所谓Exocenter就是垂心。不难证明。
#include
#include
#include
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;
}
int main()
{
int n;
std::cin >> n;
while (n--)
{
point a, b, c;
std::cin >> a.x >> a.y >> b.x >> b.y >> c.x >> c.y;
point center = perpencenter(a, b, c);
printf("%.4f %.4f\n", center.x, center.y);
}
}
#include
#include
#include
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