判断平面上两线段是否相交

#include "stdafx.h"
typedef struct point
{
    int x;
    int y;
}vector;
struct line{
    point start;
    point end;
};
struct rec{
    int up;
    int down;
    int left;
    int right;
};
int max(int x, int y)
{
    return x>y ? x : y;
}
int min(int x, int y)
{
    return x<y ? x : y;
}
vector VectorSubtraction(vector a, vector b){
    vector v;
    v.x = a.x - b.x;
    v.y = a.y - b.y;
    return v;
}
line VectorToLine(vector a){
    line l;
    l.start.x = 0;
    l.start.y = 0;
    l.end.x = a.x;
    l.end.y = a.y;
    return l;
}
vector LineToVector(line a){
    vector v;
    v.x = a.end.x - a.start.x;
    v.y = a.end.y - a.start.y;
    return v;
}
rec LineToRec(line a){
    //将一条线段构造成一个有四条边界的矩形
    rec ra;
    ra.left = min(a.start.x, a.end.x);
    ra.right = max(a.start.x, a.end.x);
    ra.down = min(a.start.y, a.end.y);
    ra.up = max(a.start.y, a.end.y);
    return ra;
}
rec VectorToRec(vector v){
    return LineToRec(VectorToLine(v));
}
int IsCrossRec(rec a, rec b){
    //快速排斥实验
    rec c;//假设相交了
    c.left = max(a.left, b.left);
    c.right = min(a.right, b.right);
    c.down = max(a.down, b.down);
    c.up = min(a.up, b.up);
    if (c.left <= c.right&&c.down <= c.up){//如果相交矩形存在或者为一个点，则两矩形a，b相交，否则不相交,一条线的情况显然线段不会相交
        return 1;
    }
    else return 0;
}
int CrossProduct(vector a, vector b){
    return a.x*b.y - a.y*b.x;
}
int IsBetween(vector a, vector b, vector c){
    //跨立实验，判定向量a是否在b、c之间，考虑共线的问题
    if (CrossProduct(a, b)*CrossProduct(a,c)<0)
    {
        return 1;
    }
    else if (CrossProduct(a, b) == 0 && (IsCrossRec(VectorToRec(a), VectorToRec(c)) || IsCrossRec(VectorToRec(b), VectorToRec(c)))){
        return 1;//借用相交矩形函数解决是否在线段上的问题
    }
    else if (CrossProduct(a, c) == 0 && (IsCrossRec(VectorToRec(a), VectorToRec(b)) || IsCrossRec(VectorToRec(c), VectorToRec(b)))){
        return 1;
    }
    else
    {
        return 0;
    }
}
int SegmentIntersect(line a, line b){
    point p1, p2, p3, p4;
    if (!IsCrossRec(LineToRec(a), LineToRec(b)))return 0;
    p1 = a.start;
    p2 = a.end;
    p3 = b.start;
    p4 = b.end;
    if (IsBetween(VectorSubtraction(p4, p3), VectorSubtraction(p2, p3), VectorSubtraction(p1, p3)) && IsBetween(VectorSubtraction(p2, p1), VectorSubtraction(p3, p1), VectorSubtraction(p4, p1))){
        //向量的减法得出新的向量然后判定方位
        return 1;
    }
    return 0;
}
int _tmain(int argc, _TCHAR* argv[])
{
    line a, b;
    printf("输入线段a的x点的横纵坐标如\"0 0\"\n");
    scanf("%d %d",&a.start.x,&a.start.y);
    printf("输入线段a的y点的横纵坐标如\"0 0\"\n");
    scanf("%d %d",&a.end.x,&a.end.y);
    printf("输入线段b的x点的横纵坐标如\"0 0\"\n");
    scanf("%d %d",&b.start.x,&b.start.y);
    printf("输入线段b的y点的横纵坐标如\"0 0\"\n");
    scanf("%d %d",&b.end.x,&b.end.y);
    if (SegmentIntersect(a, b)){
        printf("Y\n");
    }
    else
    {
        printf("N\n");
    }
    return 0;
}