OpenCasCade数学库 - 轴（gp_Ax1）

╰半夏微凉° 2021-12-12 14:51 280阅读 1赞

gp\_Ax1描述了三维空间中的一个轴。

### 1.gp\_Ax1的作用 ###

*  描述三维几何体(如：旋转体的轴)
 *  描述几何变换（如：对称轴、旋转轴）

### 2.gp\_Ax1的定义 ###

*  位置
 *  方向

class gp_Ax1 
    {
    public:
        ...
    private:
        gp_Pnt loc;
        gp_Dir vdir;
    };

默认情况下，位置为原点，方向为Z轴正向。

inline gp_Ax1::gp_Ax1() : loc(0.,0.,0.), vdir(0.,0.,1.){ }

### 3.相等     ###

两个轴是否相同的判断：位置相同，方向相同（夹角为0度）。

Standard_Boolean gp_Ax1::IsCoaxial(const gp_Ax1& Other, const Standard_Real AngularTolerance,const Standard_Real LinearTolerance) const
    {
      gp_XYZ XYZ1 = loc.XYZ();
      XYZ1.Subtract (Other.loc.XYZ());
      XYZ1.Cross (Other.vdir.XYZ());
      Standard_Real D1 = XYZ1.Modulus();
    
      gp_XYZ XYZ2 = Other.loc.XYZ();
      XYZ2.Subtract (loc.XYZ());
      XYZ2.Cross (vdir.XYZ());
      Standard_Real D2 = XYZ2.Modulus();
      
      return (vdir.IsEqual (Other.vdir, AngularTolerance) && D1 <= LinearTolerance && D2 <= LinearTolerance);
    }

### 4.垂直  ###

两个轴是否垂直的判断：轴的方向垂直（夹角为90度）。

inline Standard_Boolean gp_Ax1::IsNormal(const gp_Ax1& Other,const Standard_Real AngularTolerance) const
    { 
        return vdir.IsNormal(Other.vdir, AngularTolerance); 
    }

inline Standard_Boolean gp_Dir::IsNormal(const gp_Dir& Other,const Standard_Real AngularTolerance) const
    {
      Standard_Real Ang = M_PI / 2.0 - Angle (Other);
      if (Ang < 0) Ang = - Ang;
      return   Ang <= AngularTolerance;
    }

### 5.平行 ###

两个轴是否平行的判断：轴的夹角为0度或180度。

inline Standard_Boolean gp_Ax1::IsParallel(const gp_Ax1& Other,const Standard_Real AngularTolerance) const
    { 
        return vdir.IsParallel(Other.vdir, AngularTolerance); 
    }

inline Standard_Boolean gp_Dir::IsParallel(const gp_Dir& Other, const Standard_Real AngularTolerance) const
    {
      Standard_Real Ang = Angle (Other);
      return Ang <= AngularTolerance || M_PI - Ang <= AngularTolerance;
    }

### 6.相反     ###

两个轴是否相反的判断：轴的夹角为180度。

inline Standard_Boolean gp_Ax1::IsOpposite(const gp_Ax1& Other, const Standard_Real AngularTolerance) const
    { 
        return vdir.IsOpposite(Other.vdir, AngularTolerance); 
    }

inline Standard_Boolean gp_Dir::IsOpposite(const gp_Dir& Other,const Standard_Real AngularTolerance) const
    { 
        return M_PI - Angle (Other) <= AngularTolerance; 
    }