Graham(GiftWraping)求凸包算法

step1: 对于一点列，选出y值最小的点；
step2: 将该点列绕该y最小值点逆时针排列；
step3: 判断每一个点的凹凸性。

程序设计：
step1: 确定input和output.
       input: 原始输入的一个点列inputPoints；
       output: 所求凸包上的点构成的点列outputPoints。
step2: 求出inputPoints中y值最小的那个点,并与其第一个元素交换位置，设计函数SortbyAngle()。向量点乘可以得到角的cosin值,用stl中的sort()函数排序。
step3: 求outputPonts,确保放入该点列的三个点是一个凸折线段。

 

类设计如下：

GrahamConvex.hclass CGrahamConvex{public:CGrahamConvex(void);~CGrahamConvex(void);CGrahamConvex(const vector<CPoint>& originalPoints);vector<CPoint> GetOutputPoints();private:vector<CPoint> inputPoints; void SortbyAngle();};GrahamConvex.cppCGrahamConvex::CGrahamConvex(void){}CGrahamConvex::CGrahamConvex( const vector<CPoint>& originalPoints ){inputPoints = originalPoints;}CGrahamConvex::~CGrahamConvex(void){}struct ID_CosAngle{int idofPoint;double cosAngle;CPoint pos;friend bool operator <(const ID_CosAngle& first, const ID_CosAngle& second){return first.cosAngle < second.cosAngle;}};void CGrahamConvex::SortbyAngle(){if (inputPoints.size() == 0)return;//get the id of the y_min point int y_min = INT_MAX; int id_ymin = 0; for (int i = 0; i < (int)inputPoints.size(); i++) { if (y_min > inputPoints[i].y) { id_ymin = i; y_min = inputPoints[i].y; } } //swap the position between point_ymin and the first point of inputPointsCPoint temp = inputPoints[id_ymin];inputPoints[id_ymin] = inputPoints[0];inputPoints[0] = temp; // sort the points according to the cos value by default(small-big), so the points a] //arranged clockwisely vector<ID_CosAngle> Id_cosAngles; for (int i = 1; i < (int)inputPoints.size(); i++) {CVector_2D vi(inputPoints[i], inputPoints[0]);double cosAngle = vi.x / vi.Modulus();ID_CosAngle temp;temp.idofPoint = i;temp.cosAngle = cosAngle;temp.pos = inputPoints[i];Id_cosAngles.push_back(temp); }sort(Id_cosAngles.begin(), Id_cosAngles.end());//get sorted inputPointsfor (int i = 0; i < (int)Id_cosAngles.size(); i++){inputPoints[i + 1] = Id_cosAngles[i].pos;}}vector<CPoint> CGrahamConvex::GetOutputPoints(){//sort the inputpoints by angle - here is clockwise SortbyAngle();//if the input points'number is none or only one, then outputPoints //are the same with the inputPointsif (inputPoints.size() <= 1){return inputPoints;}//add the points which are convex and remove the points which are concavevector<CPoint> outputPoints;outputPoints.push_back(inputPoints[0]);outputPoints.push_back(inputPoints[1]);for ( int i = 2; i < (int)inputPoints.size(); i++){//check the current input point with possible output pointsCVector_2D v1(outputPoints[outputPoints.size() - 1], outputPoints[outputPoints.size() - 2]);CVector_2D v2(inputPoints[i], outputPoints[outputPoints.size() - 1]);if (CrossProductSign(v1, v2) <= 0) {outputPoints.push_back(inputPoints[i]);}else{while (CrossProductSign(v1, v2) >= 0 ){outputPoints.pop_back();if (outputPoints.size() > 1){v1 = CVector_2D(outputPoints[outputPoints.size() - 1], outputPoints[outputPoints.size() - 2]);v2 = CVector_2D(inputPoints[i], outputPoints[outputPoints.size() - 1]);}else{break;}}outputPoints.push_back(inputPoints[i]);}}return outputPoints;}