Reformulate package

[carlos-adir]

This is an idea to transform this package into a more general purpose mathematical one.

So far :

The main object of this package is shapes : a set of points in a plane.
For example, a disk of center $(0, \ 0)$ and radius $1$ can be represented by:

$$\left\{\left(x, \ y\right) \in \mathbf{R}^2 \ : \ x^2 + y^2 \le 1 \right\}$$

It's represented by the region described by a jordan curve
But it's also possible to have a set of points that describes a curve, for exemple the circle

$$\left\{\left(x, \ y\right) \in \mathbf{R}^2 \ : \ x^2 + y^2 = 1 \right\}$$

It would be nice to be possible the intersection of a curve and shape

The idea of change :

We model five types of objects:

• Empty : represented by the open set with zero elements, or $\varnothing$
• Point : A single point
• Curve : A set of infinite points
  • Open / Closed
  • Parametrized (or not)
• Shape : A set of infinite points
  • Simple : Defined by only one Jordan curve
  • Connected : Intersection of simples shapes
  • Disjoint : Defined by the union of simples shapes and connected shapes
• Whole : The entire plane $\mathbf{R}^2$