C++ GeomGlut::segment方法代码示例

/*------------------------------------------------------------------*\
|*			Visualization functions	     	            *|
 \*------------------------------------------------------------------*/
void plotFunction(FunctionENUM function)
    {
    switch (function)
	{
    case FUNCTION1:
	for (double i = LEFT; i <= RIGHT; i += 0.001)
	    {
	    graphWin.plot(i, f1(i), 1);
	    }
	break;

    case FUNCTION2:
	for (double i = LEFT; i <= RIGHT; i += 0.0001)
	    {
	    graphWin.plot(i, f2(i), 1);
	    }
	break;
    case GOLD_FUNCTION:
	for (int i = 0; i < 19; i++)
	    {
	    graphWin.segment(map(i, 0, 19, 0, RIGHT), map(arrayGold[i], 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(arrayGold[i + 1], 250, 1700, 0, TOP));
	    }
	break;
    default:
	cout << "The given function does not exist";
	break;
	}
    }

void bolzanoBisectionRecursive(double a, double b, double epsilon)
{
    if(fabs(b-a) <= epsilon)
    {
#ifdef USING_FIRST_FUNCTION
        if (f(a) <= epsilon )
#else
            if (g(a) <= epsilon )
#endif
                cout << endl << ">>> " << b << " <<<<" << endl << endl;
        return;
    }
    double c = (a+b)/2;

    graphWin.segment(a,MAXHEIGHT,a,MINHEIGHT);
    graphWin.segment(b,MAXHEIGHT,b,MINHEIGHT);
    graphWin.segment(c,MAXHEIGHT,c,MINHEIGHT);

    cout << "Analysing interval [" << a <<", " << b << "] with middle point at : "<< c <<endl;
    if (c == 0)
    {
        cout << "0 is in " << c << endl;
    }
#ifdef USING_FIRST_FUNCTION
    if (oppositeSigns(f(a),f(c)))
#else
        if (oppositeSigns(g(a),g(c)))
#endif
        {
            cout << " Narrowing interval to [" << a <<", " << c << "]" << endl;
            bolzanoBisectionRecursive(a,c,epsilon);
        }

#ifdef USING_FIRST_FUNCTION
    if (oppositeSigns(f(c), f(b)))
#else
        if (oppositeSigns(g(c), g(b)))
#endif
        {
            cout << " Narrowing interval to [" << c <<", " << b << "]" << endl;
            bolzanoBisectionRecursive(c,b,epsilon);
        }
}

void fixedPoint(double epsilon, double lambda, double startingPoint,bool isFirst)
{
    double previousPoint = startingPoint;
    int loopCounter = 0;
    while (fabs(fixedPointAdapterFunction(previousPoint) - previousPoint) > epsilon && loopCounter < LOOP_LIMIT)
    {
        previousPoint=fixedPointAdapterFunction(previousPoint, lambda);
        if(numberLine == 2)
        {
            plotAdaptedFunction(lambda);//we plot it here to have the proper lamda drawn
            graphWin.segment(previousPoint, fixedPointAdapterFunction(previousPoint, lambda), fixedPointAdapterFunction(previousPoint, lambda), fixedPointAdapterFunction(previousPoint, lambda));
            graphWin.segment(previousPoint, previousPoint, previousPoint, fixedPointAdapterFunction(previousPoint, lambda));
        }
        loopCounter++;
    }

#ifdef USING_FIRST_FUNCTION
    if(f(previousPoint) <= epsilon)
#else
        if(g(previousPoint) <= epsilon)
#endif
        {
            graphWin.plot(previousPoint,fixedPointAdapterFunction(previousPoint, lambda),5);
            cout << "x = " << previousPoint << endl;
        }
        else
        {
            cout << "x MAUVAIS = " << previousPoint << endl;
        }

    double tester = 2.0;
    if(lambda > tester)
    {
        numberLine++;
        lambda -= tester;
        fixedPoint(epsilon, lambda,startingPoint);
    }
}

void plotSecondDegreeDerivatedFunction(FunctionENUM function, double h)
    {
    if (function != GOLD_FUNCTION)
	{
	for (double i = LEFT; i <= RIGHT; i += 0.001)
	    {
	    graphWin.plot(i, calculateSecondDegreeDerivative(function, i, h), 1);
	    }
	}
    else
	{
	for (double i = 0; i < 18; i += 1)
	    {
	    double secondDegreeDerivative = calculateSecondDegreeDerivative(function, i, h);
	    double secondDegreeDerivativePlusOne = calculateSecondDegreeDerivative(function, i + 1, h);
	    graphWin.segment(map(i, 0, 19, 0, RIGHT), map(secondDegreeDerivative, 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(secondDegreeDerivativePlusOne, 250, 1700, 0, TOP));
	    }
	}
    }

void plotDerivatedFunction(FunctionENUM function, DerivationMethodENUM derivationMethod, double h)
    {
    if (function != GOLD_FUNCTION)
	{
	for (double i = LEFT; i <= RIGHT; i += 0.001)
	    {
	    graphWin.plot(i, calculateDerivative(function, i, h, derivationMethod), 1);
	    }
	}
    else
	{
	double leftLimit = derivationMethod == CENTRAL_DIFFERENCE ? 1 : 0;

	for (double i = leftLimit; i < 18; i += 1)
	    {
	    double derivative = calculateDerivative(function, i, h, derivationMethod);
	    double derivativePlusOne = calculateDerivative(function, i + 1, h, derivationMethod);
	    graphWin.segment(map(i, 0, 19, 0, RIGHT), map(derivative, 250, 1700, 0, TOP), map(i + 1, 0, 19, 0, RIGHT), map(derivativePlusOne, 250, 1700, 0, TOP));
	    }
	}

    }

void plotDerivationMethod(FunctionENUM function, double x, double h, DerivationMethodENUM derivativeMethod)
    {
    switch (function)
	{
    case FUNCTION1:
	switch (derivativeMethod)
	    {
	case PROGRESSIVE_DIFFERENCE:
	    for (double delta = 0; delta <= h; delta += h)
		{
		graphWin.plot(x + delta, f1(x + delta), 4);
		graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
		graphWin.segment(0, f1(x + delta), x + delta, f1(x + delta));
		}

	    //Segment between two points
	    graphWin.segment(x, f1(x), x + h, f1(x + h));

	    break;
	case CENTRAL_DIFFERENCE:
	    for (double delta = -h; delta <= h; delta += h)
		{
		//Points
		graphWin.plot(x + delta, f1(x + delta), 4);
		//Lines from X axe
		graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
		//Lines from Y axe
		graphWin.segment(0, f1(x + delta), x + delta, f1(x + delta));
		}
	    //Segment between two points
	    graphWin.segment(x - h, f1(x - h), x + h, f1(x + h));
	    break;
	case FOURTH_DEGREE_POLYNOM:
	    for (double delta = -h; delta <= h; delta += h / 2)
		{
		graphWin.segment(x + delta, 0, x + delta, f1(x + delta));
		graphWin.plot(x + delta, f1(x + delta), 4);
		}
	    break;
	default:
	    break;
	    }
	break;
    case FUNCTION2:
	switch (derivativeMethod)
	    {
	case PROGRESSIVE_DIFFERENCE:
	    for (double delta = 0; delta <= h; delta += h)
		{
		graphWin.plot(x + delta, f2(x + delta), 4);
		graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
		graphWin.segment(0, f2(x + delta), x + delta, f2(x + delta));
		}

	    //Segment between two points
	    graphWin.segment(x, f2(x), x + h, f2(x + h));
	    break;
	case CENTRAL_DIFFERENCE:
	    for (double delta = -h; delta <= h; delta += h)
		{
		//Points
		graphWin.plot(x + delta, f2(x + delta), 4);
		//Lines from X axe
		graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
		//Lines from Y axe
		graphWin.segment(0, f2(x + delta), x + delta, f2(x + delta));
		}
	    //Segment between two points
	    graphWin.segment(x - h, f2(x - h), x + h, f2(x + h));
	    break;
	case FOURTH_DEGREE_POLYNOM:
	    for (double delta = -h; delta <= h; delta += h / 2)
		{
		graphWin.segment(x + delta, 0, x + delta, f2(x + delta));
		graphWin.plot(x + delta, f2(x + delta), 4);
		}
	    break;
	default:
	    break;
	    }
	break;
    default:
	break;
	}
    }

std::vector<long double> findRoot()
{
    const long double epsilon = std::numeric_limits<double>::epsilon();
    const long double STEP = 2*epsilon;
     std::vector<long double> solutions;

    //FindRoot

    //Recherche les racines du côté x >= 0
    long double oldStep = 2*epsilon;
    for(long double x=oldStep; x<graphWin.xMax(); x+=fabsl(g(x)-x))
    {
        //Dessin des barres comme dans le cours
        graphWin.segment(x-oldStep,x-oldStep,x-oldStep,g(x-oldStep));
        if(x > g(x))
        {
            if(f == f1)
                graphWin.segment(x-oldStep,g(x-oldStep),x,g(x-oldStep));
            else
                graphWin.segment(x-oldStep,x-oldStep,x,x-oldStep);
        }
        else
            graphWin.segment(x-oldStep,x,x,x);

        if(fabsl(g(x)-x) <= epsilon)
        {
            solutions.push_back(x);
            x+=STEP;//On ajoute suffisement de STEP pour que la fonction puisse repartir et chercher d'autres solutions
        }
        oldStep = fabsl(g(x)-x);
    }

    oldStep = 2*epsilon;
    //Recherche les racines du côté x < 0
    for(long double x=-epsilon; x > graphWin.xMin(); x-=fabsl(g(x)-x))
    {
        //Dessin des barres comme dans le cours
        graphWin.segment(x+oldStep,x+oldStep,x+oldStep,g(x+oldStep));
        if(x < g(x))
        {
            if(f == f1)
                graphWin.segment(x+oldStep,g(x+oldStep),x,g(x+oldStep));
            else
                graphWin.segment(x+oldStep,x+oldStep,x,x+oldStep);
        }
        else
            graphWin.segment(x+oldStep,x,x,x);

        if(fabsl(g(x)-x) <= epsilon)
        {
            solutions.push_back(x);
            x-=STEP;//On ajoute le STEP initiale pour que la fonction puisse repartir et chercher d'autres solutions
        }

        oldStep = fabsl(g(x)-x);
    }

    sort(solutions.begin(),solutions.end());

    return solutions;
}

void plotLinearFunction()
{
    graphWin.segment(LEFTLIMIT, LEFTLIMIT, RIGHTLIMIT, RIGHTLIMIT);
}