OpenGL 9点圆 三角形垂心/垂足 三角形中线

                                             OpenGL 9点圆 三角形垂心/垂足 三角形中线

 

点此下载：

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

 

 

 //rorger,2011 //night points circle #include "myglbase.h" #include "glut.h" #include "math.h" int GetLinesIntersect(Point2 A, Vector2 c,Point2 B,Vector2 n, double& tHit,Point2& PHit) { if (n*c==0) { //射线与直线平行 return 0 ; } else { tHit= (n*(B-A))/(n*c); PHit=A+c*tHit; if(n*c >0) { return 1; //射线沿着法向量方向 } else { return -1 ; //射线与法向量相反 } } } //判断是否为三角形 //如果三点共线返回0 //否则返回1 int IsTriangle(Point2 A,Point2 B,Point2 C) { Vector2 a = B-A; Vector2 b = C-B ; Vector2 c = A-C; if (a*b.GetNormalVector() ==0 ) // { return 0 ; } else return 1; } // 取得三角形的内点；内切圆的点 //成功返回1，否则返回0 int GetTangentPoints(Point2 A,Point2 B,Point2 C,Point2& R,Point2& S,Point2& T) { //the order is important Vector2 a = B-A; Vector2 b = C-B ; Vector2 c = A-C; double absa = a.GetLength(); double absb = b.GetLength(); double absc = c.GetLength(); if (!IsTriangle(A,B,C)) { return 0; } double la = (absa + absc-absb)/2.0 ; double lb = (absa + absb-absc)/2.0; R = A + la*(a/absa); S = B + lb*(b/absb); T = A - la*(c/absc); return 1; } int GetCircumCenter (Point2 A,Point2 B,Point2 C, Point2& S,double& radius) { Vector2 a,b,c,na; a=B-A; b=C-B; c=A-C; na = a.GetNormalVector(); S=A+ (a+na*((b*c)/(na*c))) / ((double)2.0); double temp = (b*c)/(na*c); radius=(a.GetLength())/2.0 * (sqrt( temp * temp + 1)); return 0; } void drawArc(double x,double y,double start_angle,double end_angle,double delta_angle,double radius,bool fill) { if (fill) { glBegin(GL_TRIANGLE_FAN); } else { glBegin(GL_LINE_STRIP); } for (double i=start_angle;i<=end_angle;i+=delta_angle) { double vx=x+radius * cos(i); double vy=y+radius*sin(i); glVertex2d(vx,vy); } glEnd(); } void drawCircle(double x, double y, double radius,bool fill) { double pi=acos(-1.0); drawArc(x,y,0,2*pi,pi/360,radius,fill); } void drawPie(double x,double y,double start_angle,double end_angle,double delta_angle,double radius,bool fill) { drawArc(x,y,start_angle,end_angle,delta_angle,radius,fill); if (fill) { glBegin(GL_TRIANGLE_FAN); } else { glBegin(GL_LINES); } glVertex2d(x,y); glVertex2d(x+radius*cos(start_angle),y+radius*sin(start_angle)); if (!fill) { glVertex2d(x,y); } glVertex2d(x+radius*cos(end_angle),y+radius*sin(end_angle)); glEnd(); } //calculates the center point of line AB,BC,CA //return 1 if success //else 0 int GetCenterPoint(Point2 A,Point2 B,Point2 C,Point2& abP,Point2& bcP, Point2& caP) { if (!IsTriangle(A,B,C)) { return 0 ; } abP = (A+B)/2.0; bcP = (B+C)/2.0; caP = (C+A)/2.0; return 1; } // calculates the perpendicular point of line AB,BC,CA ,pay attention to the order //成功返回0 //其它返回1 int GetPerpendicularPoint(Point2 A, Point2 B,Point2 C,Point2& abP,Point2&bcP,Point2& caP) { //用参数形式表示line CA: C+c*t //用点法向量表示line BP ; n=c; //使用公式 double t = n*(B-A)/(n*c); if(!IsTriangle(A,B,C)) { return 0 ; } Vector2 c; Vector2 n; double tHit; //calculate abP c=B-A; n=c; tHit = (n * (C-A)) / (n*c); abP = A + c * tHit; //calaculate bcP c=C-B; n=c; tHit = (n * (A-B)) / (n*c); bcP = B + c * tHit; //calculate caP c=A-C; n=c; tHit = (n * (B-C)) / (n*c); caP = C + c * tHit; return 1; } //参数P为垂足 //计算各个端点和垂足连线中点 void GetCenterOfPointIntersectPerPendicularPoint(Point2 A,Point2 B,Point2 C,Point2 P,Point2& apP,Point2& bpP,Point2& cpP) { apP = (A+P)/2.0; bpP = (B+P)/2.0; cpP = (C+P)/2.0; } //如果没有提供垂心，先计算，然后在调用重载函数 void GetCenterOfPointIntersectPerPendicularPoint(Point2 A,Point2 B,Point2 C,Point2& apP,Point2& bpP,Point2& cpP) { Point2 P ; double radius ; GetPerpendicularPoint(A,B,C,apP,bpP,cpP); GetCircumCenter(apP,bpP,cpP,P,radius); GetCenterOfPointIntersectPerPendicularPoint(A,B,C,P,apP,bpP,cpP); } //画九点图 void drawNightPointCircle(Point2 A,Point2 B,Point2 C) { //画9点图最简单的方式是画出中点的外接圆，但这里尝试了新的方式 Point2 R,S,T,O,P; // R/S/T是垂足,O是圆心,P是垂心 double radius ; Point2 abP,bcP,caP; //计算垂足 GetPerpendicularPoint(A,B,C,R,S,T); //计算中点 GetCenterPoint(A,B,C,abP,bcP,caP); //画出三角形 glColor3f(0.0,1.0,1.0); glBegin(GL_LINE_LOOP); glVertex2d(A.x,A.y); glVertex2d(B.x,B.y); glVertex2d(C.x,C.y); glEnd(); //取得垂心 /*AS直线参数表示： A+(S-A)*t CR直线点法向量表示: n= B-A; 那么就是GetLinesIntersect(A,S-A,C,B-A))*/ Vector2 c = S-A ; Vector2 n = B-A; double tHit ; GetLinesIntersect(A,c,C,n,tHit,P); //取得垂足所在圆心 radius=0; GetCircumCenter(R,S,T,O,radius); //画出垂线和中线 glEnable(GL_LINE_STIPPLE); glColor3f(0.0,0.0,1.0); glLineStipple(1,0x00e1); glBegin(GL_LINES); //垂线 glVertex2d(R.x,R.y); glVertex2d(C.x,C.y); glVertex2d(S.x,S.y); glVertex2d(A.x,A.y); glVertex2d(T.x,T.y); glVertex2d(B.x,B.y); //中线 glColor3f(1.0,0.0,1.0); glVertex2d(abP.x,abP.y); glVertex2d(C.x,C.y); glVertex2d(bcP.x,bcP.y); glVertex2d(A.x,A.y); glVertex2d(caP.x,caP.y); glVertex2d(B.x,B.y); glEnd(); glDisable(GL_LINE_STIPPLE); //画出垂足的外接圆 glColor3f(1.0,1.0,0.0); drawCircle(O.x,O.y,radius,false); //画出三个垂足 glPointSize(6.0); glColor3f(0.0,1.0,0.0); glBegin(GL_POINTS); glVertex2d(R.x,R.y); glVertex2d(S.x,S.y); glVertex2d(T.x,T.y); glEnd(); //画出中点 glPointSize(6.0); glColor3f(0.0,1.0,0.0); glBegin(GL_POINTS); glVertex2d(abP.x,abP.y); glVertex2d(bcP.x,bcP.y); glVertex2d(caP.x,caP.y); glEnd(); //画出顶点和垂心的中点 Point2 apP,bpP,cpP; GetCenterOfPointIntersectPerPendicularPoint(A,B,C,P,apP,bpP,cpP); glPointSize(6.0); glColor3f(0.0,1.0,0.0); glBegin(GL_POINTS); glVertex2d(apP.x,apP.y); glVertex2d(bpP.x,bpP.y); glVertex2d(cpP.x,cpP.y); glColor3f(1.0,1.0,0.0); glVertex2d(P.x,P.y); glEnd(); glFlush(); }

 

myglbase有进一步更新

 

看看效果吧:

 

 

 

蓝色的表示垂线；

9个点都用绿色表示出来了

另外的分别是中线。