基础题，直线间关系

 

#include 
    
     #include 
     
      #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0bool 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) < distance(p, l.b) ? l.a : l.b;	return intersection(p, t, l.a, l.b);}//点到线段距离double disptoseg(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) < distance(p, l.b) ? distance(p, l.a) : distance(p, l.b);	return fabs(xmult(p, l.a, l.b)) / distance(l.a, l.b);}//矢量V 以P 为顶点逆时针旋转angle 并放大scale 倍point rotate(point v, point p, double angle, double scale){	point ret = p;	v.x -= p.x, v.y -= p.y;	p.x = scale*cos(angle);	p.y = scale*sin(angle);	ret.x += v.x*p.x - v.y*p.y;	ret.y += v.x*p.y + v.y*p.x;	return ret;}//计算三角形面积,输入三顶点double area_triangle(point p1, point p2, point p3){	return fabs(xmult(p1, p2, p3)) / 2;}//计算三角形面积,输入三边长double area_triangle(double a, double b, double c){	double s = (a + b + c) / 2;	return sqrt(s*(s - a)*(s - b)*(s - c));}//计算多边形面积,顶点按顺时针或逆时针给出double area_polygon(int n, point* p){	double s1 = 0, s2 = 0;	int i;	for (i = 0; i < n; i++)		s1 += p[(i + 1)%n].y*p[i].x, s2 += p[(i + 1)%n].y*p[(i + 2)%n].x;	return fabs(s1 - s2) / 2;}//计算圆心角lat 表示纬度,-90<=w<=90,lng 表示经度//返回两点所在大圆劣弧对应圆心角,0<=angle<=pidouble angle(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 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 - Vpoint3 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;}///三维/////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.y) + (p1.z - p2.z)*(p1.z - p2.z));}//向量大小double vlen(point3 p){	return sqrt(p.x*p.x + p.y*p.y + p.z*p.z);}//判三点共线bool dots_inline(point3 p1, point3 p2, point3 p3){	return vlen(xmult(subt(p1, p2), subt(p2, p3))) < eps;}//判四点共面bool dots_onplane(point3 a, point3 b, point3 c, point3 d){	return zero(dmult(pvec(a, b, c), subt(d, a)));}//判点是否在线段上,包括端点和共线bool dot_online_in(point3 p, line3 l){	return zero(vlen(xmult(subt(p, l.a), subt(p, l.b)))) && (l.a.x - p.x)*(l.b.x - p.x) < eps && (l.a.y - p.y)*(l.b.y - p.y) < eps && (l.a.z - p.z)*(l.b.z - p.z) < eps;}//判点是否在线段上,不包括端点bool dot_online_ex(point3 p, line3 l){	return dot_online_in(p, l) && (!zero(p.x - l.a.x) || !zero(p.y - l.a.y) || !zero(p.z - l.a.z)) && (!zero(p.x - l.b.x) || !zero(p.y - l.b.y) || !zero(p.z - l.b.z));}//判点是否在空间三角形上,包括边界,三点共线无意义bool dot_inplane_in(point3 p, plane3 s){	return zero(vlen(xmult(subt(s.a, s.b), subt(s.a, s.c))) - vlen(xmult(subt(p, s.a), subt(p, s.b))) - vlen(xmult(subt(p, s.b), subt(p, s.c))) - vlen(xmult(subt(p, s.c), subt(p, s.a))));}//判点是否在空间三角形上,不包括边界,三点共线无意义bool dot_inplane_ex(point3 p, plane3 s){	return dot_inplane_in(p, s) && vlen(xmult(subt(p, s.a), subt(p, s.b))) > eps && vlen(xmult(subt(p, s.b), subt(p, s.c))) > eps && vlen(xmult(subt(p, s.c), subt(p, s.a))) > eps;}//判两点在线段同侧,点在线段上返回0,不共面无意义bool same_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0bool 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0bool 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))) < eps;}//判两平面平行bool parallel(plane3 u, plane3 v){	return vlen(xmult(pvec(u), pvec(v))) < eps;}//判直线与平面平行bool parallel(line3 l, plane3 s){	return zero(dmult(subt(l.a, l.b), pvec(s)));}bool parallel(point3 l1, point3 l2, point3 s1, point3 s2, point3 s3){	return zero(dmult(subt(l1, l2), pvec(s1, s2, s3)));}//判两直线垂直bool perpendicular(line3 u, line3 v){	return zero(dmult(subt(u.a, u.b), subt(v.a, v.b)));}//判两平面垂直bool perpendicular(plane3 u, plane3 v){	return zero(dmult(pvec(u), pvec(v)));}//判直线与平面平行bool perpendicular(line3 l, plane3 s){	return vlen(xmult(subt(l.a, l.b), pvec(s))) < eps;}//判两线段相交,包括端点和部分重合bool intersect_in(line3 u, line3 v){	if (!dots_onplane(u.a, u.b, v.a, v.b))		return 0;	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(line3 u, line3 v){	return dots_onplane(u.a, u.b, v.a, v.b) && opposite_side(u.a, u.b, v) && opposite_side(v.a, v.b, u);}//判线段与空间三角形相交,包括交于边界和(部分)包含bool intersect_in(line3 l, plane3 s){	return !same_side(l.a, l.b, s) && !same_side(s.a, s.b, l.a, l.b, s.c) && !same_side(s.b, s.c, l.a, l.b, s.a) && !same_side(s.c, s.a, l.a, l.b, s.b);}//判线段与空间三角形相交,不包括交于边界和(部分)包含bool intersect_ex(line3 l, plane3 s){	return opposite_side(l.a, l.b, s) && opposite_side(s.a, s.b, l.a, l.b, s.c) && opposite_side(s.b, s.c, l.a, l.b, s.a) && opposite_side(s.c, s.a, l.a, l.b, s.b);}//计算两直线交点,注意事先判断直线是否共面和平行!//线段交点请另外判线段相交(同时还是要判断是否平行!)point3 intersection(line3 u, line3 v){	point3 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;	ret.z += (u.b.z - u.a.z)*t;	return ret;}//计算直线与平面交点,注意事先判断是否平行,并保证三点不共线!//线段和空间三角形交点请另外判断point3 intersection(line3 l, plane3 s){	point3 ret = pvec(s);	double t = (ret.x*(s.a.x - l.a.x) + ret.y*(s.a.y - l.a.y) + ret.z*(s.a.z - l.a.z)) / (ret.x*(l.b.x - l.a.x) + ret.y*(l.b.y - l.a.y) + ret.z*(l.b.z - l.a.z));	ret.x = l.a.x + (l.b.x - l.a.x)*t;	ret.y = l.a.y + (l.b.y - l.a.y)*t;	ret.z = l.a.z + (l.b.z - l.a.z)*t;	return ret;}point3 intersection(point3 l1, point3 l2, point3 s1, point3 s2, point3 s3){	point3 ret = pvec(s1, s2, s3);	double t = (ret.x*(s1.x - l1.x) + ret.y*(s1.y - l1.y) + ret.z*(s1.z - l1.z)) /		(ret.x*(l2.x - l1.x) + ret.y*(l2.y - l1.y) + ret.z*(l2.z - l1.z));	ret.x = l1.x + (l2.x - l1.x)*t;	ret.y = l1.y + (l2.y - l1.y)*t;	ret.z = l1.z + (l2.z - l1.z)*t;	return ret;}//计算两平面交线,注意事先判断是否平行,并保证三点不共线!line3 intersection(plane3 u, plane3 v){	line3 ret;	ret.a = parallel(v.a, v.b, u.a, u.b, u.c) ? intersection(v.b, v.c, u.a, u.b, u.c) : intersection(v.a, v.b, u.a, u.b, u.c);	ret.b = parallel(v.c, v.a, u.a, u.b, u.c) ? intersection(v.b, v.c, u.a, u.b, u.c) : intersection(v.c, v.a, u.a, u.b, u.c);	return ret;}line3 intersection(point3 u1, point3 u2, point3 u3, point3 v1, point3 v2, point3 v3){	line3 ret;	ret.a = parallel(v1, v2, u1, u2, u3) ? intersection(v2, v3, u1, u2, u3) : intersection(v1, v2, u1, u2, u3);	ret.b = parallel(v3, v1, u1, u2, u3) ? intersection(v2, v3, u1, u2, u3) : intersection(v3, v1, u1, u2, u3);	return ret;}//点到直线距离double ptoline(point3 p, line3 l){	return vlen(xmult(subt(p, l.a), subt(l.b, l.a))) / distance(l.a, l.b);}//点到平面距离double ptoplane(point3 p, plane3 s){	return fabs(dmult(pvec(s), subt(p, s.a))) / vlen(pvec(s));}//直线到直线距离double linetoline(line3 u, line3 v){	point3 n = xmult(subt(u.a, u.b), subt(v.a, v.b));	return fabs(dmult(subt(u.a, v.a), n)) / vlen(n);}//两直线夹角cos 值double angle_cos(line3 u, line3 v){	return dmult(subt(u.a, u.b), subt(v.a, v.b)) / vlen(subt(u.a, u.b)) / vlen(subt(v.a, v.b));}//两平面夹角cos 值double angle_cos(plane3 u, plane3 v){	return dmult(pvec(u), pvec(v)) / vlen(pvec(u)) / vlen(pvec(v));}//直线平面夹角sin 值double angle_sin(line3 l, plane3 s){	return dmult(subt(l.a, l.b), pvec(s)) / vlen(subt(l.a, l.b)) / vlen(pvec(s));}int main(){	int t;	std::cin >> t;	std::cout << "INTERSECTING LINES OUTPUT" << std::endl;	while (t--)	{		line a, b;		std::cin >> a.a.x >> a.a.y >> a.b.x >> a.b.y >> b.a.x >> b.a.y >> b.b.x >> b.b.y;		if (xmult(a.a, a.b, b.a) == 0 && xmult(a.a, a.b, b.b) == 0)		{			std::cout << "LINE" << std::endl;		}		else if (parallel(a, b))		{			std::cout << "NONE" << std::endl;		}		else		{			point temp;			temp = intersection(a, b);			std::cout << std::fixed << std::setprecision(2) << "POINT" << ' ' << temp.x << ' ' << temp.y << std::endl;		}	}	std::cout << "END OF OUTPUT" << std::endl;}