## Bisectors

A bisector is an operator that takes a box \([x]\) as input and returns two sub-boxes \(([x]^{(1)},[x]^{(2)})\) that
form a partition of \([x]\), that is, \([x]=[x]^{(1)}\cup[x]^{(2)}\). This partition is obtained by
selecting one component \([x_i]\) and splitting this interval at some point.

Each bisector implements a specific strategy for chosing the component. The bisection point in the interval is
defined as a *ratio* of the interval width, e.g., a ratio of 0.5 corresponds to the midpoint.

### Bisecting each component in turn

*(to be completed)*

### Bisecting the largest component

*(to be completed)*

### Setting different precision for variables

In real-world applications, variables often correspond to physical quantities with different units.
The order of magnitude greatly varies with the unit.
For example, consider Coulomb’s law:

\[F=k_e\frac{q_1q_2}{r^2}\]

applied to two charges \(q_1\) and \(q_2\) or ~1e-6 coulomb, with a distance \(r\) of ~1e-2 meter.
With Coulomb’s contant ~ 1e10, the resulting force will be in the order of 1e2 Newton.

If one introduces Coulomb’s equation in a solver, using a bisector that handles
variables uniformly, i.e., that uses the same precision value for all of them, is certainly not adequate.

Each bisector can be given a vector of different precisions (one for each variable) instead of a
unique value. We just have to give a `Vector` in argument in place of a `double`.
For instance, with the round-robin bisector:

double _prec[]={1e-8,1e-8,1e-4,1};
Vector prec(4,_prec);
RoundRobin rr(prec);

### Respecting proportions of a box

If you want to use a relative precision that respects the proportion betweeen
the interval widths of an “initial” box, you can simply initialize the vector
of precision like this:

Vector prec=1e-07*box.diam(); // box is the initial domain

### The Smear Function

*(to be completed)*

#### Smear function with maximum impact

*(to be completed)*

#### Smear function with maximal sum of impacts

*(to be completed)*

#### Smear function with maximal normalized impact

*(to be completed)*

#### Smear function with maximal sum of normalized impacts

*(to be completed)*

maximal sum of impacts