ACM 三角形模板

#include <math.h> 
struct point{double x,y;}; 
struct line{point a,b;}; 

double distance(point p1,point p2){ 
return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y)); 
} 

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; 
} 

//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; 
}