OpenGL 凸多边形截取线段 Cyrus-Beck算法的实现

                                      OpenGL 凸多边形截取线段   Cyrus-Beck算法的实现

2011-04-26

16:01

计算机图形学中 凸多边形截取 线段的问题

下面是示例代码，有点抽象，不过关键是算法：

该代码对书上不是很清楚的地方进行修炼。

 

点此下载相关资源：

http://download.youkuaiyun.com/user/rorger

 

 

 //rorger, 2011 //凸多边形截取线段 #include "myglbase.h" #include "glut.h" #include "vector" #include "iostream" using namespace std; class Line2Segment { public: Point2 first ; Point2 second ; Vector2 norm() { Vector2 c = second - first ; Vector2 normalVector = c.GetNormalVector(); return normalVector; } Line2Segment() { first.x=first.y=0; second.x=second.y=0; } Line2Segment(Point2 first,Point2 second) { this->first = first; this->second = second; } Line2Segment(Line2Segment& line2) { first = line2.first; second = line2.second; } }; class Line2 { public: Point2 pt ; Vector2 norm; Line2() { pt.x=pt.y=0; norm.x=0; norm.y=0; } Line2(Point2 pt,Vector2 norm) { this->pt=pt; this->norm=norm; } Line2(const Line2& line2) { pt=line2.pt; norm = line2.norm; } }; class Line2List { public: vector<Line2> line; int num() { return line.size(); } void push_back(Line2 newLine) { line.push_back(newLine); } Line2& operator[](int index) { if ((unsigned int)index >= line.size()) //注意size是unsigned int { throw "Out of range in Line2List"; } return line[index]; } }; int chopCI(double&tIn,double&tOut,double number,double denom) { double tHit ; if(denom < 0) //射线是射入 { tHit = number / denom ; if (tHit > tOut) { return 0 ; } else if(tHit>tIn) { tIn = tHit; } } else if(denom > 0) { tHit = number / denom; if (tHit<tIn) { return 0 ; } if (tHit<tOut) { tOut = tHit; } } else if(number<=0) //denom为0，射线与直线平行 { return 0 ; //在外半空间 } return 1; } //线段和凸多边形的交点 (二维) int CyrusBeckClip(Line2Segment& seg,Line2List& L) { double number,denom; double tIn = 0.0,tOut = 1.0 ; //候选区间为[0,1] Vector2 c, tmp ; c = seg.second-seg.first; //直线的参数表示 R(t)=A+c*tHit for (int i=0;i<L.num();i++) { //利用公式 tHit=n*(B-A)/(n*c) 其中A和c是目的直线参数表示，B和n是另一条直线点法向量 tmp = L.line[i].pt - seg.first; number = L.line[i].norm * tmp ; denom = L.line[i].norm * c ; if (!chopCI(tIn,tOut,number,denom)) { return 0 ; //提前结束 } } //注意tIn和tOut都是基于A+c*tHit ;所以在计算seg截点时，先计算seg.second; //否则，A的值，即seg.first就变化了 if(tOut <1.0) { seg.second = seg.first + c * tOut; } if (tIn>0.0) { seg.first = seg.first + c * tIn; } return 1; } int main() { //6边形 double point2Array[6][2] = {​{0,3},{0,6},{4,6}, {6,4},{6,0},{3,0}}; Line2List polygon; Line2 tempLine2 ; Point2 tempPoint ; Point2 tempPoint2; Vector2 tempNorm; //转化为点法向量的形式 for (int i=0;i<6;i++) { tempPoint.x = point2Array[i][0]; tempPoint.y = point2Array[i][1]; tempPoint2.x = point2Array[(i+1)%6][0]; tempPoint2.y = point2Array[(i+1)%6][1]; tempLine2.norm = ((Vector2)(tempPoint2-tempPoint)).GetNormalVector(); tempLine2.pt = tempPoint; polygon.push_back(tempLine2); } //两个点都在多边形外，穿过多边形 Line2Segment AC ; tempPoint.set(0,0); tempPoint2.set(6,6); AC.first = tempPoint; AC.second = tempPoint2; cout <<"测试AC: A="<<AC.first<<" B="<<AC.second<<endl; int result = CyrusBeckClip(AC,polygon); if (result ==0) { cout<<"线段在多边形外"<<endl ; } else { cout <<"截取结果："; cout<<"A'="<<AC.first<<"/t"<<"B'="<<AC.second<<endl ; } cout<<"---------------------------------------------------------------"<<endl; //点(2,3)在多边形内,另一个点在多边形外 tempPoint.set(2,3); tempPoint2.set(5,7); AC.first = tempPoint; AC.second = tempPoint2; cout <<"测试AC: A="<<AC.first<<" B="<<AC.second<<endl; result = CyrusBeckClip(AC,polygon); if (result ==0) { cout<<"线段在多边形外"<<endl ; } else { cout <<"截取结果："; cout<<"A'="<<AC.first<<"/t"<<"B'="<<AC.second<<endl ; } cout<<"---------------------------------------------------------------"<<endl; //外半空间 tempPoint.set(7,0); tempPoint2.set(7,4); AC.first = tempPoint; AC.second = tempPoint2; cout <<"测试AC: A="<<AC.first<<" B="<<AC.second<<endl; result = CyrusBeckClip(AC,polygon); if (result ==0) { cout<<"线段在多边形外"<<endl ; } else { cout <<"截取结果："; cout<<"A'="<<AC.first<<"/t"<<"B'="<<AC.second<<endl ; } cout<<"---------------------------------------------------------------"<<endl; //内半空间 tempPoint.set(1,5); tempPoint2.set(4,5); AC.first = tempPoint; AC.second = tempPoint2; cout <<"测试AC: A="<<AC.first<<" B="<<AC.second<<endl; result = CyrusBeckClip(AC,polygon); if (result ==0) { cout<<"线段在多边形外"<<endl ; } else { cout <<"截取结果："; cout<<"A'="<<AC.first<<"/t"<<"B'="<<AC.second<<endl ; } return 0 ; } /*output: 测试AC: A=(0,0) B=(6,6) 截取结果：A'=(1.5,1.5) B'=(5,5) --------------------------------------------------------------- 测试AC: A=(2,3) B=(5,7) 截取结果：A'=(2,3) B'=(4.14286,5.85714) --------------------------------------------------------------- 测试AC: A=(7,0) B=(7,4) 线段在多边形外 --------------------------------------------------------------- 测试AC: A=(1,5) B=(4,5) 截取结果：A'=(1,5) B'=(4,5) Press any key to continue . . . */

下一次我将会给出opengl图像展示。。。