Face_index_observer (Arrangement_2& arr) :
CGAL::Arr_observer<Arrangement_2> (arr),
n_faces (0)
{
CGAL_precondition (arr.is_empty());
arr.unbounded_face()->set_data (0);
n_faces++;
}
Point_3 operator()(const Vertex& v) const {
CGAL_precondition((CGAL::circulator_size(v.vertex_begin()) & 1) == 0);
std::size_t degree = CGAL::circulator_size(v.vertex_begin()) / 2;
double alpha = (4.0 - 2.0 * std::cos(2.0 * CGAL_PI / degree)) / 9.0;
Vector_3 vec = (v.point() - CGAL::ORIGIN) * (1.0 - alpha);
HV_circulator h = v.vertex_begin();
do {
vec = vec + (h->opposite()->vertex()->point() - CGAL::ORIGIN)
* alpha / static_cast<double> (degree);
++h;
CGAL_assertion(h != v.vertex_begin()); // even degree guaranteed
++h;
} while (h != v.vertex_begin());
return (CGAL::ORIGIN + vec);
}
// Moves to the closest target (appending the motion).
// Returns whether a motion was successfully found.
// Updates source to the target selected.
// Removes said target from targets.
bool BufferingPlayer::move_to_closest_target(Reference_point& source, Reference_point_vec& targets, Motion& motion) {
TIMED_TRACE_ENTER("move_to_closest_target");
CGAL_precondition(!env->get_target_configurations().empty());
Ref_p_vec::iterator target_reached;
int target_index;
// Plan a motion to the closest remaining target
bool path_found = planner.query_closest_point(
source,
targets,
target_index,
// Append it to the output motion
motion);
ASSERT_CONDITION(path_found, "targets are connected but could not find path!");
// Reached another target
target_reached = targets.begin() + target_index;
source = *target_reached;
targets.erase(target_reached);
TIMED_TRACE_EXIT("move_to_closest_target");
return true;
}
static void
FindPolynomialRoots(
const FLOAT *a, /* Coefficients */
FLOAT *u, /* Real component of each root */
FLOAT *v, /* Imaginary component of each root */
FLOAT *conv, /* Convergence constant associated with each root */
register long n, /* Degree of polynomial (order-1) */
long maxiter, /* Maximum number of iterations */
long fig /* The number of decimal figures to be computed */
)
{
int number_of_ITERATE=0;
int number_of_INIT=0;
CGAL_precondition(static_cast<unsigned int>(fig) < MAXN);
int i;
register int j;
FLOAT h[MAXN + 3], b[MAXN + 3], c[MAXN + 3], d[MAXN + 3], e[MAXN + 3];
/* [-2 : n] */
FLOAT K, ps, qs, pt, qt, s, rev, r= std::numeric_limits<double>::infinity();
int t;
FLOAT p=std::numeric_limits<double>::infinity(), q=std::numeric_limits<double>::infinity();
/* Zero elements with negative indices */
b[2 + -1] = b[2 + -2] =
c[2 + -1] = c[2 + -2] =
d[2 + -1] = d[2 + -2] =
e[2 + -1] = e[2 + -2] =
h[2 + -1] = h[2 + -2] = 0.0;
/* Copy polynomial coefficients to working storage */
for (j = n; j >= 0; j--)
h[2 + j] = *a++; /* Note reversal of coefficients */
t = 1;
K = std::pow(10.0, (double)(fig)); /* Relative accuracy */
for (; h[2 + n] == 0.0; n--) { /* Look for zero high-order coeff. */
*u++ = 0.0;
*v++ = 0.0;
*conv++ = K;
}
INIT:
++number_of_INIT;
if (number_of_INIT > 1000) {
std::cerr << "Too many INITs" << std::flush;
return;
}
if (n == 0)
return;
ps = qs = pt = qt = s = 0.0;
rev = 1.0;
K = std::pow(10.0, (double)(fig));
if (n == 1) {
r = -h[2 + 1] / h[2 + 0];
goto LINEAR;
}
for (j = n; j >= 0; j--) /* Find geometric mean of coeff's */
if (h[2 + j] != 0.0)
s += std::log(std::fabs(h[2 + j]));
s = std::exp(s / (n + 1));
for (j = n; j >= 0; j--) /* Normalize coeff's by mean */
h[2 + j] /= s;
if (std::fabs(h[2 + 1] / h[2 + 0]) < std::fabs(h[2 + n - 1] / h[2 + n])) {
REVERSE:
t = -t;
for (j = (n - 1) / 2; j >= 0; j--) {
s = h[2 + j];
h[2 + j] = h[2 + n - j];
h[2 + n - j] = s;
}
}
if (qs != 0.0) {
p = ps;
q = qs;
}
else {
if (h[2 + n - 2] == 0.0) {
q = 1.0;
p = -2.0;
}
else {
q = h[2 + n] / h[2 + n - 2];
p = (h[2 + n - 1] - q * h[2 + n - 3]) / h[2 + n - 2];
}
if (n == 2)
goto QADRTIC;
r = 0.0;
}
ITERATE:
++number_of_ITERATE;
if (number_of_ITERATE > 1000) {
std::cerr << "Too many ITERATEs" << std::flush;
return;
}
for (i = maxiter; i > 0; i--) {
for (j = 0; j <= n; j++) { /* BAIRSTOW */
b[2 + j] = h[2 + j] - p * b[2 + j - 1] - q * b[2 + j - 2];
c[2 + j] = b[2 + j] - p * c[2 + j - 1] - q * c[2 + j - 2];
}
if ((h[2 + n - 1] != 0.0) && (b[2 + n - 1] != 0.0)) {
if (std::fabs(h[2 + n - 1] / b[2 + n - 1]) >= K) {
b[2 + n] = h[2 + n] - q * b[2 + n - 2];
}
if (b[2 + n] == 0.0)
goto QADRTIC;
if (K < std::fabs(h[2 + n] / b[2 + n]))
goto QADRTIC;
}
for (j = 0; j <= n; j++) { /* NEWTON */
/* Calculate polynomial at r */
d[2 + j] = h[2 + j] + r * d[2 + j - 1];
/* Calculate derivative at r */
e[2 + j] = d[2 + j] + r * e[2 + j - 1];
}
if (d[2 + n] == 0.0)
goto LINEAR;
if (K < std::fabs(h[2 + n] / d[2 + n]))
goto LINEAR;
c[2 + n - 1] = -p * c[2 + n - 2] - q * c[2 + n - 3];
s = c[2 + n - 2] * c[2 + n - 2] - c[2 + n - 1] * c[2 + n - 3];
if (s == 0.0) {
p -= 2.0;
q *= (q + 1.0);
}
else {
p += (b[2 + n - 1] * c[2 + n - 2] - b[2 + n] * c[2 + n - 3]) / s;
q += (-b[2 + n - 1] * c[2 + n - 1] + b[2 + n] * c[2 + n - 2]) / s;
}
if (e[2 + n - 1] == 0.0)
r -= 1.0; /* Minimum step */
else
r -= d[2 + n] / e[2 + n - 1]; /* Newton's iteration */
}
ps = pt;
qs = qt;
pt = p;
qt = q;
if (rev < 0.0)
K /= 10.0;
rev = -rev;
goto REVERSE;
LINEAR:
if (t < 0)
r = 1.0 / r;
n--;
*u++ = r;
*v++ = 0.0;
*conv++ = K;
for (j = n; j >= 0; j--) { /* Polynomial deflation by lin-nomial */
if ((d[2 + j] != 0.0) && (std::fabs(h[2 + j] / d[2 + j]) < K))
h[2 + j] = d[2 + j];
else
h[2 + j] = 0.0;
}
if (n == 0)
return;
goto ITERATE;
QADRTIC:
if (t < 0) {
p /= q;
q = 1.0 / q;
}
n -= 2;
if (0.0 < (q - (p * p / 4.0))) { /* Two complex roots */
*(u + 1) = *u = -p / 2.0;
u += 2;
s = sqrt(q - (p * p / 4.0));
*v++ = s;
*v++ = -s;
} /* Two real roots */
else {
s = std::sqrt(((p * p / 4.0)) - q);
if (p < 0.0)
*u++ = -p / 2.0 + s;
else
*u++ = -p / 2.0 - s;
*u = q / u[-1];
++u; // moved from lhs of before
*v++ = 0.0;
*v++ = 0.0;
}
*conv++ = K;
*conv++ = K;
for (j = n; j >= 0; j--) { /* Polynomial deflation by quadratic */
if ((b[2 + j] != 0.0) && (std::fabs(h[2 + j] / b[2 + j]) < K))
h[2 + j] = b[2 + j];
else
h[2 + j] = 0.0;
}
goto INIT;
}
