OpenCasCade拓扑变换（使用gp_trsf）（转）
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
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
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)。
(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
网络文档资料
————————————————
版权声明：本文为CSDN博主「小哈龙」的原创文章，遵循CC 4.0 BY-SA版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/qq_22642239/article/details/102608607
