OpenCascade Law Function
eryar@163.com
1.Introduction
在OpenCASCADE的TKGeomAlgo Toolkit中提供了一個Law Package，在Law包中有一個基類：Law_Function，字面上翻譯為 規則函數。其類圖如下所示：
Figure 1. Law Function class diagram
本文主要對Law_Function的子類進行介紹，進一步理解OpenCASCADE中Law相關類的作用。
2.Law Functions
根據Law_Function可知，Law_Function的子類有常量規則Law_Constant、線性規則Law_Linear、組合規則Law_Composite及B樣條規則Law_BSpFunc。抽象類Law_Function的純虛函數有：
l Continuity()： 規則函數的連續性；
l Value()：計算對應參數X的函數值Y；
l D1()：計算規則函數在參數X處的一階導數；
l D2()：計算規則函數在參數X處的二階導數；
l Bounds()：規則函數的定義區間；
從上面的虛函數可以看出類Law_Function是一個一元變量的函數，與類math_Function的功能類似。
3.Test Code
下面的代碼將規則函數Law_Function的幾個子類通過生成Draw腳本，在Draw Test Harness中進行可視化，直觀地顯示出了幾個規則函數，便于理解。
/*
Copyright(C) 2018 Shing Liu(eryar@163.com)
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files(the "Software"), to deal
in the Software without restriction, including without limitation the rights
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The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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*/
#include <TColgp_Array1OfPnt2d.hxx>
#include <Law_Constant.hxx>
#include <Law_Linear.hxx>
#include <Law_BSpFunc.hxx>
#include <Law_S.hxx>
#include <Law_Interpol.hxx>
#pragma comment(lib, "TKernel.lib")
#pragma comment(lib, "TKMath.lib")
#pragma comment(lib, "TKG2d.lib")
#pragma comment(lib, "TKG3d.lib")
#pragma comment(lib, "TKGeomBase.lib")
#pragma comment(lib, "TKGeomAlgo.lib")
Standard_Integer aId = 0;
void draw(const Handle(Law_Function)& theLaw, std::ostream& theOutput)
{
const Standard_Integer aStep = 20;
Standard_Real aFirst = 0.0;
Standard_Real aLast = 0.0;
Standard_Real aDelta = 0.0;
Standard_Real aX = 0.0;
Standard_Real aY = 0.0;
theLaw->Bounds(aFirst, aLast);
aDelta = (aLast - aFirst) / aStep;
theOutput << "polyline law" << ++aId;
for (Standard_Integer i = 0; i <= aStep; ++i)
{
aX = aFirst + i * aDelta;
aY = theLaw->Value(aX);
theOutput << " " << aX << " " << aY << " 0.0";
}
theOutput << "\n vdisplay law" << aId << std::endl;
theOutput << "vaspects law" << aId << " -setColor " << ((aId % 2) ? " red " : " yellow ") << std::endl;
}
void test(std::ostream& theOutput)
{
// 1. Constant law.
Handle(Law_Constant) aConstantLaw = new Law_Constant();
aConstantLaw->Set(2.0, 0.0, 1.0);
draw(aConstantLaw, theOutput);
// 2. Linear evolution law.
Handle(Law_Linear) aLinearLaw = new Law_Linear();
aLinearLaw->Set(1.0, 2.0, 3.0, 5.0);
draw(aLinearLaw, theOutput);
// 3. An "S" evolution law.
Handle(Law_S) aSLaw = new Law_S();
aSLaw->Set(3.0, 5.0, 6.0, 8.0);
draw(aSLaw, theOutput);
// 4. Provides an evolution law that interpolates a set of parameter and value pairs (wi, radi)
TColgp_Array1OfPnt2d aPoints(1, 4);
aPoints.SetValue(1, gp_Pnt2d(6.0, 8.0));
aPoints.SetValue(2, gp_Pnt2d(7.0, 5.0));
aPoints.SetValue(3, gp_Pnt2d(8.0, 9.0));
aPoints.SetValue(4, gp_Pnt2d(9.0, 2.0));
Handle(Law_Interpol) anInterpolativeLaw = new Law_Interpol();
anInterpolativeLaw->Set(aPoints);
draw(anInterpolativeLaw, theOutput);
}
int main(int argc, char* argv[])
{
std::ofstream aTclFile("d:/tcl/law.tcl");
test(aTclFile);
return 0;
}
程序會在d:/tcl中生成一個law.tcl文件，將此文件加載到Draw 中即可顯示出規則函數對應的曲線，如下圖所示：
Figure 2. Visualization Law Function Curves
由圖可知，常量規則函數在定義區間內是一條直線；線性規則函數是一條直線；S型函數是S型的B樣條曲線；插值函數是根據指定點插值得到的B樣條曲線。
4.Conclusion
在OpenCASCADE中經常可以看到一些與Law相關的類，本文介紹了TKGeomAlgo中的Law包，綜上所述可知，Law就是一元函數，與math_Function的概念一致。
本文顯示規則曲線的方式可供借鑒，提高開發效率。只需要生成一個文本文件，就可以將結果可視化，對于其他三維的也是一樣。
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