Surface and Solid Modeling
The field of surface and solid modeling deals with design and representation
of physical objects.
Currently, most solid modelers are able to support
solids composed of polyhedral models and quadric surfaces (like spheres,
cylinders etc.) and their Boolean combinations.
At the same time, the field of surface
modeling has been developed to model classes of piecewise surfaces based
on particular conditions of shape and smoothness. Such models are also
referred to as sculptured models.
Over the years there has been considerable effort
put into integrating surface and solid modeling. In particular, there is
considerable interest in building complete solid representations from
spline/NURBS surfaces and their Boolean combinations.
However, the major bottle necks are in performing robust,
efficient and accurate Boolean operations on the sculptured models. The
main difficulty is in evaluating and representing the intersection of
parametric surface patches and it has hindered the development of
solid modelers that incorporate parametric surface models.
The topology of a surface patch becomes quite complicated when
Boolean operations are performed and finding a convenient
representation for these topologies has been a major challenge.
As a result, most of the current solid modelers use polyhedral
approximations to these surfaces and
apply existing algorithms to design and manipulate these polyhedral
objects. Not only does this approach lead to data proliferation, the resulting
algorithms are inefficient and inaccurate.