UVA_191_Intersection

#include<iostream>
#include<sstream>
#include<string>
#include<vector>
#include<list>
#include<set>
#include<map>
#include<stack>
#include<queue>
#include<algorithm>
#include<numeric>
#include<cmath>
#pragma warning(disable:4996)
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::string;
using std::vector;
using std::list;
using std::pair;
using std::set;
using std::multiset;
using std::map;
using std::multimap;
using std::stack;
using std::queue;
using std::priority_queue;
class Point
{
public:
	long double x, y;
	Point() {}
	Point(const long double &X, const long double &Y)
	{
		x = X;
		y = Y;
	}
};
class Line
{
public:
	long double a, b, c;//ax+by=c
	long double x_min, x_max, y_min, y_max;//直線的值域
	Line() {}
	Line(const Point &first, const Point &second)
	{
		x_min = std::min(first.x, second.x);
		x_max = std::max(first.x, second.x);
		y_min = std::min(first.y, second.y);
		y_max = std::max(first.y, second.y);
		if (first.x != second.x)//斜率式可行
		{
			b = 1;
			a = -(first.y - second.y) / (first.x - second.x);
			c = first.y + a*first.x;
		}
		else//k->無窮
		{
			b = 0;
			a = 1;
			c = first.x;
		}
	}
	bool lineIntersected(const Line &line)//直線相交的判定
	{
		auto D = a*line.b - line.a*b;
		if (D)
		{
			return true;
		}
		return false;
	}
	bool lineParallel(const Line&line)//判斷兩直線是否平行
	{
		auto D = a*line.b - line.a*b;
		if (!D)
		{
			return true;
		}
		return false;
	}
	bool lineOverlapped(const Line&line)//判斷兩直線是否重合（平行的特例）
	{
		auto D = a*line.b - line.a*b;
		auto Dx = c*line.b - line.c*b;
		auto Dy = a*line.c - line.a*c;
		if (!D&&!Dx&&!Dy)
		{
			return true;
		}
		return false;
	}
	long double fixed(long double value)
	{
		value *= (long double)1000000000000.0;
		value += 0.5;
		value = floor(value);
		value /= (long double)1000000000000.0;
		return value;
	}
	Point getIntersection(const Line&line)//行列式求兩直線交點,要修正誤差
	{
		auto D = a*line.b - line.a*b;
		auto Dx = c*line.b - line.c*b;
		auto Dy = a*line.c - line.a*c;
		return{ fixed(Dx / D),fixed(Dy / D) };
	}
	bool segmentIntersected(const Line &line)
	{
		if (lineIntersected(line))
		{
			auto point = getIntersection(line);
			if (point.x >= x_min&&point.x <= x_max
				&&point.y >= y_min&&point.y <= y_max
				&&point.x >= line.x_min&&point.x <= line.x_max
				&&point.y >= line.y_min&&point.y <= line.y_max
				)//交點在兩線段的值域內
			{
				return true;
			}
		}
		return false;
	}
	bool segmentOverlapped(const Line &line)
	{
		if (lineOverlapped(line))
		{
			if ((x_min <= line.x_max&&x_min >= line.x_min) || (x_max <= line.x_max&&x_max >= line.x_min))
			{
				return true;
			}
		}
		return false;
	}
};
class Rectangle
{
public:
	long double left, right, top, bottom;
	bool inRectangle(const Point &point)
	{
		if (point.x >= left&&point.x <= right&&point.y >= bottom&&point.y <= top)
		{
			return true;
		}
		return false;
	}
};
int main()
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int n;
	while (cin >> n)
	{
		for (int i = 0; i < n; i++)
		{
			long double x1, y1, x2, y2;
			cin >> x1 >> y1 >> x2 >> y2;
			Rectangle rectangle;
			cin >> rectangle.left >> rectangle.top >> rectangle.right >> rectangle.bottom;
			if (rectangle.left > rectangle.right)
			{
				std::swap(rectangle.left, rectangle.right);
			}
			if (rectangle.bottom > rectangle.top)
			{
				std::swap(rectangle.bottom, rectangle.top);
			}
			if (rectangle.inRectangle({ x1,y1 }) || rectangle.inRectangle({ x2,y2 }))
			{
				//只要一個端點在矩形內，就有交點  
				cout << 'T' << endl;
			}
			else
			{
				Line line({ x1,y1 }, { x2,y2 });
				vector<long double>segment(4);
				segment[0] = rectangle.top;
				segment[1] = rectangle.right;
				segment[2] = rectangle.bottom;
				segment[3] = rectangle.left;
				bool flag = false;
				for (int i = 0; i < 4; i++)
				{
					Line another({ segment[i],segment[(i + 1) % 4] }, { segment[(i + 1) % 4],segment[(i + 2) % 4] });
					if (line.segmentIntersected(another)||line.lineOverlapped(another))
					{
						flag = true;
						break;
					}
				}
				if (flag)
				{
					cout << 'T' << endl;
				}
				else
				{
					cout << 'F' << endl;
				}
			}
		}
	}
	return 0;
}

<pre name="code" class="cpp">#include<iostream>  
#include<sstream>  
#include<string>  
#include<vector>  
#include<list>  
#include<set>  
#include<map>  
#include<stack>  
#include<queue>  
#include<algorithm>  
#include<numeric>  
#include<cmath>  
#pragma warning(disable:4996)  
using std::cin;
using std::cout;
using std::endl;
using std::stringstream;
using std::string;
using std::vector;
using std::list;
using std::pair;
using std::set;
using std::multiset;
using std::map;
using std::multimap;
using std::stack;
using std::queue;
using std::priority_queue;
using std::swap;
using std::min;
using std::max;
class Point 
{
public:
	double x,y; 
};
const double eps = 1e-20;
bool isEqual(const double &a,const double &b) 
{
	return (abs(a - b) < eps);
}
//判斷兩點是否相等
bool operator==(const Point &p1, const Point &p2) 
{
	return (isEqual(p1.x, p2.x) && isEqual(p1.y, p2.y));
}
//比較兩點座標大小，先比較x座標，若相同則比較y座標
bool operator>(const Point &p1, const Point &p2) 
{
	return (p1.x > p2.x || (isEqual(p1.x, p2.x) && p1.y > p2.y));
}
//計算兩向量外積(叉乘)
double operator^(const Point &p1, const Point &p2)
{
	return (p1.x * p2.y - p1.y * p2.x);
}
//判定兩線段位置關係，並求出交點(如果存在)。返回值列舉如下：
//[有重合] 完全重合(6)，1個端點重合且共線(5)，部分重合(4)
//[無重合] 兩端點相交(3)，交於線上(2)，正交(1)，無交(0)，參數錯誤(-1)
int Intersection(Point p1, Point p2, Point p3, Point p4, Point &point) 
{
	//保證參數p1!=p2，p3!=p4
	if (p1 == p2 || p3 == p4)
	{
		return -1; //返回-1代表至少有一條線段首尾重合，不能構成線段
	}
	//爲方便運算，保證各線段的起點在前，終點在後。
	if (p1 > p2) 
	{
		swap(p1, p2);
	}
	if (p3 > p4) 
	{
		swap(p3, p4);
	}
	//判定兩線段是否完全重合
	if (p1 == p3 && p2 == p4) 
	{
		return 6;
	}
	//求出兩線段構成的向量
	Point v1 = { p2.x - p1.x, p2.y - p1.y }, v2 = { p4.x - p3.x, p4.y - p3.y };
	//求兩向量外積，平行時外積爲0
	double Cross = v1 ^ v2;
	//如果起點重合
	if (p1 == p3) 
	{
		point = p1;
		//起點重合且共線(平行)返回5；不平行則交於端點，返回3
		return (isEqual(Cross, 0) ? 5 : 3);
	}
	//如果終點重合
	if (p2 == p4)
	{
		point = p2;
		//終點重合且共線(平行)返回5；不平行則交於端點，返回3
		return (isEqual(Cross, 0) ? 5 : 3);
	}
	//如果兩線端首尾相連
	if (p1 == p4) 
	{
		point = p1;
		return 3;
	}
	if (p2 == p3) {
		point = p2;
		return 3;
	}
	//經過以上判斷，首尾點相重的情況都被排除了
	//將線段按起點座標排序。若線段1的起點較大，則將兩線段交換
	if (p1 > p3) {
		swap(p1, p3);
		swap(p2, p4);
		//更新原先計算的向量及其外積
		swap(v1, v2);
		Cross = v1 ^ v2;
	}
	//處理兩線段平行的情況
	if (isEqual(Cross, 0)) 
	{
		//做向量v1(p1, p2)和vs(p1,p3)的外積，判定是否共線
		Point vs = { p3.x - p1.x, p3.y - p1.y };
		//外積爲0則兩平行線段共線，下面判定是否有重合部分
		if (isEqual(v1 ^ vs, 0)) {
			//前一條線的終點大於後一條線的起點，則判定存在重合
			if (p2 > p3) {
				point = p3;
				return 4; //返回值4代表線段部分重合
			}
		}//若三點不共線，則這兩條平行線段必不共線。
		 //不共線或共線但無重合的平行線均無交點
		return 0;
	} //以下爲不平行的情況，先進行快速排斥試驗
	  //x座標已有序，可直接比較。y座標要先求兩線段的最大和最小值
	double ymax1 = p1.y, ymin1 = p2.y, ymax2 = p3.y, ymin2 = p4.y;
	if (ymax1 < ymin1) {
		swap(ymax1, ymin1);
	}
	if (ymax2 < ymin2) {
		swap(ymax2, ymin2);
	}
	//如果以兩線段爲對角線的矩形不相交，則無交點
	if (p1.x > p4.x || p2.x < p3.x || ymax1 < ymin2 || ymin1 > ymax2) {
		return 0;
	}//下面進行跨立試驗
	Point vs1 = { p1.x - p3.x, p1.y - p3.y }, vs2 = { p2.x - p3.x, p2.y - p3.y };
	Point vt1 = { p3.x - p1.x, p3.y - p1.y }, vt2 = { p4.x - p1.x, p4.y - p1.y };
	double s1v2, s2v2, t1v1, t2v1;
	//根據外積結果判定否交於線上
	if (isEqual(s1v2 = vs1 ^ v2, 0) && p4 > p1 && p1 > p3) {
		point = p1;
		return 2;
	}
	if (isEqual(s2v2 = vs2 ^ v2, 0) && p4 > p2 && p2 > p3) {
		point = p2;
		return 2;
	}
	if (isEqual(t1v1 = vt1 ^ v1, 0) && p2 > p3 && p3 > p1) {
		point = p3;
		return 2;
	}
	if (isEqual(t2v1 = vt2 ^ v1, 0) && p2 > p4 && p4 > p1) {
		point = p4;
		return 2;
	} //未交於線上，則判定是否相交
	if (s1v2 * s2v2 > 0 || t1v1 * t2v1 > 0) {
		return 0;
	} //以下爲相交的情況，算法詳見文檔
	  //計算二階行列式的兩個常數項
	double ConA = p1.x * v1.y - p1.y * v1.x;
	double ConB = p3.x * v2.y - p3.y * v2.x;
	//計算行列式D1和D2的值，除以係數行列式的值，得到交點座標
	point.x = (ConB * v1.x - ConA * v2.x) / Cross;
	point.y = (ConB * v1.y - ConA * v2.y) / Cross;
	//正交返回1
	return 1;
}
bool in(const double &value,const double &lower_bound,const double&higher_bound)
{
	if (value-lower_bound>eps&&higher_bound-value>eps)
	{
		return true;
	}
	return false;
}
//主函數
int main() 
{
	//freopen("input.txt", "r", stdin);  
	//freopen("output.txt", "w", stdout); 
	int n;
	while (cin >> n)
	{
		while (n--)
		{
			double x1, y1, x2, y2; cin >> x1 >> y1 >> x2 >> y2;
			double left, top, right, bottom; cin >> left >> top >> right >> bottom;
			if (left > right) swap(left, right);
			if (bottom > top) swap(bottom, top);
			if ((in(x1,left,right)&&in(y1,bottom,top))||(in(y2,bottom,top) && in(x2, left, right)))
			{
				cout << 'T' << endl;
				continue;
			}
			else
			{
				vector<double>rectangle;
				rectangle.push_back(left);
				rectangle.push_back(top);
				rectangle.push_back(right);
				rectangle.push_back(bottom);
				bool flag = false;
				for (int i = 0; i < 4; i++)
				{
					Point point;
					int type = Intersection({ x1,y1 }, { x2,y2 }, { rectangle[i % 4],rectangle[(i + 1) % 4] }, { rectangle[(i + 1) % 4] ,rectangle[(i + 2) % 4] }, point);
					if (type>0)
					{
						cout << 'T' << endl;
						flag = true;
						break;
					}
				}
				if (!flag)
				{
					cout << 'F' << endl;
				}
			}
		}
	}
	return 0;
}