double powellMethod::goldenSectionSearch(double a, double b, double c, double tau, std::vector<Expression> x_next,double preValue) {
double x;
double valueX, valueB;
b = (a + c) / 2;
if (b < c)
x = b + resphi * (c - b);
else
x = b - resphi * (b - a);
//std::cout << "a = " << a << std::endl;
//std::cout << "c = " << c << std::endl;
//std::cout << "x = " << x << std::endl;
//std::cout << " " << std::endl;
if ((std::abs(c - a) < tau * (std::abs(b) + std::abs(x))) || std::abs(preValue - x) <= tau ) {
return (c + a) / 2;
}
if (x_next.size() == 1) {
valueX = myExpression.getValue(x_next[0].getValue(x), 0);
valueB = myExpression.getValue(x_next[0].getValue(b), 0);
}
else if (x_next.size() == 2) {
valueX = myExpression.getValue(x_next[0].getValue(x), x_next[1].getValue(x));
valueB = myExpression.getValue(x_next[0].getValue(b), x_next[1].getValue(b));
}
//std::cout << "f(x) = " << valueX << std::endl;
//std::cout << "f(b) = " << valueB << std::endl;
//std::cout << "---" << std::endl;
if (valueX < valueB) {
return (b < c) ? goldenSectionSearch(b, x, c, tau, x_next, x) : goldenSectionSearch(a, x, b, tau, x_next, x);
}
else {
return (b < c) ? goldenSectionSearch(a, b, x, tau, x_next, x) : goldenSectionSearch(x, b, c, tau, x_next, x);
}
//if (x_next.size() == 1) {
// if (myExpression.getValue(x_next[0].getValue(x), 0) < myExpression.getValue(x_next[0].getValue(b), 0))
// return (b < c) ? goldenSectionSearch(b, x, c, tau, x_next, x) : goldenSectionSearch(a, x, b, tau, x_next,x);
// else
// return (b < c) ? goldenSectionSearch(a, b, x, tau, x_next, x) : goldenSectionSearch(x, b, c, tau, x_next, x);
//}
//else if (x_next.size() == 2) {
// if (myExpression.getValue(x_next[0].getValue(x), x_next[1].getValue(x)) < myExpression.getValue(x_next[0].getValue(b), x_next[1].getValue(b)))
// return (b < c) ? goldenSectionSearch(b, x, c, tau, x_next, x) : goldenSectionSearch(a, x, b, tau, x_next, x);
// else
// return (b < c) ? goldenSectionSearch(a, b, x, tau, x_next, x) : goldenSectionSearch(x, b, c, tau, x_next, x);
//}
}
double goldenSectionSearch(const GEdge *ge, const SPoint3 &q, double x1,
double x2, double x3, double tau)
{
// Create a new possible center in the area between x2 and x3, closer to x2
double x4 = x2 + GOLDEN2 * (x3 - x2);
// Evaluate termination criterion
if (fabs(x3 - x1) < tau * (fabs(x2) + fabs(x4)))
return (x3 + x1) / 2;
const SVector3 dp4 = q - ge->position(x4);
const SVector3 dp2 = q - ge->position(x2);
const double d4 = dp4.norm();
const double d2 = dp2.norm();
if (d4 < d2)
return goldenSectionSearch(ge, q, x2, x4, x3, tau);
else
return goldenSectionSearch(ge,q , x4, x2, x1, tau);
}
GPoint GEdge::closestPoint(const SPoint3 &q, double &t) const
{
// printf("looking for closest point in curve %d to point %g %g\n",tag(),q.x(),q.y());
const int nbSamples = 100;
Range<double> interval = parBounds(0);
double tMin = std::min(interval.high(), interval.low());
double tMax = std::max(interval.high(), interval.low());
double DMIN = 1.e22;
double topt = tMin;
const double DT = (tMax - tMin) / (nbSamples - 1.) ;
for (int i = 0; i < nbSamples; i++){
t = tMin + i * DT;
const SVector3 dp = q - position(t);
const double D = dp.norm();
if (D < DMIN) {
topt = t;
DMIN = D;
}
}
// printf("parameter %g as an initial guess (dist = %g)\n",topt,DMIN);
if (topt == tMin)
t = goldenSectionSearch (this, q, topt, topt + DT/2, topt + DT, 1.e-9);
else if (topt == tMax)
t = goldenSectionSearch (this, q, topt - DT, topt - DT/2 , topt, 1.e-9);
else
t = goldenSectionSearch (this, q, topt - DT, topt, topt + DT, 1.e-9);
const SVector3 dp = q - position(t);
// const double D = dp.norm();
// printf("after golden section parameter %g (dist = %g)\n",t,D);
return point(t);
}
