OpenGL 凸多边形截取线段，Cyrus-Beck算法

                                OpenGL  凸多边形截取线段，Cyrus-Beck算法

 

 

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

 

//roger, 2011 //OpenGL 凸多边形截取线段 #include "myglbase.h" #include "glut.h" #include "vector" #include "iostream" #include "glut.h" using namespace std; //线段类 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; } }; //点法向量表示的直线类 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; } }; //点法向量表示的多边形 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]; } }; //这段代码摘自 计算机图形学 --清华大学出版社，略有修改 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) ////这段代码摘自 计算机图形学 --清华大学出版社，略有修改 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; } void testLineSegment(Line2Segment& AC,Line2List& polygon) { //画出线段，蓝色 glColor3f(0.0,0.0,1.0); glBegin(GL_LINES); glVertex2d(AC.first.x,AC.first.y); glVertex2d(AC.second.x,AC.second.y); glEnd(); //端点颜色 glColor3f(0.0,1.0,1.0); glBegin(GL_POINTS); glVertex2d(AC.first.x,AC.first.y); glVertex2d(AC.second.x,AC.second.y); glEnd(); int result = CyrusBeckClip(AC,polygon); if (result ==0) { //do nothing } else { //被截取的线段是绿色 glColor3f(0.0,1.0,0.0); glBegin(GL_LINES); glVertex2d(AC.first.x,AC.first.y); glVertex2d(AC.second.x,AC.second.y); glEnd(); //用不同的颜色表示截取的点 glColor3f(1.0,0.0,1.0); glBegin(GL_POINTS); glVertex2d(AC.first.x,AC.first.y); glVertex2d(AC.second.x,AC.second.y); glEnd(); } } void testCyrusBeck() { //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 //画出多边形 glColor3f(1.0,1.0,0.0); glBegin(GL_LINE_LOOP); 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); glVertex2d(tempPoint.x,tempPoint.y); } glEnd(); //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; testLineSegment(AC,polygon); //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; testLineSegment(AC,polygon); //外半空间 tempPoint.set(7,0); tempPoint2.set(7,4); AC.first = tempPoint; AC.second = tempPoint2; testLineSegment(AC,polygon); //内半空间 tempPoint.set(1,5); tempPoint2.set(4,5); AC.first = tempPoint; AC.second = tempPoint2; testLineSegment(AC,polygon); }

 

看看结果吧:

 

如图：展示了四条线段；

分别代表不同的情况；

 

首先用蓝色表示线段，Lime表示端点

我用绿色区域绘制出了被截取后的线段，用cyan表示被截取后线段的颜色；