Image Processing Reference
In-Depth Information
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FIGURE 7.14: Demonstration of algorithm DCR for radius 106 (see text
for explanation).
algorithm is not as e
cient for circles (1st octant) of small radii, or to find
a run length of small value, such as when j/i 6 4 or so, since the operations
(comparisons, etc.) needed in the binary search for small run lengths would
raise the overall runtime of the algorithm. Hence, the algorithm DCR may be
used in some models of hybridization, whose one possible realization can be
seen in [14].
7.2.5 Creating Realistic Potteries
As explained in Sec. 7.2.3, the surface S
G
is generated from the digital gen-
eratrix G as an ordered set of voxels. For each digital circle C
Z
i
corresponding
to each voxel p
i
∈G, the voxels inclusive of the missing voxels are generated
in a definite order, starting from Octant 1 and ending at Octant 8. All the
circles, namely C
Z
1
,C
Z
2
,...,C
Z
n
, in turn, are also generated in order. The
above ordering to represent a wheel-thrown piece helps to map textures in a
straightforward way. We map adjacent and equal-area rectangular parts from
the texture image to each of the quads. The circle is approximated as a regular
polygon. Clearly, there is always a trade-off between the number of vertices
of the approximate polygon and the rendering speed, apart from the fact that
a coarse approximation gives a polyhedral effect (Fig. 7.11). The nature of
approximation error has been studied in a recent work [15] (a part of which
is illustrated in Fig. 7.2.4 and also through the 3-D plot in Fig. 7.13), which
shows that if we have polygons with k > 20 or so, then for r 6 100, we have
2% or less error. For higher radii, of course, we should increase k accordingly
to have the desired error control. Note that an error point is that which lies
inside the polygon but outside the digital circle [15].
The number of sides, numSides, in the polygon approximation is kept the
same for each of the digital points of G. We find the maximum among the
distances of the points on G from the axis of revolution, say, maxDis. We
use maxDis to determine the value of numSides. We want to map a square
portion of texture-image to each of the quads. The distance between two
adjacent points in G is either 1 or
√
2). We determine the value of numSides
