In a paper (chapter 3, the paper is in Italian) I'm reading I found:
A Bézier curve of degree $n$ is a parametric polynomial curve $X:[0;1]\to\mathbb{E}^d$ defined as follows:
I'm not an expert in the field and I've never seen this set "$\mathbb{E}^d$". What is it? The only thing I found online is the expected value, but I don't see how that would apply here.
The space in which Bezier curves describe the object does not possess a preferred coordinate system—so you have to define yourselves. Many such systems could be picked (and some will certainly be more practical than others). But whichever one you choose, it should not affect any properties of the object itself. Our interest is in the object and not in its relationship to some arbitrary coordinate system. Therefore, the methods one wants to develop must be independent of a particular choice of a coordinate system. We say that those methods must be coordinate-free or coordinate-independent. This geometry is called affine geometry. Bezier curves "live" in affine spaces, not in linear spaces. So to distinguish $\mathbb{R}^d$ as a vector space and as an affine space, we introduce $\mathbb{E}^d$ as the affine space.