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Modeling bonsai tree using positional information

Authors:

Abstract

To model {\it bonsai} tree, we propose to use positional information of most important branches of the shape. From the measured data of selected branches, we can derive spline function approximating data which are used to write L-system. The L-system then reconstructs the tree skeleton with the same shape of spline function.
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2tr9 Modeling Bonsaa
Tree
Using Positional
Information
o Yuka Wakabayashi and Roman Durikovid
Department of Information Systems, the University of Aizu
E-mail: m505 1 139@u-aizu.
ac.j
p, roman@u-aizu.
ac.j
p
1 Introduction
The plants morphology models using formal languages
or geometry were researched [1]. However these models are
not capable to control the form of plant, therefore we sug-
gest the model of bonsa'i tree which is hard to model with
previous methods. Up to now L-system are random gen-
erator in all branches were used to model trees and plants.
Because L-system is deterministic systems, the overall sil-
houette of the tree and the plant is given and hard to
control with input paxameters.
To model bonsa'ittee, we propose to use positional infor-
mation of most importa,nt branches of the shape. FYom the
measured data of selected branches, we can derive spline
function approximating data which are used to write L-
system. The L-system then reconstructs the tree skeleton
with the same shape of spline function. This paper will fo-
cus on three essential elements, in particular: shape data
acquisition and modeling curved limb explained in Section
2 and random distribution of small branches around the
tree skeleton discussed Section 3.
2 Tlunk and Limb
The positional information data of a trunk and each limb
are acquired from a photo of lhe bonsai tree. The mea-
sured points are shown on a Figure la. Let the measured
data of a limb B; are
{(xt,yt,zt)...(r^,a*,2*)}. We can
then approximate data by a spline function 17,;(s), where
s is arc-length parameter. If we note the tangent vec-
tor of spline at point I,[(s), as t'(s) : (tt,,ly,t'.) then
the heading direction fI is rotated to tangent direction by
two rotations. First one about angle AQy around axis
U and second one about angle AC); around axis .L. Lo-
cal rotations AQu and AQ; measured in radiance can be
expressed in local coordinate system (U, L, H) as follows:
AQn - t'(s) ' E and' LQr: -t'(s) ' t7. Usually the ro-
tations around local coordinate axes have the syntax as
shown in Figure 1b. For example positive rotation about
angle a around [/ axis is noted as t(o).
Figure 1: a) Measured data points. b) Local coordi-
nate system (U, L, H) and. the rotation syntax.
3 Make branch
The algorithm approximating and framing a given spline
I%(s) using sequence of a local motions and rotations is
given below.
of cylindrical segments of length As. Rotations f,)u d7r,
are calculated by multiplying the vectors [/ ancl at cur-
rent position with the tangent vector of the curve i(line
Algorithm 1
| ffdefine W; \' curve ID *\
2 ffdefite I< 57.29 \* radians to degrees *\
3 Axiom: A(0, W;)
4 A(s,
W;):
{s'
:s*As}s' (l
5 {t' : (w;(s') - w;(s))/ll(W;(s') - wtls)
6 AOu:K*t'E
7 Ari.t-_-K*l.A] +
8 + (AQu) & (Ao;)F(as)A(a', I7,)
The parameter of the apex A represents the c posi-
tion measured as its arc-length distance from the
spline 171. The production (line 4 to 8) creates a isin of
then
sec-
6 and 7). The arc-length parameter s' should be
the total curve length I (line 4).
4 Small Branches
Small branches a,re distributed randomlv to
a density function ,\(s). Small branches Sener-
ated with standard L-system approarh as a
by Prusinkiewicz [1]. The algorithm for small
branches according to a given function I(s) is
below.
Algorithm 2
1 Axiom: A(0,0)
2 A(s, a):
{ s':s}As}s'(I
3 {"': a*As)(s); r: random numberl
4 ir(a'(rk r<)(s)) {flas=oI
5 else{a'
:a'-l;flag:f ;}}-+
6 F(As) B(fl.as) A(s',a')
7 B\flas) : flas:: Q --; 6
8 B(flas) : fl.as -= | -+ o
The first pararneter is the arc-length parameter.
ond para,rrreter represents the number of small anches
tion in
along the limb generated by apex A. The
line 2 to 6 creates the axis as a seouence of Fof
uence
anches
and
'in the
potential branch locations B. If the fl,ag
is one the
are generated.
5 Result and Conclusion
We have succeeded to model the trunk limbs
branches of a given bonsai tree. An example is
Figure 2.
Figure
References
[1] P.Prusinkiewicz, L. Miindermann, R. Kar
B. Lane "The use of posi,tional inf'
moileli,ng of plants," SIGGRAPH 2001
Con
small
vn in
ceedings,
ACM SIGGRAPH pp. 289-300, 2001 Pro-
ResearchGate has not been able to resolve any citations for this publication.
The use of posi,tional inf' moileli,ng of plants
  • P Prusinkiewicz
  • L Miindermann
  • R Kar
  • B Lane
P.Prusinkiewicz, L. Miindermann, R. Kar B. Lane "The use of posi,tional inf' moileli,ng of plants," SIGGRAPH 2001 Con small vn in ceedings, ACM SIGGRAPH pp. 289-300, 2001 Pro-