OpenCascade Law Function
eryar@163.com
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(eryar@163.com)
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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。
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