计算几何基本函数

#include<bits/stdc++.h>
#include <ctime>
using namespace std;
typedef long long ll;
const double eps = 1e-8;
const double PI = acos(-1.0);

int sgn(double x)
{
if (fabs(x) < eps)
{
return 0;
}
if (x < 0)
{
return -1;
}
else
{
return 1;
}
}
struct Point
{
double x, y;
Point() {}
Point(double _x, double _y)
{
x = _x;
y = _y;
}
Point operator -(const Point &b)const
{
return Point(x - b.x, y - b.y);
}
//叉积
double operator ^(const Point &b)const
{
return x * b.y - y * b.x;
}
//点积
double operator *(const Point &b)const
{
return x * b.x + y * b.y;
}
//绕原点旋转角度B（弧度值），后x,y的变化（逆时针）
void transXY(double B)
{
double tx = x, ty = y;
x = tx * cos(B) - ty * sin(B);
y = tx * sin(B) + ty * cos(B);
}
};

struct Line
{
Point s, e;
Line() {}
Line(Point _s, Point _e)
{
s = _s;
e = _e;
}
//两直线相交求交点
//第一个值为0表示直线重合，为1表示平行，为0表示相交,为2是相交
//只有第一个值为2时，交点才有意义
pair<int, Point> operator &(const Line &b)const
{
Point res = s;
if (sgn((s - e) ^ (b.s - b.e)) == 0)
{
if (sgn((s - b.e) ^ (b.s - b.e)) == 0)
{
return make_pair(0, res);    //重合
}
else
{
return make_pair(1, res);    //平行
}
}
double t = ((s - b.s) ^ (b.s - b.e)) / ((s - e) ^ (b.s - b.e));
res.x += (e.x - s.x) * t;
res.y += (e.y - s.y) * t;
return make_pair(2, res);
}
};

//*两点间距离
double dist(Point a, Point b)
{
return sqrt((a - b) * (a - b));
}

//*判断线段相交
bool inter(Line l1, Line l2)
{
return
max(l1.s.x, l1.e.x) >= min(l2.s.x, l2.e.x) &&
max(l2.s.x, l2.e.x) >= min(l1.s.x, l1.e.x) &&
max(l1.s.y, l1.e.y) >= min(l2.s.y, l2.e.y) &&
max(l2.s.y, l2.e.y) >= min(l1.s.y, l1.e.y) &&
sgn((l2.s - l1.e) ^ (l1.s - l1.e)) * sgn((l2.e-l1.e) ^ (l1.s - l1.e)) <= 0 &&
sgn((l1.s - l2.e) ^ (l2.s - l2.e)) * sgn((l1.e-l2.e) ^ (l2.s - l2.e)) <= 0;
}

//判断直线和线段相交
bool Seg_inter_line(Line l1, Line l2) //判断直线l1和线段l2是否相交
{
return sgn((l2.s - l1.e) ^ (l1.s - l1.e)) * sgn((l2.e-l1.e) ^ (l1.s - l1.e)) <= 0;
}

//点到直线距离
//返回为result,是点到直线最近的点
Point PointToLine(Point P, Line L)
{
Point result;
double t = ((P - L.s) * (L.e-L.s)) / ((L.e-L.s) * (L.e-L.s));
result.x = L.s.x + (L.e.x - L.s.x) * t;
result.y = L.s.y + (L.e.y - L.s.y) * t;
return result;
}

//点到线段的距离
//返回点到线段最近的点
Point NearestPointToLineSeg(Point P, Line L)
{
Point result;
double t = ((P - L.s) * (L.e-L.s)) / ((L.e-L.s) * (L.e-L.s));
if (t >= 0 && t <= 1)
{
result.x = L.s.x + (L.e.x - L.s.x) * t;
result.y = L.s.y + (L.e.y - L.s.y) * t;
}
else
{
if (dist(P, L.s) < dist(P, L.e))
{
result = L.s;
}
else
{
result = L.e;
}
}
return result;
}

//计算多边形面积
//点的编号从0~n-1
double CalcArea(Point p[], int n)
{
double res = 0;
for (int i = 0; i < n; i++)
{
res += (p[i] ^ p[(i + 1) % n]) / 2;
}
return fabs(res);
}

//*判断点在线段上
bool OnSeg(Point P, Line L)
{
return
sgn((L.s - P) ^ (L.e-P)) == 0 &&
sgn((P.x - L.s.x) * (P.x - L.e.x)) <= 0 &&
sgn((P.y - L.s.y) * (P.y - L.e.y)) <= 0;
}

//*判断点在凸多边形内
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0）
//点的编号:0~n-1
//返回值：
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inConvexPoly(Point a, Point p[], int n)
{
for (int i = 0; i < n; i++)
{
if (sgn((p[i] - a) ^ (p[(i + 1) % n] - a)) < 0)
{
return -1;
}
else if (OnSeg(a, Line(p[i], p[(i + 1) % n])))
{
return 0;
}
}
return 1;
}

//*判断点在任意多边形内
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1
//返回值
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inPoly(Point p, Point poly[], int n)
{
int cnt;
Line ray, side;
cnt = 0;
ray.s = p;
ray.e.y = p.y;
ray.e.x = -100000000000.0;//-INF,注意取值防止越界
for (int i = 0; i < n; i++)
{
side.s = poly[i];
side.e = poly[(i + 1) % n];
if (OnSeg(p, side))
{
return 0;
}
//如果平行轴则不考虑
if (sgn(side.s.y - side.e.y) == 0)
{
continue;
}
if (OnSeg(side.s, ray))
{
if (sgn(side.s.y - side.e.y) > 0)
{
cnt++;
}
}
else if (OnSeg(side.e, ray))
{
if (sgn(side.e.y - side.s.y) > 0)
{
cnt++;
}
}
else if (inter(ray, side))
{
cnt++;
}
}
if (cnt % 2 == 1)
{
return 1;
}
else
{
return -1;
}
}

//判断凸多边形
//允许共线边
//点可以是顺时针给出也可以是逆时针给出
//点的编号1~n-1
bool isconvex(Point poly[], int n)
{
bool s[3];
memset(s, false, sizeof(s));
for (int i = 0; i < n; i++)
{
s[sgn( (poly[(i + 1) % n] - poly[i]) ^ (poly[(i + 2) % n] - poly[i]) ) + 1] = true;
if (s[0] && s[2])
{
return false;
}
}
return true;
}