How to understand that the judgment point of xyz is within the convex hull template

The content of this article is about how to understand the xyz judgment point in the convex hull template. It has certain reference value. Friends in need can refer to it. I hope it will be helpful to you.

int n,m,tot;
struct point 
{
    double x,y;
}p[100000],a[100000],ss;
bool cmp(point A,point B)
{
    if(A.x!=B.x)
    return A.x<B.x;
    return A.y<B.y;
}
point operator -(point A,point B)
{
    point c;
    c.x=A.x-B.x;
    c.y=A.y-B.y;
    return c;
}
double cross(point A,point B)
{
    return A.x*B.y-B.x*A.y;
}
void dopack()
{
    tot=0;
    for(int i=1;i<=n;i++)
    {
        while(tot>1&&cross(p[tot-1]-p[tot-2],a[i]-p[tot-2])<=0)tot--;
        p[tot++]=a[i];
    }
    int k=tot;
    for(int i=n-1;i>0;i--)
    {
        while(tot>k&&cross(p[tot-1]-p[tot-2],a[i]-p[tot-2])<=0)tot--;
        p[tot++]=a[i];
    }
    if(n>1)tot--;
}
bool check(point A)
{
    int l=1,r=tot-2,mid;
    while(l<=r)
    {
        mid=(l+r)>>1;
        double a1=cross(p[mid]-p[0],A-p[0]);
        double a2=cross(p[mid+1]-p[0],A-p[0]);
        if(a1>=0&&a2<=0)
        {
            if(cross(p[mid+1]-p[mid],A-p[mid])>=0)return true;
            return false;
        }
        else if(a1<0)
        {
            r=mid-1;
        }
        else 
        {
            l=mid+1;
        }
    }
    return false;
}

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