Stochastic 3D tree simulation using substructure instancing
Tree growth is simulated using a stochastic model of organogenesis that is faithful to botanical knowledge. This model is based on the concept of bud "physiological age", on the statistical description of the transition from one physiological age to another as well as of bud death, bud growth and branching processes. In order to enhance simulation efficiency, a recurrent algorithm based on stochastic substructure instancing is proposed. The tree is hierarchically decomposed into substructures that are classified according to their physiological age, and a library of random substructure instances is constructed: the recurrent simulation starts with the simplest peripheral substructures, which are also the physiologically oldest; these substructures are then progressively assembled into more complex substructures, until the tree is completely simulated. When the size of the library of substructure instances is small, the time needed to build a single stochastic tree is much shorter than for a usual tree simulation that operates on a bud-by-bud basis. in computing a group of trees, the speed gain is even much greater, because the library of substructure instances is built for the first tree, and then is reused for computing subsequent trees. A preliminary sensitivity analysis is carried out according to the size of the library: when the library is large, the simulated distribution of the number of organs fits well with the theoretical mean and variance; the algorithm can thus be tuned in order to obtain accurate predictions. On the other hand, a small library (e.g., with only 2 or 3 instances for each substructure class) is sufficient for generating visually realistic trees. A few examples illustrate the high performance of this algorithm which paves the way for the fast simulation of large forest scenes.
| Summary: | Tree growth is simulated using a stochastic model of organogenesis that is faithful to botanical knowledge. This model is based on the concept of bud "physiological age", on the statistical description of the transition from one physiological age to another as well as of bud death, bud growth and branching processes. In order to enhance simulation efficiency, a recurrent algorithm based on stochastic substructure instancing is proposed. The tree is hierarchically decomposed into substructures that are classified according to their physiological age, and a library of random substructure instances is constructed: the recurrent simulation starts with the simplest peripheral substructures, which are also the physiologically oldest; these substructures are then progressively assembled into more complex substructures, until the tree is completely simulated. When the size of the library of substructure instances is small, the time needed to build a single stochastic tree is much shorter than for a usual tree simulation that operates on a bud-by-bud basis. in computing a group of trees, the speed gain is even much greater, because the library of substructure instances is built for the first tree, and then is reused for computing subsequent trees. A preliminary sensitivity analysis is carried out according to the size of the library: when the library is large, the simulated distribution of the number of organs fits well with the theoretical mean and variance; the algorithm can thus be tuned in order to obtain accurate predictions. On the other hand, a small library (e.g., with only 2 or 3 instances for each substructure class) is sufficient for generating visually realistic trees. A few examples illustrate the high performance of this algorithm which paves the way for the fast simulation of large forest scenes. |
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