OpenCasCade拓扑变换（使用gp_trsf）

「爱情、让人受尽委屈。」 2023-06-08 06:48 22阅读 0赞

# **一.废话** #

**在OCC中如果要实现一个拓扑（TopoDS\_Shape）的变换（平移，（点，轴，面）镜像，旋转，缩放，移位，形状），那么gp\_trsf，gp\_GTrsf是一个很好的媒介。深入理解其中的含义，可以组合起来使用，实现复杂的拓扑变换功能，要想熟练使用，必须在实践中体会**

**在此使用到的几何知识可以参考：**[几何变换之仿射变换][Link 1]

在OpenCaseCade6.8.0源代码中有介绍：

**gp\_trsf（平移，（点，轴，面）镜像，旋转，缩放，移位）**

//! Geometric transformation on a shape.  
//! The transformation to be applied is defined as a  
//! gp\_Trsf transformation, i.e. a transformation which does  
//! not modify the underlying geometry of shapes.  
//! The transformation is applied to:  
//! - all curves which support edges of a shape, and  
//! - all surfaces which support its faces.  
//! A Transform object provides a framework for:  
//! - defining the geometric transformation to be applied,  
//! - implementing the transformation algorithm, and  
//! - consulting the results.

谷歌翻译：

在3D空间中定义非持久变换。 实现了以下转换：。 平移，旋转，缩放。 关于点，线，平面的对称性。 复杂的转换可以通过使用矩阵“乘”方法组合先前的基本转换来获得。 转换可以表示如下：  
//！ V1 V2 V3 T XYZ XYZ  
//！ | a11 a12 a13 a14 | | x | | x'|  
//！ | a21 a22 a23 a24 | | y | | y'|  
//！ | a31 a32 a33 a34 | | z | = | z'|  
//！ | 0 0 0 1 | | 1 | | 1 |  
//！ 其中\{V1，V2，V3\}定义转换的矢量部分，T定义转换的平移部分。 这种转换永远不会改变对象的性质。

**gp\_GTrsf（形状变换）**

//! Defines a non-persistent transformation in 3D space.  
//! This transformation is a general transformation.  
//! It can be a Trsf from gp, an affinity, or you can define  
//! your own transformation giving the matrix of transformation.  
//!  
//! With a Gtrsf you can transform only a triplet of coordinates  
//! XYZ. It is not possible to transform other geometric objects  
//! because these transformations can change the nature of non-  
//! elementary geometric objects.  
//! The transformation GTrsf can be represented as follow :  
//!  
//! V1 V2 V3 T XYZ XYZ  
//! | a11 a12 a13 a14 | | x | | x'|  
//! | a21 a22 a23 a24 | | y | | y'|  
//! | a31 a32 a33 a34 | | z | = | z'|  
//! | 0 0 0 1 | | 1 | | 1 |  
//!  
//! where \{V1, V2, V3\} define the vectorial part of the  
//! transformation and T defines the translation part of the  
//! transformation.  
//! Warning  
//! A GTrsf transformation is only applicable to  
//! coordinates. Be careful if you apply such a  
//! transformation to all points of a geometric object, as  
//! this can change the nature of the object and thus  
//! render it incoherent!  
//! Typically, a circle is transformed into an ellipse by an  
//! affinity transformation. To avoid modifying the nature of  
//! an object, use a gp\_Trsf transformation instead, as  
//! objects of this class respect the nature of geometric objects.

谷歌翻译：

在3D空间中定义非持久变换。此转换是一般转换。它可以是来自gp的Trsf，相似性，也可以定义自己的转换以提供转换矩阵。使用Gtrsf，您只能变换坐标XYZ的三元组。无法变换其他几何对象，因为这些变换可以改变非基本几何对象的性质。转换GTrsf可以表示为：  
//！ V1 V2 V3 T XYZ XYZ  
//！ | a11 a12 a13 a14 | | x | | x'|  
//！ | a21 a22 a23 a24 | | y | | y'|  
//！ | a31 a32 a33 a34 | | z | = | z'|  
//！ | 0 0 0 1 | | 1 | | 1 |  
//！  
其中\{V1，V2，V3\}定义转换的矢量部分，T定义转换的平移部分。  
警告  
GTrsf转换仅适用于坐标。如果将这样的变换应用于几何对象的所有点，请小心，因为这会改变对象的性质，从而使其变得不连贯！  
通常，通过亲和力转换将圆转换为椭圆。为避免修改对象的性质，请改用gp\_Trsf转换，因为此类的对象尊重几何对象的性质。

**下面介绍参考自网络资料，稍有改动，Occ6.8.0版，其它版本可能会有稍许变动。**

# **二.拓扑变换的基本描述** #

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## **1.BRepBuilderAPI\_Transform** ##

**（类，Occ标准头文件BRepBuilderAPI\_Transform.hxx）**

### **(1)** 功能说明：拓扑变换 ###

此对象与gp\_Trsf相关联进行变换

### **(2)** 构造函数： ###

BRepBuilderAPI_Transform(const gp_Trsf& T);
    
    BRepBuilderAPI_Transform(const TopoDS_Shape& S, const gp_Trsf& T, const Standard_Boolean Copy = Standard_False);

### **(3)** 参数说明： ###

T：要进行的变换

S：进行变换的拓扑图形

Copy：是否用副本进行变换

### **(4)** 备注： ###

Perform是该对象的一个方法。

BRepBuilderAPI_Transform(gp_Trsf T) 与public void Perform(TopoDS_Shape S, bool Copy)
    相等于
    BRepBuilderAPI_Transform(TopoDS_Shape S, gp_Trsf T, bool Copy)。

### **(5)** 实例： ###

**例1：点对称**

OCC源码：

Makes the transformation into a symmetrical transformation.
      //! P is the center of the symmetry.
          void SetMirror (const gp_Pnt& P) ;

使用示例：

TopoDS_Shape S;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Pnt PntCenterOfTheTransformation = new gp_Pnt(110, 60, 60);
    
    theTransformation.SetMirror(PntCenterOfTheTransformation);//点对称镜像
    
    BRepBuilderAPI_Transform myBRepTransformation =new BRepBuilderAPI_Transform(S,theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape();  //获得通过镜像转换后的新的拓扑

**例2：轴对称**

OCC源码：

//! Makes the transformation into a symmetrical transformation.
    //! A1 is the center of the axial symmetry.
    Standard_EXPORT   void SetMirror (const gp_Ax1& A1) ;

使用实例：

TopoDS_Shape S ;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Ax1 axe = new gp_Ax1(new gp_Pnt(110, 60, 60), new gp_Dir(0.0, 1.0, 0.0));                   
    
    theTransformation.SetMirror(axe);//镜像
    
    BRepBuilderAPI_Transform myBRepTransformation =
    
    new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape(); //获取通过轴对称转换的新的拓扑

**例3：面对称**

OCC源代码：

//! Makes the transformation into a symmetrical transformation.
    //! A2 is the center of the planar symmetry
    //! and defines the plane of symmetry by its origin, "X
    //! Direction" and "Y Direction".
    Standard_EXPORT   void SetMirror (const gp_Ax2& A2) ;

使用示例：

TopoDS_Shape S = new BRepPrimAPI_MakeWedge(60.0, 100.0, 80.0, 20.0).Shape();        
    
    gp_Trsf theTransformation = new OCgp_Trsf();
    
    gp_Ax2 axe2 = new gp_Ax2(new gp_Pnt(0, 0, 0), new gp_Dir(1, 0, 0));
    
    theTransformation.SetMirror(axe2);//镜像
    
    BRepBuilderAPI_Transform myBRepTransformation =
    
    new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape();  //获取通过面对称转换的新的拓扑

**关于面对称，需要说明一下：**

gp\_Ax1（3D空间中的一个轴）

gp\_Ax2（右手坐标系）

gp\_Ax3（左手坐标系）

此示例中使用的是gp\_Ax2右手坐标系，面对称会以该定义的坐标系中x轴y轴所构成的面作为对称的面来转换。

**例4：旋转变换**

OCC源代码：

//! Changes the transformation into a rotation.
     //! A1 is the rotation axis and Ang is the angular value of the
     //! rotation in radians.
     Standard_EXPORT   void SetRotation (const gp_Ax1& A1, const Standard_Real Ang) ;
      
    
     //! Changes the transformation into a rotation defined by quaternion.
     //! Note that rotation is performed around origin, i.e.
     //! no translation is involved.
     Standard_EXPORT   void SetRotation (const gp_Quaternion& R) ;

使用示例：

TopoDS_Shape S;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Ax1 axe = new gp_Ax1(new gp_Pnt(200, 60, 60), new gp_Dir(0.0, 1.0, 0.0));//指定旋转轴         
    
    theTransformation.SetRotation(axe, 30 * System.Math.PI / 180); //旋转角度（单位：弧度）
    
    BRepBuilderAPI_Transform myBRepTransformation =
    
    new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape();//获取旋转转换的新的拓扑

**例5：缩放变换**

OCC源代码：

//! Changes the transformation into a scale.
    //! P is the center of the scale and S is the scaling value.
    //! Raises ConstructionError  If <S> is null.
    Standard_EXPORT   void SetScale (const gp_Pnt& P, const Standard_Real S) ;

使用示例：

TopoDS_Shape S;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Pnt theCenterOfScale = new gp_Pnt(100, 60, 60);  //旋转基本点
     
    theTransformation.SetScale(theCenterOfScale, 0.3);  //缩放比例
    
    BRepBuilderAPI_Transform myBRepTransformation =new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape();//获取缩放转换后的新的拓扑

**例6：平移变换**

OCC源代码：

//! Changes the transformation into a translation.
    //! V is the vector of the translation.
        void SetTranslation (const gp_Vec& V) ;
      
    //! Makes the transformation into a translation where the translation vector
    //! is the vector (P1, P2) defined from point P1 to point P2.
        void SetTranslation (const gp_Pnt& P1, const gp_Pnt& P2) ;

使用示例：

TopoDS_Shape S;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Vec theVectorOfTranslation = new gp_Vec(-6, -6, 6);  //此处平移向量是带有长度与方向的
    
    theTransformation.SetTranslation(theVectorOfTranslation);
    
    BRepBuilderAPI_Transform myBRepTransformation =
    
    new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape();

**例7：移位（Displacement）变换**

OCC源代码：

//! Modifies this transformation so that it transforms the
     //! coordinate system defined by FromSystem1 into the
     //! one defined by ToSystem2. After this modification, this
     //! transformation transforms:
     //! -   the origin of FromSystem1 into the origin of ToSystem2,
     //! -   the "X Direction" of FromSystem1 into the "X
     //! Direction" of ToSystem2,
     //! -   the "Y Direction" of FromSystem1 into the "Y
     //! Direction" of ToSystem2, and
     //! -   the "main Direction" of FromSystem1 into the "main
     //! Direction" of ToSystem2.
     //! Warning
     //! When you know the coordinates of a point in one
     //! coordinate system and you want to express these
     //! coordinates in another one, do not use the
     //! transformation resulting from this function. Use the
     //! transformation that results from SetTransformation instead.
     //! SetDisplacement and SetTransformation create
     //! related transformations: the vectorial part of one is the
     //! inverse of the vectorial part of the other.
     Standard_EXPORT   void SetDisplacement (const gp_Ax3& FromSystem1, const gp_Ax3& ToSystem2) ;

使用示例：

TopoDS_Shape S;
    
    gp_Trsf theTransformation = new gp_Trsf();
    
    gp_Ax3 ax3_1 = new gp_Ax3(new OCgp_Pnt(0, 0, 0), new gp_Dir(0, 0, 1));  //左手坐标系
    
    gp_Ax3 ax3_2 = new OCgp_Ax3(new gp_Pnt(60, 60, 60), new gp_Dir(1, 1, 1));
    
    theTransformation.SetDisplacement(ax3_1, ax3_2);
    
    BRepBuilderAPI_Transform myBRepTransformation =new BRepBuilderAPI_Transform(S, theTransformation, false);
    
    TopoDS_Shape TransformedShape = myBRepTransformation.Shape();

## **例8：组合变换** ##

**功能：可以将上述多个变换组合在一起，组合方式即：每一个gp\_Trsf对象相乘即可（OCC提供对应方法与重载的\*运算符）**

**OCC源码：**

gp_Trsf Multiplied (const gp_Trsf& T)  const;   //两个变换gp_Trsf相乘的函数
    
    
    gp_Trsf operator * (const gp_Trsf& T)  const     //重载的*运算符，可以直接使用两个对象相乘
    {
      return Multiplied(T);
    }
      
    
      //! Computes the transformation composed with <me> and T.
      //! <me> = <me> * T
    Standard_EXPORT   void Multiply (const gp_Trsf& T) ;  //如注释<me> = <me> * T
    
    void operator *= (const gp_Trsf& T)                   //重载的*=  运算符
    {
      Multiply(T);
    }

**使用示例：**

假如要实现旋转加平移，直接将旋转的**gp\_Trsf**对象与平移的**gp\_Trsf** 对象相乘即可其它操作类似，虽然是相乘但是实际是OCC内部对转换矩阵平移部分与旋转部分做了矩阵运算，构成了一个新的变换矩阵，将旋转部分与平移部分结合到了一起，详细矩阵变化请查阅文章开头仿射变换 文章介绍的各种图形变换的转换矩阵规则与运算。

## **2.BRepBuilderAPI\_GTransform** ##

（类，Occ标准头文件BRepBuilderAPI\_GTransform.hxx）

### **(1)** 功能说明：拓扑变换 ###

此对象与gp\_GTrsf相关联进行变换

### **(2)** 构造函数： ###

//! Constructs a framework for applying the geometric
    //! transformation T to a shape. Use the function
    //! Perform to define the shape to transform.
    Standard_EXPORT BRepBuilderAPI_GTransform(const gp_GTrsf& T);
      
    //! Constructs a framework for applying the geometric
    //! transformation T to a shape, and applies it to the shape S.
    //! -   If the transformation T is direct and isometric (i.e. if
    //! the determinant of the vectorial part of T is equal to
    //! 1.), and if Copy equals false (default value), the
    //! resulting shape is the same as the original but with
    //! a new location assigned to it.
    //! -   In all other cases, the transformation is applied to
    //! a duplicate of S.
    //! Use the function Shape to access the result.
    //! Note: the constructed framework can be reused to
    //! apply the same geometric transformation to other
    //! shapes: just specify them with the function Perform.
    Standard_EXPORT BRepBuilderAPI_GTransform(const TopoDS_Shape& S, const gp_GTrsf& T, const Standard_Boolean Copy = Standard_False);

### **(3)** 参数说明： ###

T：要进行的变换

S：进行变换的拓扑图形

Copy：是否用副本进行变换

### **(4)** 实例： ###

**例1：变形（deform）变换**

OCC源代码：

//! Replaces the vectorial part of this transformation by Matrix.
        void SetVectorialPart (const gp_Mat& Matrix) ;
    
    
    //! Replaces the translation part of
    //! this transformation by the coordinates of the number triple Coord.
      Standard_EXPORT   void SetTranslationPart (const gp_XYZ& Coord) ;

使用示例：

TopoDS_Shape S;
    
    gp_GTrsf theTransformation = new gp_GTrsf();
    
    gp_Mat rot = new gp_Mat(1, 0, 0, 0, 0.5, 0, 0, 0, 1.5);  //描述一个三行三列的矩阵，用以替换转换的矢量部分
    
    theTransformation.SetVectorialPart(rot);
    
    theTransformation.SetTranslationPart(new gp_XYZ(5, 5, 5)); //使用一个给定的坐标系作为转换，即替换原图形的局部坐标系
    
    BRepBuilderAPI_GTransform myBRepTransformation =new BRepBuilderAPI_GTransform(S, theTransformation, false);
    
    TopoDS_Shape S2 = myBRepTransformation.Shape(); //改变形状以及位置后的拓扑

参考资料：

[http://www.cppblog.com/eryar/archive/2015/01/22/209612.html][http_www.cppblog.com_eryar_archive_2015_01_22_209612.html]

网络文档资料

[Link 1]: https://blog.csdn.net/qq_22642239/article/details/102612207
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzIyNjQyMjM5_size_16_color_FFFFFF_t_70]: /images/20230531/48af816860f3408598fdb6184fc57ebf.png
[http_www.cppblog.com_eryar_archive_2015_01_22_209612.html]: http://www.cppblog.com/eryar/archive/2015/01/22/209612.html