计算几何板子（点）

最新推荐文章于 2023-02-12 01:57:56 发布

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最新推荐文章于 2023-02-12 01:57:56 发布

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原文链接：http://www.cnblogs.com/Andromeda-Galaxy/p/10451643.html

本文深入探讨了在计算机图形学中使用的各种几何计算方法，包括向量操作、点积与叉积、向量旋转及法向量计算等。通过具体的代码实现，详细解释了如何判断直线与点的关系，以及如何求解两直线交点的问题，为读者提供了丰富的几何处理技巧。

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#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.h>
#define ll long long
using namespace std;
const int maxn=1e6+10;
const double pi=acos(-1.0);
const double D_MAX=1e100;
const double D_MIN=-1e100;
const double eps=1e-9;
int sgn(double x){ if(fabs(x) < eps)return 0;  if(x >0) return 1; return -1; }
int dcmp(double x, double y){ if(fabs(x - y) < eps) return 0; if(x > y) return 1;return -1;}
void usehanshu(){double x;}//floor(x)向下取整函数ceil(x)向上取整函数round(x)四舍五入函数
struct Point  { double x,y; Point(double x=0,double y=0) { x=x;y=y; };   };
struct Segment{ Point a,b;  Segment(Point x,Point y)     { a=x;b=y; };   };
struct Line   { Point a,b;  Line(Point x,Point y)        { a=x;b=y; };   };
typedef Point Vector;
Vector operator + (Vector A, Vector B){ return Vector(A.x+B.x, A.y+B.y); } // 向量相加
Vector operator - (Point  A, Point  B){ return Vector(A.x-B.x, A.y-B.y); } // 向量生成
double operator * (Vector A, Vector B){ return A.x*B.x-A.y*B.y;          } // 点积
double operator ^ (Vector A, Vector B){ return A.x*B.y-A.y*B.x;          } // 叉积
double Dot(Vector A, Vector B)   { return A.x*B.x + A.y*B.y; }  // 点积
double Cross(Vector A, Vector B) { return A.x*B.y-A.y*B.x;   }  // 叉积
double Length(Vector A) { return sqrt(Dot(A, A));}           // 向量长度
double Angle(Vector A, Vector B){ return acos(Dot(A, B)/Length(A)/Length(B));}  // 角度
double Area2(Point A, Point B, Point C) { return Cross(B-A, C-A); }  // 四边形面积
Vector Rotate(Vector A, double rad){ return Vector(A.x*cos(rad)-A.y*sin(rad), A.x*sin(rad)+A.y*cos(rad));}//rad为弧度 且为逆时针旋转的角
Vector Normal(Vector A)            {double L = Length(A);return Vector(-A.y/L, A.x/L);}//向量A左转90°的单位法向量
bool ToLeftTest(Point a, Point b, Point c){return Cross(b - a, c - b) > 0;}
bool xx(Line A,point a){if( sgn( Cross(A.a-a,A.b-a) )==0 ) return 1;return 0;}  // 直线和点
void XX(Line A,Line B)  // 直线和直线的情况
{
    Point a=A.a; Point b=A.b;Point c=B.a; Point d=B.b;
    double A1=b.y-a.y,B1=-(b.x-a.x),C1=b.y*a.x-b.x*a.y;
    double A2=d.y-c.y,B2=-(d.x-c.x),C2=d.y*c.x-d.x*c.y;
    double k=A1*B2-A2*B1;
    if(fabs(k)<eps)
    {
        if( fabs( C2*A1-C1*A2)<eps && fabs(B1*C2-C1*B2)<eps ) printf("LINE\n");
        else                   printf("NONE\n");
    }
    else
    {
            double x=-(B1*C2-C1*B2)*1.000000000/k;
            double y=(A1*C2-C1*A2)*1.00000000/k;
            printf("POINT %.2f %.2f\n",x,y);
    }
}

int main()
{
    int T;scanf("%d",&T);
    printf("INTERSECTING LINES OUTPUT\n");
    while(T--)
    {
        Point a,b,c,d;
        scanf("%lf %lf %lf %lf",&a.x,&a.y,&b.x,&b.y);
        scanf("%lf %lf %lf %lf",&c.x,&c.y,&d.x,&d.y);
        XX(Line(a,b),Line(c,d));
    }
    printf("END OF OUTPUT\n");
    return 0;
}