Package gp in the OpenCASCADE

eryar@163.com China

一、简介 Introduction to Package gp

gp是几何处理程序包（Geometric Processor package），简称gp。包gp提供以下功能：

代数计算；如坐标计算、矩阵计算；
基本解析几何元素；如变换、点、矢量、线、面、轴、二次曲线和初等曲面；

这些实体同时在二维和三维空间中定义，且包中的类都是非持续的（non-persistent），即这些类的实例都是以值的方式处理而不是引用。当复制这种对象时，是对象本体。改变一个实例不会影响到其他的实例。

可用的几何实体如下所示：

2D&3D Cartesian coordinates(x,y,z); 二维&三维笛卡尔坐标；
Matrices; 矩阵；
Cartesian points; 笛卡尔坐标点；
Vector; 矢量；
Direction; 方向；
Axis; 轴；
Line; 直线；
Circle; 圆；
Ellipse; 椭圆；
Hyperbola; 双曲线；
Parabola; 抛物线；
Plane; 面；
Infinite cylindrical surface; 柱面；
Spherical surface; 球面；
Toroidal surface; 环面；
Conical surface; 锥面；

二、几何元素的集合 Collections of Primitive Geometric Types

创建几何对象之前，根据你是将几何对象用于二维还是三维来确定。若你需要一个几何对象集而不是单一的几何对象，即用来处理一类几何元素，包TColgp就是提供这种功能的。

Package TColgp提供类如：XY, XYZ, Pnt, Pnt2d, Vec, Vec2d, Lin, Lin2D, Circ, Circ2d的TCollection的实例。包中的类简单列举如下：

TColgp_Array1OfCirc;
TColgp_Array1OfDir;
TColgp_Array1OfPnt;
TColgp_Array1OfVec;
TColgp_Array2OfCirc2d;
TColgp_Array2OfPnt;
TColgp_HArray1OfCirc2d;
TColgp_HArray2OfDir;
TColgp_HSequenceOfDir;
TColgp_SequenceOfDir;
TColgp_SequenceOfPnt;
TColgp_SequenceOfXYZ;

个人意见，若使用标准C++的容器类(The STL Template Container)，就不需要创建这么多类了。

三、基本几何库 Basic Geometric Libraries

有几个库提供了曲线和曲面的基本计算功能。若要处理由包gp创建的几何对象，初等曲线曲面的有用算法库在包：ElCLib和ElSLib中。包Precision提供两个数字比较的功能。

Package ElCLib; ElCLib代表：Elementary Curves Library. 提供初等曲线曲面的基本几何计算功能；
Package ElSLib; ElSLib代表：Elementary Surfaces Library. 提供初等曲面的基本几何计算。
Package Bnd；提供二维和三维空间中几何元素包围盒的计算功能；
Package Precision; 由于浮点数在计算机内实际上是一个近似表示，在手工计算看来为正确的结果，在计算机中运算未必得出正确的结果。所以，我们得到一个重要的经验：使用浮点数进行相等（==）和不等（！=）比较的操作通常是有问题的。浮点数的相等比较，一般总是使用两者相减的值是否落在0的邻域中来判断。这就是邻域比较技术。在OpenCASCADE中专门提供包Precision来处理两个数值的比较问题。

四、代码示例 Code Sample

//------------------------------------------------------------------------------

//    Copyright (c) 2012 eryar All Rights Reserved.

//

//        File    : Main.cpp

//        Author  : eryar@163.com

//        Date    : 2012-6-23 21:30

//        Version : 1.0v

//

//    Description : Test primitive Geometric Types in OpenCASCADE.

//

//      The Geometric Processor package, called gp.

//

//      The pg package offers classes for both 2D and 3D objects which

//      are handled by value rather than by reference. When this sort of object

//      is copied, it is copied entirely. Changes in one instance will not be

//      reflected in another.

//

//==============================================================================

// Use Toolkit TKernel.

#pragma comment(lib,"TKernel.lib")

// Use Toolkit TKMath.

#pragma comment(lib, "TKMath.lib")

#include <gp.hxx>

#include <gp_Pnt.hxx>

#include <gp_Trsf.hxx>

#include <Precision.hxx>

void DumpPoint(const gp_Pnt& p);

int main(int argc, char* argv[])

    gp_Pnt  aPoint(0, 0, 0);

    // 1. Translate a point in a direction.

    // The direction determined by a gp_Vec or two gp_Pnt.

    cout<<"Before translated:";

    DumpPoint(aPoint);

    aPoint.Translate(gp_Pnt(2, 2, 3), gp_Pnt(10, 10, 0));

    cout<<"After translated:";

    DumpPoint(aPoint);

    // 2. Rotate a point.

    // Rotate a point by an axis and the rotate angle.

    cout<<"Before rotated:";

    DumpPoint(aPoint);

    // Roate 45 degree about Z axis.

    // Positive angle value will be rotated counterclockwise.

    aPoint.Rotate(gp::OZ(), PI/4);

    cout<<"After rotated 45 degree about Z axis:";

    DumpPoint(aPoint);

    // 2.1 Test Package Precision.

    if (aPoint.X() < Precision::Confusion() && aPoint.X() > -Precision::Confusion())

        cout<<"Point X value:"<<aPoint.X()<<endl;

        cout<<"Precision::Confusion() value:"<<Precision::Confusion()<<endl;

    aPoint.Rotate(gp::OZ(), PI/4);

    cout<<"After rotate 45 degree about Z axis:";

    DumpPoint(aPoint);

    // 3. Transform a point by gp_Trsf.

    gp_Trsf transform;

    transform.SetMirror(gp::OX());

    cout<<"Before gp_Trsf:";

    DumpPoint(aPoint);

    aPoint.Transform(transform);

    cout<<"After gp_Trsf:";

    DumpPoint(aPoint);

    // 4. Mirror a point.

    // 4.1 Performs the symmetrical transformation of

    // a point with respect to an axis placement which

    // is the axis of the symmetry.

    cout<<"Before mirrored with a symmetric axis:";

    DumpPoint(aPoint);

    aPoint.Mirror(gp::OY());

    cout<<"After mirrored with a symmetric axis:";

    DumpPoint(aPoint);

    // 4.2 Performs the symmetrical transformation of

    // a point with respect to a plane.

    cout<<"Before mirrored with a symmetric plane:";

    DumpPoint(aPoint);

    aPoint.Mirror(gp::XOY());

    cout<<"After mirrored with a symmetric plane";

    DumpPoint(aPoint);

    // 5. Scale a point.

    aPoint.SetCoord(1, 2, 1);

    cout<<"Before Scaled:";

    DumpPoint(aPoint);

/*

    // Scale point source code...

    inline void gp_Pnt::Scale (const gp_Pnt& P,

    const Standard_Real S)

    gp_XYZ XYZ = P.coord;

    XYZ.Multiply (1.0 - S);

    coord.Multiply (S);

    coord.Add      (XYZ);

*/

    aPoint.Scale(gp_Pnt(1, 2, 2), 2);

    cout<<"After Scaled:";

    DumpPoint(aPoint);

    return 0;

/**

* Description: Dump point information.

*/

void DumpPoint( const gp_Pnt& p )

    cout<<"("<<p.X()<<","<<p.Y()<<","<<p.Z()<<")"<<endl;

输出结果如下：

   1:  Before translated:(0,0,0)

   2:  After translated:(8,8,-3)

   3:  Before rotated:(8,8,-3)

   4:  After rotated 45 degree about Z axis:(8.88178e-016,11.3137,-3)

   5:  Point X value:8.88178e-016

   6:  Precision::Confusion() value:1e-007

   7:  After rotate 45 degree about Z axis:(-8,8,-3)

   8:  Before gp_Trsf:(-8,8,-3)

   9:  After gp_Trsf:(-8,-8,3)

  10:  Before mirrored with a symmetric axis:(-8,-8,3)

  11:  After mirrored with a symmetric axis:(8,-8,-3)

  12:  Before mirrored with a symmetric plane:(8,-8,-3)

  13:  After mirrored with a symmetric plane(8,-8,3)

  14:  Before Scaled:(1,2,1)

  15:  After Scaled:(1,2,0)

  16:  Press any key to continue . . .

五、结论

包gp提供了基本的几何元素表示及初等解析几何计算功能。对于几何元素的集合也有自己的类库。对于两个数值的比较采用了邻域比较技术。