void Miniball<CoordAccessor>::mtf_mb (Sit n)
{
// Algorithm 1: mtf_mb (L_{n-1}, B), where L_{n-1} = [L.begin, n)
// B: the set of forced points, defining the current ball
// S: the superset of support points computed by the algorithm
// --------------------------------------------------------------
// from B. Gaertner, Fast and Robust Smallest Enclosing Balls, ESA 1999,
// http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf
// PRE: B = S
assert (fsize == ssize);
support_end = L.begin();
if ((fsize) == d+1) return;
// incremental construction
for (Sit i = L.begin(); i != n;)
{
// INV: (support_end - L.begin() == |S|-|B|)
assert (std::distance (L.begin(), support_end) == ssize - fsize);
Sit j = i++;
if (excess(*j) > nt0)
if (push(*j)) { // B := B + p_i
mtf_mb (j); // mtf_mb (L_{i-1}, B + p_i)
pop(); // B := B - p_i
mtf_move_to_front(j);
}
}
// POST: the range [L.begin(), support_end) stores the set S\B
}
void Miniball::build (bool pivoting)
{
B.reset();
support_end = L.begin();
if (pivoting)
pivot_mb (L.end());
else
mtf_mb (L.end());
}
void Miniball::pivot_mb (It i)
{
It t = ++L.begin();
mtf_mb (t);
double max_e, old_sqr_r;
do {
It pivot;
max_e = max_excess (t, i, pivot);
if (max_e > 0) {
t = support_end;
if (t==pivot) ++t;
old_sqr_r = B.squared_radius();
B.push (*pivot);
mtf_mb (support_end);
B.pop();
move_to_front (pivot);
}
} while ((max_e > 0) && (B.squared_radius() > old_sqr_r));
}
void Miniball::mtf_mb (It i)
{
support_end = L.begin();
if ((B.size())==BSIZE) return;
for (It k=L.begin(); k!=i;) {
It j=k++;
if (B.excess(*j) > 0) {
if (B.push(*j)) {
mtf_mb (j);
B.pop();
move_to_front(j);
}
}
}
}
void Miniball<CoordAccessor>::pivot_mb (Pit n)
{
// Algorithm 2: pivot_mb (L_{n-1}), where L_{n-1} = [L.begin, n)
// --------------------------------------------------------------
// from B. Gaertner, Fast and Robust Smallest Enclosing Balls, ESA 1999,
// http://www.inf.ethz.ch/personal/gaertner/texts/own_work/esa99_final.pdf
NT old_sqr_r;
const NT* c;
Pit pivot, k;
NT e, max_e, sqr_r;
Cit p;
do {
old_sqr_r = current_sqr_r;
sqr_r = current_sqr_r;
pivot = points_begin;
max_e = nt0;
for (k = points_begin; k != n; ++k) {
p = coord_accessor(k);
e = -sqr_r;
c = current_c;
for (int j=0; j<d; ++j)
e += mb_sqr<NT>(*p++-*c++);
if (e > max_e) {
max_e = e;
pivot = k;
}
}
if (max_e > nt0) {
// check if the pivot is already contained in the support set
if (std::find(L.begin(), support_end, pivot) == support_end) {
assert (fsize == 0);
if (push (pivot)) {
mtf_mb(support_end);
pop();
pivot_move_to_front(pivot);
}
}
}
} while (old_sqr_r < current_sqr_r);
}
