3维计算几何模板

Posted 2020-06-10

#include <iostream>
#include <cmath>
#include <vector>
#include <string.h>
#include <stdlib.h>
#include <algorithm>
using namespace std;

#define MAX_N 110

/*------------------常量区-------------------*/

const double INF        = 1e10;      // 无穷大
const double EPS        = 1e-8;      // 计算精度
const double PI         = acos(-1.0);// PI
const int PINXING       = 0;         // 平行
const int XIANGJIAO     = 1;         // 相交
const int XIANGLI       = 0;         // 相离
const int GONGXIAN      = 2;         // 共线
const int CHONGDIE      = -1;        // 重叠
const int INSIDE        = 1;         // 点在图形内部
const int OUTSIDE       = 0;         // 点在图形外部
const int BORDER        = 2;         // 点在图形边界

/*-----------------类型定义区----------------*/

struct Point {              // 二维点或矢量
    double x, y;
    //double angle, dis;
    Point() {}
    Point(double x0, double y0): x(x0), y(y0) {}
    void read()
    {
        scanf("%lf%lf",&x,&y);
    }
};

struct Line {               // 二维的直线或线段
    Point p1, p2;
    Line() {}
    Line(Point p10, Point p20): p1(p10), p2(p20) {}
    void read()
    {
        scanf("%lf%lf%lf%lf",&p1.x,&p1.y,&p2.x,&p2.y);
    }
};

struct Rect {              // 用长宽表示矩形的方法 w, h分别表示宽度和高度
    double w, h;
    Rect() {}
    Rect(double _w,double _h) : w(_w),h(_h) {}
};
struct Rect_2 {             // 表示矩形，左下角坐标是(xl, yl)，右上角坐标是(xh, yh)
    double xl, yl, xh, yh;
    Rect_2() {}
    Rect_2(double _xl,double _yl,double _xh,double _yh) : xl(_xl),yl(_yl),xh(_xh),yh(_yh) {}
};
struct Circle {            //圆
    Point c;
    double r;
    Circle() {}
    Circle(Point _c,double _r) :c(_c),r(_r) {}
};

typedef vector<Point> Polygon;      // 二维多边形
typedef vector<Point> Points;       // 二维点集

/*-------------------基本函数区---------------------*/

inline double max(double x,double y)
{
    return x > y ? x : y;
}
inline double min(double x, double y)
{
    return x > y ? y : x;
}
inline bool ZERO(double x)              // x == 0
{
    return (fabs(x) < EPS);
}
inline bool ZERO(Point p)               // p == 0
{
    return (ZERO(p.x) && ZERO(p.y));
}

inline bool EQ(double x, double y)      // eqaul, x == y
{
    return (fabs(x - y) < EPS);
}
inline bool NEQ(double x, double y)     // not equal, x != y
{
    return (fabs(x - y) >= EPS);
}
inline bool LT(double x, double y)     // less than, x < y
{
    return ( NEQ(x, y) && (x < y) );
}
inline bool GT(double x, double y)     // greater than, x > y
{
    return ( NEQ(x, y) && (x > y) );
}
inline bool LEQ(double x, double y)     // less equal, x <= y
{
    return ( EQ(x, y) || (x < y) );
}
inline bool GEQ(double x, double y)     // greater equal, x >= y
{
    return ( EQ(x, y) || (x > y) );
}

// 输出浮点数前，防止输出-0.00调用该函数进行修正！
inline double FIX(double x)
{
    return (fabs(x) < EPS) ? 0 : x;
}



/*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*/
//-------------------3D 区域----------------------------//

struct Point3D {            //三维点或矢量
    double x, y, z;
    Point3D() {}
    Point3D(double x0, double y0, double z0): x(x0), y(y0), z(z0) {}
};

struct Line3D {             // 三维的直线或线段
    Point3D p1, p2;
    Line3D() {}
    Line3D(Point3D p10, Point3D p20): p1(p10), p2(p20) {}
};


inline bool ZERO(Point3D p)              // p == 0
{
    return (ZERO(p.x) && ZERO(p.y) && ZERO(p.z));
}

//////////////////////////////////////////////////////////////////////////////////////
//三维矢量运算
bool operator==(Point3D p1, Point3D p2)
{
    return ( EQ(p1.x, p2.x) && EQ(p1.y, p2.y) && EQ(p1.z, p2.z) );
}
bool operator<(Point3D p1, Point3D p2)
{
    if (NEQ(p1.x, p2.x)) {
        return (p1.x < p2.x);
    } else if (NEQ(p1.y, p2.y)) {
        return (p1.y < p2.y);
    } else {
        return (p1.z < p2.z);
    }
}
Point3D operator+(Point3D p1, Point3D p2)
{
    return Point3D(p1.x + p2.x, p1.y + p2.y, p1.z + p2.z);
}
Point3D operator-(Point3D p1, Point3D p2)
{
    return Point3D(p1.x - p2.x, p1.y - p2.y, p1.z - p2.z);
}
Point3D operator*(Point3D p1, Point3D p2) // 计算叉乘 p1 x p2
{
    return Point3D(p1.y * p2.z - p1.z * p2.y,
                   p1.z * p2.x - p1.x * p2.z,
                   p1.x * p2.y - p1.y * p2.x );
}
double operator&(Point3D p1, Point3D p2) { // 计算点积 p1·p2
    return (p1.x * p2.x + p1.y * p2.y + p1.z * p2.z);
}
double Norm(Point3D p) // 计算矢量p的模
{
    return sqrt(p.x * p.x + p.y * p.y + p.z * p.z);
}

//求三维空间中两点间的距离
double Dis(Point3D p1, Point3D 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));
}
// 求三维空间中点到直线的距离
double Dis(Point3D p, Line3D L)
{
    if(L.p1==L.p2) return Dis(p, L.p1);
    return Norm((p - L.p1) * (L.p2 - L.p1)) / Norm(L.p2 - L.p1);
}

bool OnLine(Point3D p, Line3D L) // 判断三维空间中点p是否在直线L上
{
    if(L.p1==L.p2 && p==L.p1) return true;//共点时，返回true
    return ZERO( (p - L.p1) * (L.p2 - L.p1) );
}
bool OnLineSeg(Point3D p, Line3D L) // 判断三维空间中点p是否在线段l上
{
    return ( ZERO((L.p1 - p) * (L.p2 - p)) &&
            EQ( Norm(p - L.p1) + Norm(p - L.p2), Norm(L.p2 - L.p1)) );
}

//////////////////////////////////////////////////////////////////////////////////////


/*---------------------代码区---------------------------*/