OpenCascade Law Function

Posted 2020-10-28 OPEN CASCADE

在OpenCASCADE的TKGeomAlgo Toolkit中提供了一个Law Package，在Law包中有一个基类：Law_Function，字面上翻译为 规则函数。 本文主要对Law_Function的子类进行介绍，进一步理解OpenCASCADE中Law相关类的作用。

OpenCascade Law Function

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1.Introduction

在OpenCASCADE的TKGeomAlgo Toolkit中提供了一个Law Package，在Law包中有一个基类：Law_Function，字面上翻译为 规则函数。其类图如下所示：

Figure 1. Law Function class diagram

本文主要对Law_Function的子类进行介绍，进一步理解OpenCASCADE中Law相关类的作用。

2.Law Functions

根据Law_Function可知，Law_Function的子类有常量规则Law_Constant、线性规则Law_Linear、组合规则Law_Composite及B样条规则Law_BSpFunc。抽象类Law_Function的纯虚函数有：

l Continuity()： 规则函数的连续性；

l Value()：计算对应参数X的函数值Y；

l D1()：计算规则函数在参数X处的一阶导数；

l D2()：计算规则函数在参数X处的二阶导数；

l Bounds()：规则函数的定义区间；

从上面的虚函数可以看出类Law_Function是一个一元变量的函数，与类math_Function的功能类似。

3.Test Code

下面的代码将规则函数Law_Function的几个子类通过生成Draw脚本，在Draw Test Harness中进行可视化，直观地显示出了几个规则函数，便于理解。

/*
Copyright(C) 2018 Shing Liu([e-mail])

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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;
}

程序会在d:/tcl中生成一个law.tcl文件，将此文件加载到Draw 中即可显示出规则函数对应的曲线，如下图所示：

Figure 2. Visualization Law Function Curves

由图可知，常量规则函数在定义区间内是一条直线；线性规则函数是一条直线；S型函数是S型的B样条曲线；插值函数是根据指定点插值得到的B样条曲线。

4.Conclusion

在OpenCASCADE中经常可以看到一些与Law相关的类，本文介绍了TKGeomAlgo中的Law包，综上所述可知，Law就是一元函数，与math_Function的概念一致。

本文显示规则曲线的方式可供借鉴，提高开发效率。只需要生成一个文本文件，就可以将结果可视化，对于其他三维的也是一样。