Information Technology Reference
In-Depth Information
Then, the two boundary curves are generated using the two sets of points
{
P
0
−
SR
(
ʸ
0
)
,P
1
−
MR
(
ʸ
1
)
,P
2
−
ER
(
ʸ
2
)
}
,
{
P
0
+
SR
(
ʸ
0
)
,P
1
+
MR
(
ʸ
1
)
,P
2
+
ER
(
ʸ
2
)
}
.
where
R
(
ʸ
)=(cos(
ʸ
)
,
sin(
ʸ
))
T
. This new definition controls the shape of each
boundary curve segment. Fig. 1 (b) shows a tree generated by this new method.
Here, all curve segments have different thicknesses. However, the tree is drawn
smoothly and there is no inconsistency.
Fig. 1.
(a) A general path is generated from quadratic curves with a fixed thickness.
(b) A tree is drawn by different thicknesses for branches. (c,d) The thicknesses are
changing by adding new nodes as a result of extending by the feature of adjustable
thickness. (e) A tree is visualized using the adjustable thickness and adding circles for
fruits.
Holton [1] was one of the first who proposed a strand model to investigate
the tree drawing. Based on this model, we adjust the thicknesses automatically.
Suppose
ʱ
is a basic default thickness and
l
0
is the number of levels we want
to consider. Hence, the thickness of a node is computed by the number of its
children and the children of its children up to the level
l
0
, multiplied by
ʱ
. Figs. 1
(c,d) illustrate this model in the evolution of the tree. Computing this thickness
for each node through the tree and interpolating the connection of two curve
segments produce Fig. 1 (e). In this figure, circles are added as fruits only in
favour of a better visualization.
References
1. Holton, M.: Strands, gravity and botanical tree imagery. Computer Graphics Fo-
rum 13(1), 57-67 (1994)
2. Hoory, S., Linial, N., Wigderson, A., Overview, A.: Expander graphs and their
applications. Bull. Amer. Math. Soc. (N.S.) 43, 439-561 (2006)
3. Rostami, M.A., Azadi, A., Seydi, M.: GraphTea: Interactive Graph Self-Teaching
Tool. In: Proc. 2014 Int. Conf. Edu. & Educat. Technol. II, pp. 48-52 (2014)
4. Rostami, M.A., Bucker, H.M., Azadi, A.: Illustrating a graph coloring algorithm
based on the principle of inclusion and exclusion using GraphTea. In: Rensing, C.,
de Freitas, S., Ley, T., Munoz-Merino, P.J. (eds.) EC-TEL 2014. LNCS, vol. 8719,
pp. 514-517. Springer, Heidelberg (2014)
