Image Processing Reference
In-Depth Information
quires the following transformation matrices for a real-geometric realization:
0
@
cosθ
i
1
0
sinθ
i
0
A
0
1
0
0
M
i
=
−sinθ
i
0
cosθ
i
0
0
0
0
1
where, θ
i
= 2πi/k,i = 0,1,...,k−1 [99]. Clearly, in order to generate circles
of varying radii describing the surface of revolution, the number of steps, k,
becomes a concerning issue.
In the domain of digital geometry, the idea of digital wheel-throwing has
recently been proposed in [126, 125]. The algorithm works purely in the digital
domain and banks on a few primitive integer computations only. Its input is
a digital generatrix, taken in the form of an irreducible digital curve segment
(Sec. 4.1). The digital surface produced from the digital generatrix by dig-
ital wheel-throwing is both connected and irreducible in a digital-geometric
sense. This, in turn, ensures its successful rendition with a realistic finish
that involves conventional processing of quad decomposition, texture map-
ping, illumination, etc. The method is robust and e
cient, and guarantees
easy implementation in Java3D
TM
and OpenGL
TM
with all relevant features
incorporated. The rendered visualization is found to be absolutely free of
any bugs or degeneracies, regardless of the zoom factor. Further, producing a
monotone or a non-monotone digital surface of revolution is also feasible with-
out destroying its digital connectivity and irreducibility by respective input
of a monotone or a non-monotone digital generatrix. To create the exquisite
digital products having the desired resemblance with on-the-shelf potteries in
toto, a double-layered generatrix can be, therefore, supplied as the genera-
trix, which is its ultimate benefit. Some typical products from the software
developed by Kumar et al. [125] and their corresponding statistical figures
including CPU times to generate them, have been furnished in Section 7.2.6
of this topic to exhibit the e
ciency and elegance of the proposed technique.
7.2.1 Various Techniques
Almost all methods for modeling potteries start with an initial cylindrical
piece of clay and use deformation techniques, as described in [104, 120]. The
deformation is based either on shifting the individual points horizontally or
on using devices that accept feedback by means of touch sensation at multiple
points [207]. As a result, the user has direct control over the geometry of the
shape to be constructed, which, poses more and more di
culties to represent
the surface mathematically. In addition, it requires large memory for display
and storage. Some of the major approaches are as follows.
Polyhedra Representation: The whole surface of a pottery is represented
by a finite set of surface polygons. Its major drawback is that many polygons
are often required to create a realistic feel. For example, in the interactive
