#326 - Template directions

[schillic]

Closes #326.

• add box and oct directions iterator types
• add unit tests for iterator types
• add overapproximate function with iterator types
• add overapproximate unit tests
• fix bug for 1D direction iterators
• implement length with BigInts --> see Implement length in template directions with BigInt's #338
• add overapproximate(X, BoxDirections) = overapproximate(X, BoxDirections(dim(X))), etc. --> see overapproximate signature for template directions #339

[schillic]

using LazySets, LazySets.Approximations
B = Ball2([0., 0.], 2.);
box = overapproximate(B, BoxDirections(2));
oct = overapproximate(B, OctDirections(2));

using Plots
plot(oct, 1e-4, alpha=.5)
plot!(box, 1e-4, alpha=.5)
plot!(B, 1e-4)

EDIT:
Previously I could not plot HPolytopes, so I needed two workarounds. But now suddenly it worked (so confused now). Below is the old comment.

1. HPolytope cannot be plotted, so we use HPolygon. (We have to use addconstraint! because the constraints are not sorted.)
2. HPolygon uses Line, which uses Vector (see Revisit Line #332) (hence the convert).

using LazySets, LazySets.Approximations, Polyhedra
B = Ball2([0., 0.], 2.)
box = HPolygon()
for c in overapproximate(B, BoxDirections(2)).constraints
    addconstraint!(box, LinearConstraint(convert(Vector{Float64}, c.a), c.b))
end
oct = HPolygon()
for c in overapproximate(B, OctDirections(2)).constraints
    addconstraint!(oct, LinearConstraint(convert(Vector{Float64}, c.a), c.b))
end

using Plots
plot(oct, alpha=.5)
plot!(box, alpha=.5)
plot!(B, 1e-4)

[mforets]

LGTM. I'm moving the 2 new tasks to issues.