/*------------------------------------------------------------------*\
|* 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;
}
}
/****************************************************
* Helper functions
****************************************************/
void plotCurrentFunction()
{
for(double i = LEFTLIMIT; i <= RIGHTLIMIT; i = i + 0.01)
{
#ifdef USING_FIRST_FUNCTION
graphWin.plot(i,f(i),1);
#else
graphWin.plot(i,g(i),1);
#endif
}
}
void plotAdaptedFunction(double lambda)
{
for(double i = LEFTLIMIT; i < RIGHTLIMIT; i += 0.01)
{
graphWin.plot(i, fixedPointAdapterFunction(i, lambda), 1);
}
}
void drawFunctions()
{
const float STEP = graphWin.findSmartStepX();
glPointSize(2.0f);
//Draw selected (f(x))
for(float x=graphWin.xMin(); x<graphWin.xMax(); x+=STEP)
graphWin.plot(x, f(x), 1.0f,0.5f,0.0f);
//Draw f(x) = x
for(float x=graphWin.xMin(); x<graphWin.xMax(); x+=STEP)
graphWin.plot( x, x, 0.5f,0.5f,0.5f);
//Draw g(x)
for(float x=graphWin.xMin()+STEP; x<graphWin.xMax(); x+=STEP)
graphWin.plot(x, g(x), 1.0f,0.5f,1.0f);
clear();
printHeader();
std::cout << "x est compris dans l'ensemble [" << graphWin.xMin() << ";" << graphWin.xMax() << "[" << std::endl;
std::cout << "y est compris dans l'ensemble [" << graphWin.yMin() << ";" << graphWin.yMax() << "[" << std::endl << std::endl;
std::cout << "Information graphique : " << std::endl
<< "- Fonction choisie (f(x)) en orange" << std::endl
<< "- Fonction h(x) = x, en gris" << std::endl
<< "- Fonction g(x) = x + l*f(x), l = 1, en rose" << std::endl
<< "- Les axes x,y en bleu " << std::endl
<< "- Les vecteurs unitaires en rouge " << std::endl
<< "- Les solutions de la fonction en vert" << std::endl << std::endl;
vector<long double> solutions = findRoot();
std::cout << "Solutions : " << std::endl;
glColor3f(0.0f, 1.0f, 0.0f);
glPointSize(10);
//Draw solutions
for(unsigned int i = 0;i < solutions.size(); ++i)
{
std::cout << "[" << i << "] -> " << static_cast<double>(solutions[i]) << std::endl;
glBegin( GL_POINTS );
glVertex3d(solutions[i], 0, 0.0);
glEnd();
}
}
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 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 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;
}
}