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。