A natural definition of a curved planar object is the *splinegon*,
a polygon bounded by algebraic curves, which can either be defined
parametrically (x and y being polynomial functions of a parameter t) or
implicitly as the solution to a polynomial equation in x and y.
Every parametric curve can be represented implicitly but not vice versa;
which form one uses depends on where the problem comes from.
An important measure of the complexity of these curves is the *degree*
of the associated polynomials.

Anyway, the most basic data structure for straight-sided polygons
is a *triangulation*, a partition of the polygon into three-sided regions
using the same vertices as the original polygon.
Many other geometric algorithms are based on the existence of a triangulation.
What similar thing should we use for splinegons?

Obviously we can define triangulations in exactly the same way. Unfortunately, to triangulate splinegons we may need to increase the degree. Any diagonal in the following splinegon quadrilateral, formed from four arcs of an ellipse, has degree at least three.

More generally, examples like this show that the degree of a diagonal may be up to double the degree of the splinegon edges. However, we don't know whether it is always possible to triangulate splinegons, even with high-degree diagonals.

In the same four-cusp example, we can use four circular arcs instead of
a cubic spline diagonal, if we introduce an extra *Steiner point*
in the middle of the splinegon.

Is it always possible to triangulate splinegons, using diagonals of degree matching the splinegon sides, and only introducting Steiner points in the splinegon interior? If so how many Steiner points are needed?