判断线是否相交、判断点是否在线上、求线相交交点

先定义个点、线结构

typedef struct tagStruVertex
{
    double x;
    double y;
    double distanceTo(const tagStruVertex& point) const
    {
        return sqrt((x - point.x) * (x - point.x) + (y - point.y) * (y - point.y));
    }
    bool equal(const tagStruVertex& point) const
    {
        if (point.x == x && point.y == y)
        {
            return true;
        }
        return false;
    }
}StruVertex;

typedef struct tagStruSegment
{
    StruVertex start;
    StruVertex end;
}StruSegment;

计算叉乘

double mult(StruVertex a, StruVertex b, StruVertex c)
{
    return (a.x - c.x) * (b.y - c.y) - (b.x - c.x) * (a.y - c.y);
}

判断两线是否相交

//start1, end1为一条线段两端点 start2, end2为另一条线段的两端点 相交返回true, 不相交返回false  
bool intersect(StruVertex start1, StruVertex end1, StruVertex start2, StruVertex end2)
{
    if (max(start1.x, end1.x) < min(start2.x, end2.x))
    {
        return false;
    }
    if (max(start1.y, end1.y) < min(start2.y, end2.y))
    {
        return false;
    }
    if (max(start2.x, end2.x) < min(start1.x, end1.x))
    {
        return false;
    }
    if (max(start2.y, end2.y) < min(start1.y, end1.y))
    {
        return false;
    }
    //ac*ab < 0 或者 ab*ad<0
    if (mult(start2, end1, start1) * mult(end1, end2, start1) < 0)
    {
        return false;
    }
    //ca*cd<0 或者 cd*cb<0
    if (mult(start1, end2, start2) * mult(end2, end1, start2) < 0)
    {
        return false;
    }
    return true;
}

获取交点

StruVertex getLineNode(StruVertex start1, StruVertex end1, StruVertex start2, StruVertex end2)
{
    StruVertex ret = start1;
    double t = ((start1.x - start2.x) * (start2.y - end2.y) - (start1.y - start2.y) * (start2.x - end2.x)) / ((start1.x - end1.x) * (start2.y - end2.y) - (start1.y - end1.y) * (start2.x - end2.x));
    ret.x += (end1.x - start1.x) * t;
    ret.y += (end1.y - start1.y) * t;

    return ret;
}

判断点是否在线上

bool onSegment(StruVertex pi, StruVertex pj, StruVertex Q)
{
    if ((Q.x - pi.x) * (pj.y - pi.y) == (pj.x - pi.x) * (Q.y - pi.y) && 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;
    }
}