poj1673

所谓Exocenter就是垂心。不难证明。

#include <iostream>

#include <math.h>

#include <stdio.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;

}

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);

	}

}