建構在以L-System為基礎的植物模型上的階層式限制容積架構

在電腦圖學的領域中，有效且寫實的生成植物一直是個很重要的議題，目前植物生成的主流是使用L-System。L-System是根據文法對字串不斷的迭代，其中每個字元都代表了一個植物的部位。L-System不只能系統性的描述植物的外觀，還可以模擬植物和環境間的生長和互動。由於L-System擁有和樹狀結構相似的階層架構，利用L-System的’[]’機制，我們可以分辨植物的分枝並取出其中的資訊。在這篇論文中，我們提出一個根據上述L-System特性並建構在植物上的階層式限制容積架構，在系統裡，所有分枝的樹冠皆以簡單的幾何形狀來包覆，例如圓、圓錐、圓柱等；此外，任一分枝的限制容積皆是由其子分枝的限制容積計算而來的，藉此達成一個階層式的限制容積架構，以有效率地表達樹的外貌。最後，Level of Detail的觀念被直接且自然地整合進我們的系統，實驗顯示我們的系統能夠根據樹和使用者的距離，適當地調整解析度，並最終改善繪製如森林這般複雜場景的效率。

關鍵字

L-系統；細節層次；模擬；限制容積

並列摘要

In Computer Graphics, it has been an important issue to represent plants realistically and efficiently. To achieve this goal, the L-System is a popular way. L-System can not only systematically represent the appearance of plants, but also simulate the growth and interaction between plants and environment. This is done by iteratively expanding a grammar string, in which each letter of alphabet stands for an organ of a plant, with parameters. Moreover, because L-grammar has a hierarchical structure similar to a tree structure, by utilizing the bracket mechanism of L-System, the information of branches of plants can be effectively identified and extracted. In this research, we propose a system that constructs a bounding volume hierarchy of plants according to the above-mentioned properties of L-System. In our system, the tree-crowns of all branches are clustered and bounded by simple geometrical primitives such as spheres, cones, or cylinders, etc. In addition, the bounding volume of each branch is calculated from its sub-branch’s bounding volume so that the system can build a hierarchical bounding volume structure to represent tree-crowns efficiently. And then, our system randomly transforms the L-System structure with the extracted hierarchical bounding volumes to represent the variety of a forest. Finally, the concept of Level of Detail is naturally and directly integrated with our system. The experiment results show that our system can adequately adjust the visual resolution of each tree and crown according to the distance between them and the observer/camera, and consequently improve the efficiency of rendering the complex appearance of a forest.