McGlone - 2 
2.1. Nodal models 
A basic nodal model consists of a set of points and their coordinates. There may 
also be explicit connectivity information between the points, as in a triangulated 
irregular network (TIN) [Polis and McKeown, 1993] or a finite element model (FEM) 
[Terzopoulos, 1988], or the connectivity information may be implicit, as in a gridded 
elevation model. Additional properties of the points or of the relationships between 
them may also be specified; for instance, deformable sheet models include parameters 
for stiffness and tension which determine the derivatives of the surface shape or 
the deformations of the object. Discontinuities in the surface, where the overall 
properties do not hold, may also be specified. 
2.2. Boundary representation models 
As the name implies, the elements of a boundary representation are the boundaries 
between surface patches on an object, along with a description of the surfaces in 
volved. The boundaries may be simple straight lines, if the surfaces are planar, or 
may be complicated curves if the surfaces patches have more general geometries, 
such as Coons patches [Foley and van Dam, 1992]. 
Boundary representations are popular for CAD applications, especially where the 
surfaces used are simple. Where surfaces are more complex, or their intersections 
are not well defined, boundary representations become difficult to use. As surface 
models they are well suited for graphics applications where the surfaces are of interest 
but are less suitable for volumetric computations. 
2.3. Parametric models 
Parametric models use a vocabulary of elementary shapes to represent a variety of 
objects by varying defining parameters of the shapes, such as length or width. An 
elementary shape may be a geometric solid, such as a rectangular prism, or a more 
complicated shape with a number of defining parameters. 
An extreme version of the parametric model is the superquadric, whose very shape 
is determined by the values of the parameters [Barr, 1981]. 
2 _ 
«1 
+ 
= 1 
Due to their extremely non-linear parameterization, superquadrics are difficult to 
extract without prior assumptions on basic shapes or the use of regularization tech 
niques [Solina and Bajcsy, 1990]. 
Parametric models are very efficient to store and transmit, since an object is de 
scribed by only a few parameters, but the range of objects which can be represented 
is limited by the number of basic shapes available. The resolution of the represen 
tation of any particular type of object is determined by the number of parameters, 
and the resolution with which each parameter is determined.