One of the main objectives of scientific work is the analysis
of complex phenomena in order to reveal the underlying structures
and to explain them by means of elementary rules which are easily
understood.
In this paper we study how the well-known process of triangle
mesh subdivision can be expressed in terms of the simplest
mesh modification, namely the vertex split.
Although this basic operation is capable of reproducing all
common subdivision schemes if applied in the correct manner,
we focus on Butterfly subdivision only for the purpose of
perspicuity.
Our observations lead to an obvious representation of subdivision
meshes as selectively refined progressive meshes, making them most
applicable to view-dependent level-of-detail rendering.
