Convolution Surfaces is a class of implicit surfaces that was introduced in Computer Graphics. They are the boundaries of smooth volumes around a graph of geometric elements (such as points, line segments, polygons), thus offering intuitive shape control thanks to a skeleton plus radius abstraction. They are defined as level sets of a function obtained by integrating a kernel function along this skeleton. To allow interactive modeling, the technique has relied on closed form formulae for integration obtained through symbolic computation software. With the impetus of Marie-Paule Cani and her group, together with the input of F. Chyzak, B. Salvy, N. Takayama, H. Nakayama, we study the qualitative behaviour of those surfaces and generalized the formulae defining them for one-dimensional and two dimensional basic skeleton elements with polynomial weights. The generalizations come in term of recurrence formulae with which the already known and used formulae can be recovered, and new ones generated.