判断点在直线上,需要满足两个条件,如判断Q点是否在线段p1p2上

1:(Q-P1)X(P2-P1)=0;//叉乘为0

2:Q在以P1,P2为对角顶点的矩形内//保证点Q不在线段P1P2的延长线或反向延长线上

判断点在三角形内:

如果点P在三角形内,那么Spab+Spac+Spbc=Sabc

三角形面积公式由叉积给出 S=1/2×|crossProduct(a,b,c)|;

这种方法有浮点误差

另一种是沿三角形的边顺时针方向,判断P点是否在每条边的右边,如果是,就在三角形内

此法没有浮点误差

下面只给出了有浮点误差的

#include <stdio.h>
#include <math.h>
#include <iostream>
#include <algorithm>

#define eps 1e-8
using namespace std;

typedef struct node
{
    double x,y;
}point;

typedef struct triangle
{
    point A;
    point B;
    point C;
};

double crossProduct(point p1,point p2,point p0)//(p1-p0)X(p2-p0)
{
    double x1,x2,y1,y2;
    x1=p1.x-p0.x;
    y1=p1.y-p0.y;
    x2=p2.x-p0.x;
    y2=p2.y-p0.y;
    return x1*y2-x2*y1;
}

bool inTriangle(triangle t,point P)
{
    point A,B,C;
    A=t.A;
    B=t.B;
    C=t.C;
    double Sabc=fabs(crossProduct(A,B,C));printf("abc:%lf ",Sabc);
    double Spab=fabs(crossProduct(P,A,B));printf("pab:%lf ",Spab);
    double Spac=fabs(crossProduct(P,A,C));printf("pac:%lf ",Spac);
    double Spbc=fabs(crossProduct(P,B,C));printf("pbc:%lf ",Spbc);
    if(fabs(Sabc-(Spab+Spac+Spbc))<eps)
        return true;
    else
        return false;
}

bool onSegment(point Pi,point Pj,point Q)
{
    if((Q.x-Pi.x)*(Pj.y-Pi.y)==(Pj.x-Pi.x)*(Q.y-Pi.y)&&//x1*y2=x2*y1
    min(Pi.x,Pj.x)<=Q.x&&Q.x<=max(Pi.x,Pj.x)&&
    min(Pi.y,Pj.y)<=Q.y&&Q.y<=max(Pi.y,Pj.y))
        return true;
    else
        return false;
}

int main()
{
    point p,q,r,s;
    scanf("%lf%lf%lf%lf",&p.x,&p.y,&q.x,&q.y);//segment p--q
    scanf("%lf%lf",&r.x,&r.y);//point r
    scanf("%lf%lf",&s.x,&s.y);//point s
    if(onSegment(p,q,r))
    {
        printf("YES\n");
    }
    else
    {
        printf("NO\n");
    }

    triangle t;
    t.A=p;
    t.B=q;
    t.C=r;

    if(inTriangle(t,s))
    {
        printf("YES\n");
    }
    else
    {
        printf("NO\n");
    }

    return 0;
}
View Code