Package gp in the OpenCASCADE

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：

1. 2D&3D Cartesian coordinates(x,y,z); 二维&三维笛卡尔坐标； 
2. Matrices; 矩阵； 
3. Cartesian points; 笛卡尔坐标点； 
4. Vector; 矢量； 
5. Direction; 方向； 
6. Axis; 轴； 
7. Line; 直线； 
8. Circle; 圆； 
9. Ellipse; 椭圆； 
10. Hyperbola; 双曲线； 
11. Parabola; 抛物线； 
12. Plane; 面； 
13. Infinite cylindrical surface; 柱面； 
14. Spherical surface; 球面； 
15. Toroidal surface; 环面； 
16. 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：

Before translated:(0,0,0)
After translated:(8,8,-3)
Before rotated:(8,8,-3)
After rotated 45 degree about Z axis:(8.88178e-016,11.3137,-3)
Point X value:8.88178e-016
Precision::Confusion() value:1e-007
After rotate 45 degree about Z axis:(-8,8,-3)
Before gp_Trsf:(-8,8,-3)
After gp_Trsf:(-8,-8,3)
Before mirrored with a symmetric axis:(-8,-8,3)
After mirrored with a symmetric axis:(8,-8,-3)
Before mirrored with a symmetric plane:(8,-8,-3)
After mirrored with a symmetric plane(8,-8,3)
Before Scaled:(1,2,1)
After Scaled:(1,2,0)
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。