Qt 求两个多边形组合后的凸包，Qt里的排序方法

unique是很关键的一步，不可省略，一般的题目都给定了不会有重合点，但是实际项目应用里保不准。

可以证明，交点不会出现在凸包上。

这里的排序方法非常好用，不用单独写一个cmp函数了，相当于直接把这个函数写在sort下面

qreal DataConvert::getCrossProduct(const QPointF &iPointA,const QPointF &iPointB,const QPointF &iPointC){//获得a->b和a->c的叉积

    //x1y2-x2y1

    return ((iPointB.x()-iPointA.x())*(iPointC.y()-iPointA.y())-(iPointC.x()-iPointA.x())*(iPointB.y()-iPointA.y()));

}

QPolygonF DataConvert::getPolysConvexHull(const QPolygonF &iFirstPoly, const QPolygonF &iSecondPoly){//获取两个poly的凸包

    if(iFirstPoly.size()==0)return iSecondPoly;

    if(iSecondPoly.size()==0)return iFirstPoly;

    int Size1=iFirstPoly.size();

    int Size2=iSecondPoly.size();

    //第一步把所有结点取出来

    QVector<QPointF>AllPoints;

    for(int i=0;i<Size1;i++){

        AllPoints.push_back(iFirstPoly[i]);

    }

    for(int i=0;i<Size2;i++){

        AllPoints.push_back(iSecondPoly[i]);

    }

    //其实交点可以不加，因为交点一定不属于凸包，凸包一定是两个多边形顶点的子集

//    for(int i=0;i<Size1;i++){

//        QLineF FirstLine=QLineF(iFirstPoly[i],iFirstPoly[(i+1)%Size1]);

//        //AllPoints.push_back(FirstLine.p1());

//        for(int j=0;j<Size2;j++){

//            QLineF SecondLine=QLineF(iSecondPoly[j],iSecondPoly[(j+1)%Size2]);

//            //AllPoints.push_back(SecondLine.p1());

//            QPointF intersectionPoint;

//            int interV=FirstLine.intersect(SecondLine,&intersectionPoint);

//            if(interV==1)AllPoints.push_back(intersectionPoint);

//        }

//    }

    //第二步，寻找基点，此步可以并到第一步里，但是为了代码清晰，便于阅读，多O(n)的复杂度也不太影响

    int startPosition=0;

    for(int i=0;i<AllPoints.size();i++){

        if(AllPoints[startPosition].y()>AllPoints[i].y()||

                (AllPoints[startPosition].y()==AllPoints[i].y()&&AllPoints[startPosition].x()>AllPoints[i].x())){

            startPosition=i;

        }

        //AllPoints.swap()

    }

    if(startPosition>0){

        qSwap(AllPoints[0],AllPoints[startPosition]);

    }

    //第三，给点按照与基点的叉积排序

    qSort(AllPoints.begin()+1,AllPoints.end(),[=](const QPointF &aa,const QPointF &bb){

        qreal crossAns=DataConvert::getCrossProduct(AllPoints[0],aa,bb);

        qreal length1=QLineF(AllPoints[0],aa).length();

        qreal length2=QLineF(AllPoints[0],bb).length();

        return (crossAns>0||(crossAns==0&&length1>length2));

    });

    for(int i=0;i<AllPoints.size();i++){

        qDebug()<<AllPoints[i].x()<<" fuck "<<AllPoints[i].y()<<"\n";

    }

    //第四unique

    QVector<QPointF>uniquePoints;

    for(int i=0;i<AllPoints.size();i++){

        uniquePoints.push_back(AllPoints[i]);

        int j=i;

        while(i<AllPoints.size()){

            if(DataConvert::fuzzyEqual(AllPoints[(i+1)%AllPoints.size()].x(),AllPoints[j].x())&&

                    DataConvert::fuzzyEqual(AllPoints[(i+1)%AllPoints.size()].y(),AllPoints[j].y())){

                i++;

            }

            else break;

        }

    }

    //第五开始算凸包

    int s[1000];

    s[0]=0;

    s[1]=1;

    int top=1;

    for(int i=2;i<uniquePoints.size();i++){

        while(top&&DataConvert::getCrossProduct(uniquePoints[s[top-1]],uniquePoints[s[top]],uniquePoints[i])<0)top--;

        s[++top]=i;

    }

    top++;

    qDebug()<<"top  "<<top<<"\n";

    //把凸包里的点组成新的poly输出

    QPolygonF newpoly;

    for(int i=0;i<top;i++){

        newpoly.push_back(uniquePoints[s[i]]);

    }

    return newpoly;

}