Image Processing Reference
In-Depth Information
Algorithm 15: Major Steps of the Algorithm to Find the 3-D Isothetic
Cover of an Object A Embedded in Grid G.
Algorithm ISO-COVER-3D(A, G)
01. Find the start vertex, v
s
(Eq. 7.1).
02. Initialize an empty queue, Q.
03. Determine the front face f
s
of the UGC having v
s
as a vertex.
04. Enqueue f
s
in Q.
05. while Q is not empty
06. Dequeue face f
i
from Q.
07. Insert the vertex, edge, and face information of f
i
into DCEL.
08. for each 'eligible face' f
k
incident on some edge of f
i
09. if f
k
is not already enqueued in Q
10. then enqueue f
k
in Q.
11. else if f
k
is dequeued and f
i
and f
k
are coplanar
12. then set half-edges e
ij
∈ f
i
and e
ij
∈ f
k
as pairs.
13. Merge the contiguous coplanar faces that are parallel to each coordinate plane.
of neighboring UGCs occupied by object voxels. The complexity of the struc-
ture of the vertices increases with the category as mentioned, i.e., Type 7 is
more complex in structure than Type 1. For a particular grid size, the total
number of vertices of a higher category increases with the complexity of the
object topology.
7.2 Voxelation of Surface of Revolution
The traditional millennium-old artistry of wheel throwing for creation of
potteries has gained an enduring popularity with today's state-of-the-art ce-
ramic technology [35, 213].
2
With the proliferation of digitization techniques in
our computerized society, the digital creation and artistic visualization of pot-
teries is a call of the day. The existing graphic tools are mostly based on com-
plex trigonometric procedures involving computation in real space, which have
to be tuned properly to suit the discrete nature of the 3-D digital space [90, 99].
The method of circularly sweeping a shape/polygon/polyline/generating curve
is rotated about the axis of revolution in discrete steps, which requires a dis-
crete approximation, and choosing k equi-spaced angles about the y-axis re-
2
From a historic point of interest, a recreation of wheel-thrown potteries may be seen at
Conner Prairie (
http://www.connerprairie.org
). Conner Prairie is an interactive history
park, or living history museum, located in Fishers, Indiana, USA. With a noble objective
to preserve the William Conner home, which is listed on the National Register of Historic
Places, it recreates part of life in Indiana in the 19th century on the White River.
