圆弧插补

空间任意三点 画圆。

测试代码
平面三点
void  CCeshiDlg::OnButtonDraw() 
{
    // TODO: Add your control notification handler code here
    CWnd *pwnd=GetDlgItem(IDC_STATIC_SHOW);
    CDC *pdc=pwnd->GetDC();
    POINT p1;
    POINT p2;
    POINT p3;
    double x0=0.0,y0=0.0,z0=0.0,x2=0.0,y2=0.0,z2=0.0,x1=0.0,y1=0.0,z1=0.0;
    double xc=0.0,yc=0.0,zc=0.0,R=0.0;
    double G=0.0,E=0.0;
    double u=0.0,v=0.0,w=0.0;
    double Xi=0.0,Yi=0.0,Zi=0.0;
    double Mi=0.0,Ni=0.0,Li=0.0;
    p1.x=0;
    p1.y=140;
    p2.x=350;
    p2.y=140;
    pdc->MoveTo(p1);
    pdc->LineTo(p2);
    p1.x=175;
    p1.y=0;
    p2.x=175;
    p2.y=280;
    pdc->MoveTo(p1);
    pdc->LineTo(p2);

    p1.x=275;
    p1.y=140;
    p2.x=175;
    p2.y=40; 
    p3.x=75;
    p3.y=140;    

    x0=275;
    y0=140;
    x1=175;
    y1=40;
    x2=75;
    y2=140;
    double q[11]={0.0};
    double Paramter[11]={0.0};
    q[0]=x0;
    q[1]=y0;
    q[2]=z0;
    q[3]=x1;
    q[4]=y1;
    q[5]=z1;
    q[6]=x2;
    q[7]=y2;
    q[8]=z2;
    q[9]=10;
    q[10]=0.05;
    CircleInter(q,Paramter);
    long N=0;
    N=(long)(Paramter[0]/Paramter[1])+1;//插补次数    
    xc=Paramter[2];
    yc=Paramter[3];
    zc=Paramter[4];
    G=Paramter[6];
    E=Paramter[7];
    u=Paramter[8];
    v=Paramter[9];
    w=Paramter[10];
    
    Xi=(double)p1.x;
    Yi=(double)p1.y;
    Zi=0;
    Mi=v*(Zi-zc)-w*(Yi-yc);
    Ni=w*(Xi-xc)-u*(Zi-zc);
    Li=u*(Yi-yc)-v*(Xi-xc);
    pdc->MoveTo(p1);
    POINT pi;
    for(int i=1;i<N;i++)
    {
        Xi=xc+G*(Xi+E*Mi-xc);
        Yi=yc+G*(Yi+E*Ni-yc);
        Zi=zc+G*(Zi+E*Li-zc);
        Mi=v*(Zi-zc)-w*(Yi-yc);
        Ni=w*(Xi-xc)-u*(Zi-zc);
        Li=u*(Yi-yc)-v*(Xi-xc);
        pi.x=(long)Xi;
        pi.y=(long)Yi;
        pdc->LineTo(pi);

    }
    pdc->LineTo(p3);
             
}

_declspec(dllexport)  bool  CircleInter( double  p[ 11 ], double   * Paramter)
{

    double a00=0.0,a01=0.0,a02=0.0,a10=0.0,a11=0.0,a12=0.0;
    double a20=0.0,a21=0.0,a22=0.0,b0=0.0,b1=0.0,b2=0.0;
    double x0=0.0;
    double y0=0.0;
    double z0=0.0;
    double x1=0.0;
    double y1=0.0;
    double z1=0.0;
    double x2=0.0;
    double y2=0.0;
    double z2=0.0;
    x0=p[0];
    y0=p[1];
    z0=p[2];
    x1=p[3];
    y1=p[4];
    z1=p[5];
    x2=p[6];
    y2=p[7];
    z2=p[8];
    double xc=0.0,yc=0.0,zc=0.0;//圆心坐标
    double R=0.0;//圆半径
    double u=0.0,v=0.0,w=0.0;
    double u1=0.0,v1=0.0,w1=0.0;
    double FT=0.0;
    double G=0.0;
    double delt=0.0;
    double thelt=0.0;
    double E=0.0;
    double H=0.0;
    a00=2*(x0-x1);a01=2*(y0-y1);a02=2*(z0-z1);
    a10=2*(x1-x2);a11=2*(y1-y2);a12=2*(z1-z2);
    a20=a02*(a02*a11-a01*a12)/8;
    a21=a02*(a00*a12-a02*a10)/8;
    a22=-(a00*(a02*a11-a01*a12)+a01*(a00*a12-a02*a10))/8;
    b0=(x0*x0+y0*y0+z0*z0)-(x1*x1+y1*y1+z1*z1);
    b1=(x1*x1+y1*y1+z1*z1)-(x2*x2+y2*y2+z2*z2);
    b2=a20*x0+a21*y0+a02*z0;
    
    if(fabs(x0-x1)<=1e-5 && fabs(x1-x2)<=1e-5)
    {

        xc=x0;
        yc=(a12*b0-a02*b1)/(-a02*a11+a01*a12);    
        zc=(a11*b0-a01*b1)/(a02*a11-a01*a12);
    }
    else if(fabs(y0-y1)<=1e-5 && fabs(y1-y2)<=1e-5)
    {
    
        xc=(a12*b0-a02*b1)/(-a02*a10+a00*a12);
        yc=y0;
        zc=(a10*b0-a00*b1)/(a02*a10-a00*a12);        
    }
    else if(fabs(z0-z1)<=1e-5 && fabs(z1-z2)<=1e-5)
    {

    
        xc=(a11*b0-a01*b1)/(-a01*a10+a00*a11);
        yc=(a10*b0-a00*b1)/(a01*a10-a00*a11);
        zc=z0;
    }
    else
    {
        xc=(a12*a21*b0-a11*a22*b0-a02*a21*b1+a01*a22*b1+a02*a11*b2-a01*a12*b2)/(a02*a11*a20-a01*a12*a20-a02*a10*a21+a00*a12*a21+a01*a10*a22-a00*a11*a22);
        yc=(a12*a20*b0-a10*a22*b0-a02*a20*b1+a00*a22*b1+a02*a10*b2-a00*a12*b2)/(-a02*a11*a20+a01*a12*a20+a02*a10*a21-a00*a12*a21-a01*a10*a22+a00*a11*a22);
        zc=(a11*a20*b0-a10*a21*b0-a01*a20*b1+a00*a21*b1+a01*a10*b2-a00*a11*b2)/(a02*a11*a20-a01*a12*a20-a02*a10*a21+a00*a12*a21+a01*a10*a22-a00*a11*a22);                    
    }


    R=sqrt((x0-xc)*(x0-xc)+(y0-yc)*(y0-yc)+(z0-zc)*(z0-zc));
    u=(y1-y0)*(z2-z1)-(z1-z0)*(y2-y1);
    v=(z1-z0)*(x2-x1)-(x1-x0)*(z2-z1);
    w=(x1-x0)*(y2-y1)-(y1-y0)*(x2-x1);
    u1=(y0-yc)*(z2-z0)-(z0-zc)*(y2-y0);
    v1=(z0-zc)*(x2-x0)-(x0-xc)*(z2-z0);
    w1=(x0-xc)*(y2-y0)-(y0-yc)*(x2-x0);
    FT=p[9]*p[10];
    G=1/sqrt(1+(FT/R)*(FT/R));
    delt=FT/R;
    E=FT/(R*sqrt(u*u+v*v+w*w));
    H=u*u1+v*v1+w*w1;
    if(H>=0)
    {
        thelt=2*asin(sqrt((x2-x0)*(x2-x0)+(y2-y0)*(y2-y0)+(z2-z0)*(z2-z0))/(2*R));
    }
    else if(H<0)
    {
        thelt=2*pi-2*asin(sqrt((x2-x0)*(x2-x0)+(y2-y0)*(y2-y0)+(z2-z0)*(z2-z0))/(2*R));
    }
    Paramter[0]=thelt;
    Paramter[1]=delt;
    Paramter[2]=xc;
    Paramter[3]=yc;
    Paramter[4]=zc;
    Paramter[5]=R;
    Paramter[6]=G;
    Paramter[7]=E;
    Paramter[8]=u;
    Paramter[9]=v;
    Paramter[10]=w;
    
    return true;
}

转载于:https://www.cnblogs.com/wqj1212/archive/2008/04/07/1140653.html