Shapes of weighted points sets

We present an extension of the concept 𝒜-shape to weighted points, where each point´s weight is the radius of a disc centered at this point. Also, we show that the resultant concept, named the weighted 𝒜-shape, is a graph extracted from the regular triangulation. This new concept unifies the two descriptors, named α-shape and space filling graph. This unification is defined by the fact that the families of the last two descriptors are contained in the weighted 𝒜-shape family; this allows the 𝒜-shape to escape the limits of these two descriptors