OpenCasCade数学库 - 二维图形变换（gp_Trsf2d）

ゝ一世哀愁。 2021-12-10 05:19 446阅读 0赞

gp\_Trsf2d描述了三维空间中的图形变换。

V1    V2     T          XY         XY

![\\begin\{bmatrix\} a\_\{11\} & a\_\{12\} & a\_\{13\}\\\\ a\_\{121\} & a\_\{22\} &a\_\{23\} \\\\ 0 &0 & 1 \\end\{bmatrix\} \\cdot \\begin\{bmatrix\} x\\\\ y\\\\ 1 \\end\{bmatrix\} = \\begin\{bmatrix\} x^\{'\}\\\\ y^\{'\}\\\\ 1 \\end\{bmatrix\}][begin_bmatrix_ a_11_ _ a_12_ _ a_13_ a_121_ _ a_22_ _a_23_ _ 0 _0 _ 1 _end_bmatrix_ _cdot _begin_bmatrix_ x_ y_ 1 _end_bmatrix_ _ _begin_bmatrix_ x_ y_ 1 _end_bmatrix]

\{V1, V2\}定义了图形变换中的向量变换，T定义了图形变换中的平移变换。

gp\_Trsf2d的定义：

class gp_Trsf
    {
    public:
        ...
    private:
      Standard_Real scale;
      gp_TrsfForm shape;     //图形变换类型
      gp_Mat2d matrix;
      gp_XY loc;
    };

默认构造函数。

inline gp_Trsf2d::gp_Trsf2d () {
      shape = gp_Identity;
      scale = 1.0;
      matrix.SetIdentity ();
      loc.SetCoord (0.0, 0.0);
    }

关于点对称

inline void gp_Trsf2d::SetMirror(const gp_Pnt2d& P)
    {   
      shape = gp_PntMirror;
      scale = -1.0;
      matrix.SetIdentity ();
      loc = P.XY();
      loc.Multiply (2.0);
    }

关于轴对称

void gp_Trsf2d::SetMirror (const gp_Ax2d& A)
    {
      shape = gp_Ax1Mirror;
      scale = - 1.0;
      const gp_Dir2d& V = A.Direction ();
      const gp_Pnt2d& P = A.Location ();
      Standard_Real VX = V.X();
      Standard_Real VY = V.Y();
      Standard_Real X0 = P.X();
      Standard_Real Y0 = P.Y();
      matrix.SetCol (1, gp_XY (1.0 - 2.0 * VX * VX, -2.0 * VX * VY));
      matrix.SetCol (2, gp_XY (-2.0 * VX * VY, 1.0 - 2.0 * VY * VY));
    
      loc.SetCoord  (-2.0 * ((VX * VX - 1.0) * X0 + (VX * VY * Y0)),
                     -2.0 * ((VX * VY * X0) + (VY * VY - 1.0) * Y0));
    }

旋转，P是旋转中心，Ang是旋转角度。

inline void gp_Trsf2d::SetRotation (const gp_Pnt2d& P,const Standard_Real Ang)
    {
      shape = gp_Rotation;
      scale = 1.0;
      loc = P.XY ();
      loc.Reverse ();
      matrix.SetRotation (Ang);
      loc.Multiply (matrix);
      loc.Add (P.XY());
    }

缩放，P是缩放中心，S是缩放比例。

inline void gp_Trsf2d::SetScale (const gp_Pnt2d& P, const Standard_Real S)
    {
      shape = gp_Scale;
      scale = S;
      matrix.SetIdentity ();
      loc = P.XY ();
      loc.Multiply (1.0 - S);
    }

[begin_bmatrix_ a_11_ _ a_12_ _ a_13_ a_121_ _ a_22_ _a_23_ _ 0 _0 _ 1 _end_bmatrix_ _cdot _begin_bmatrix_ x_ y_ 1 _end_bmatrix_ _ _begin_bmatrix_ x_ y_ 1 _end_bmatrix]: https://private.codecogs.com/gif.latex?%5Cbegin%7Bbmatrix%7D%20a_%7B11%7D%20%26%20a_%7B12%7D%20%26%20a_%7B13%7D%5C%5C%20a_%7B121%7D%20%26%20a_%7B22%7D%20%26a_%7B23%7D%20%5C%5C%200%20%260%20%26%201%20%5Cend%7Bbmatrix%7D%20%5Ccdot%20%5Cbegin%7Bbmatrix%7D%20x%5C%5C%20y%5C%5C%201%20%5Cend%7Bbmatrix%7D%20%3D%20%5Cbegin%7Bbmatrix%7D%20x%5E%7B%27%7D%5C%5C%20y%5E%7B%27%7D%5C%5C%201%20%5Cend%7Bbmatrix%7D