Abstract:
Subdivision techniques are being appreciated in geometric modelling. Curves be-
ing the basic ingredient of the surfaces, have their own importance. Since no single
scheme can be fit for every situation so, there is always a room to introduce new
schemes. In this dissertation the interpolating curve subdivision scheme developed
by Weissman [50], has been analyzed, using Laurent polynomial method. More-
over, four approximating curve subdivision schemes have been developed. These
schemes have also been analyzed, using Laurent polynomial method. The local
supports of these schemes are determined as well. Regarding surface generation, a
mathematical model of a three dimensional object using cross sectional data has
been constructed. An algorithm for generating quadrilateral net is presented. The
contours have been generated interpolating the data at each section, using a linear
subdivision scheme introduced by Dyn et al. [17]. The contours have been, then,
blended using the non-linear subdivision scheme developed Aspert [2]. The im-
plementation of the schemes developed have also been depicted through different
examples.
