m=atan2(a.y-b.y,a.x-b.x);
n=atan2(c.y-b.y,c.x-b.x);
v.b.x=v.a.x+cos((m+n)/2);
v.b.y=v.a.y+sin((m+n)/2);
return intersection(u,v);
}
//垂心
point perpencenter(point a,point b,point c)
{
line u,v;
u.a=c;
u.b.x=u.a.x-a.y+b.y;
u.b.y=u.a.y+a.x-b.x;
v.a=b;
v.b.x=v.a.x-a.y+c.y;
v.b.y=v.a.y+a.x-c.x;
return intersection(u,v);
}
//重心
//到三角形三顶点距离的平方和最小的点
//三角形内到三边距离之积最大的点
point barycenter(point a,point b,point c)
{
line u,v;
u.a.x=(a.x+b.x)/2;
u.a.y=(a.y+b.y)/2;
u.b=c;
v.a.x=(a.x+c.x)/2;
v.a.y=(a.y+c.y)/2;
v.b=b;
return intersection(u,v);
}
//费马点
//到三角形三顶点距离之和最小的点
point fermentpoint(point a,point b,point c)
{
point u,v;
double step=fabs(a.x)+fabs(a.y)+fabs(b.x)+fabs(b.y)+fabs(c.x)+fabs(c.y);
int i,j,k;
u.x=(a.x+b.x+c.x)/3;
u.y=(a.y+b.y+c.y)/3;
while (step>1e-10)
{
for (k=0; k<10; step/=2,k++)
{
for (i=-1; i<=1; i++)
{
for (j=-1; j<=1; j++)
{
v.x=u.x+step*i;
v.y=u.y+step*j;
if(distance(u,a)+distance(u,b)+distance(u,c)>distance(v,a)+distance(v,b)+distance(v,c))
{
u=v;
}
}
}
}
}
return u;
}
//矢量差 U - V
point3 subt(point3 u,point3 v)
{
point3 ret;
ret.x=u.x-v.x;
ret.y=u.y-v.y;
ret.z=u.z-v.z;
return ret;
}
//取平面法向量
point3 pvec(plane3 s)
{
return xmult(subt(s.a,s.b),subt(s.b,s.c));
}
point3 pvec(point3 s1,point3 s2,point3 s3)
{
return xmult(subt(s1,s2),subt(s2,s3));
}
//两点距离,单参数取向量大小
double distance(point3 p1,point3 p2)
{
return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.