Package gp in the OpenCASCADE
eryar@163.com China
一、簡介 Introduction to Package gp
gp是幾何處理程序包（Geometric Processor package），簡稱gp。包gp提供以下功能：
- 代數計算；如坐標計算、矩陣計算；
- 基本解析幾何元素；如變換、點、矢量、線、面、軸、二次曲線和初等曲面；
這些實體同時在二維和三維空間中定義，且包中的類都是非持續的（non-persistent），即這些類的實例都是以值的方式處理而不是引用。當復制這種對象時，是對象本體。改變一個實例不會影響到其他的實例。
可用的幾何實體如下所示：
- 2D&3D Cartesian coordinates(x,y,z); 二維&三維笛卡爾坐標；
- Matrices; 矩陣；
- Cartesian points; 笛卡爾坐標點；
- Vector; 矢量；
- Direction; 方向；
- Axis; 軸；
- Line; 直線；
- Circle; 圓；
- Ellipse; 橢圓；
- Hyperbola; 雙曲線；
- Parabola; 拋物線；
- Plane; 面；
- Infinite cylindrical surface; 柱面；
- Spherical surface; 球面；
- Toroidal surface; 環面；
- Conical surface; 錐面；
二、幾何元素的集合 Collections of Primitive Geometric Types
創建幾何對象之前，根據你是將幾何對象用于二維還是三維來確定。若你需要一個幾何對象集而不是單一的幾何對象，即用來處理一類幾何元素，包TColgp就是提供這種功能的。
Package TColgp提供類如：XY, XYZ, Pnt, Pnt2d, Vec, Vec2d, Lin, Lin2D, Circ, Circ2d的TCollection的實例。包中的類簡單列舉如下：
- TColgp_Array1OfCirc;
- TColgp_Array1OfDir;
- TColgp_Array1OfPnt;
- TColgp_Array1OfVec;
- TColgp_Array2OfCirc2d;
- TColgp_Array2OfPnt;
- TColgp_HArray1OfCirc2d;
- TColgp_HArray2OfDir;
- TColgp_HSequenceOfDir;
- TColgp_SequenceOfDir;
- TColgp_SequenceOfPnt;
- TColgp_SequenceOfXYZ;
個人意見，若使用標準C++的容器類(The STL Template Container)，就不需要創建這么多類了。
三、基本幾何庫 Basic Geometric Libraries
有幾個庫提供了曲線和曲面的基本計算功能。若要處理由包gp創建的幾何對象，初等曲線曲面的有用算法庫在包：ElCLib和ElSLib中。包Precision提供兩個數字比較的功能。
- Package ElCLib; ElCLib代表：Elementary Curves Library. 提供初等曲線曲面的基本幾何計算功能；
- Package ElSLib; ElSLib代表：Elementary Surfaces Library. 提供初等曲面的基本幾何計算。
- Package Bnd；提供二維和三維空間中幾何元素包圍盒的計算功能；
- Package Precision; 由于浮點數在計算機內實際上是一個近似表示，在手工計算看來為正確的結果，在計算機中運算未必得出正確的結果。所以，我們得到一個重要的經驗：使用浮點數進行相等（==）和不等（！=）比較的操作通常是有問題的。浮點數的相等比較，一般總是使用兩者相減的值是否落在0的鄰域中來判斷。這就是鄰域比較技術。在OpenCASCADE中專門提供包Precision來處理兩個數值的比較問題。
四、代碼示例 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;}
輸出結果如下：
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、結論
包gp提供了基本的幾何元素表示及初等解析幾何計算功能。對于幾何元素的集合也有自己的類庫。對于兩個數值的比較采用了鄰域比較技術。