Fast Algorithm for Stochastic 3D Tree Computation and Forest Simulation

MengZhen
KANG

National Laboratory of Pattern Recognition, Institute
of Automation

Chinese Academy of Sciences

100080 BeiJing 2728#

China

e-mail: mzkang@nlpr.ia.ac.cn |
http:// |

**Keywords:** Stochastic,
instancing, substructure, tree growth, 3D plant simulation

**Abstract**

In this paper, we simulate the stochastic tree growth based on an
organogenesis model faithful to botanical rules, in which we consider probabilities of
death, growth and branching, according to the law of occupation and transition
of the different states of the buds that corresponds to the botanical
notion “physiological age”. To promote simulation efficiency, an
algorithm based on stochastic substructure instancing is used. In that case, a
set of random substructures is simulated starting from the highest
physiological age to the lowest one, which is the main tree. The substructures are constructed by a recursive process. Since the size of the substructure set is
limited, the time to make a single stochastic tree is shorter than a usual bud-by-bud tree simulation, and even much quicker in constructing the second tree because the
substructure set are already done. So for a
forest simulation, a
lot of time can be saved. When the set size is big, the number of
organs produced fit well with theoretical mean and variance, which provides a
base for our algorithm. The set size decides the simulation accuracy, but for visualization, small set size like two or three is
sufficient. Examples are shown to prove the high
performance this
algorithm.