# SepBox: $$\mathcal{S}_{box}$$¶

The $$\mathcal{S}_{box}$$ is separating inner and outer parts of a box around a support box of $$\mathbb{R}^n$$.

## Definition¶

Important

definition incoming

s = SepBox(b)
s.separate(x_in, x_out)

SepBox s(b);
s.separate(x_in, x_out);


Optimality

This separator is optimal as it is based on other separators optimality.

## Example¶

Let consider a support box $$[\mathbf{b}] = [1, 2]\times[3, 4]$$ for our separator.

# Build the separator
b = IntervalVector([[1, 2], [3, 4]])
sep_box = SepBox(b)

# Setup the initial box
box = IntervalVector(2, [0, 5])

# Graphics
vibes.beginDrawing()
vibes.newFigure("Set inversion")
vibes.setFigureProperties({"x":100, "y":100, "width":500, "height":500})
SIVIA(box, sep_box, 0.1, fig_name="Set inversion")
vibes.endDrawing()

// Build the separator
IntervalVector b{{1, 2}, {3, 4}};
SepBox sep_box(b);

// Setup the initial box
IntervalVector box(2, {0, 5});

// Graphics
vibes::beginDrawing();
vibes::newFigure("Set inversion");
vibes::setFigureProperties(vibesParams("x",100, "y",100, "width",500, "height",500));
SIVIA(box, sep_box, 0.1, "Set inversion");
vibes::endDrawing();


Fig. 50 SIVIA on a SepBox with a support box $$[\mathbf{b}] = [1, 2]\times[3, 4]$$.