CREATION OF THE TREE MODEL ADAPTING TO ENVIRONMENT

Transcription

1 CREATION OF THE TREE MODEL ADAPTING TO ENVIRONMENT Ryota Ueno Yoshio Ohno {ryota Graduate School of Science and Technology, Keio University Hiyoshi, Kohoku-ku Yokohama Japan ABSTRACT: In this paper, we propose a new technique for modeling trees being affected by the environments. We consider four factors: collision with other branches, amount of sunshine received, heliotropism, and avoidance of other objects (rectangular parallelepiped and cylinder). We show some results and evaluate them by comparing with existing trees. Keywords: tree, L-system, heliotropism, obstacle avoidance, collision detection 1. INTRODUCTION Recently, the need for modeling real objects has increased with the advance of computer graphics technology. Among the objects, automatic modeling technique of trees is requested often because of the complexity of their structure and the familiarity to humans. A lot of researches have been done, but most of them aim at the creation of individual tree model and the influences of the other trees or objects that stand close to the target are not considered. In real world, the space where trees can grow up freely without being influenced by other objects is rare. The subject of this paper is to create tree models for an environment automatically by considering the environmental factors that influence the structure of the tree. We consider the following four environmental factors: (1) collision of branches, (2) the amount of sunshine received, (3) heliotropism and (4) the avoidance of other objects. By using this method, we can make more natural tree models than before easily in scenes where trees contact with other objects. 2. PREVIOUS WORKS There have been various approaches for the modeling of trees. Some researches are based on the measurement data of existing trees; others rely on some procedure. The most famous and effective research of the latter approach would be the L-System [2]. By using this system, various trees, grass, and flowers can be modeled. However, it does not consider the affect of environments. In the real world, every tree receives the affect of ground shape, sunshine, other objects, and the branches of itself. The method for creating tree models considering the collision with other branches and the amount of sunshine received was introduced by Radomir Mech et al. [1]. However, there are some problems in this research: * The bend of branches is not presented because the environmental factors are considered only at branching points. * When a branch collides with other branches, the growth is stopped. It is difficult to present the avoidance of other objects. When a branch collides with other branches, the growth will be stopped because that point is occluded from the sun by leaves. But when a contact with other objects happens, the branch may grow further if the point is in the sunshine. 3. APPROACH 3.1 Light Sources We put several light sources on the orbit of the sun to represent the influence of the position of the sun on the structure of trees. As an average over a year, we assume the sun's orbit on the vernal and autumnal equinox when the angle of the sun on the south is 54.5 degree (see Fig. 1). Each light source is given the intensity that is proportional to its height.

2 Fig. 1 Arrangement of light sources. 3.2 Tree Models We model a tree using a modified L-system. We extended the original L-system to consider the environmental factors. L-system can create the fractal objects easily by applying rewriting rules recursively. It is effective to use L-system because branches diverge in rules determined by the type of the tree. 3.3 Algorithm The flow of our algorithm is shown in Fig. 2. The first step is the specification of growth procedure and the values of necessary parameters for the L-system. During the application of rewriting rules, the collision between branches and the amount of received sunshine are checked, and if the growth termination criteria are satisfied, we stop the growth of the branch. Then we decide the angle of the branch taking heliotropism in consideration. Check of collision with obstacles comes next. In our current implementation only the obstacles of rectangular parallelepiped (for a building and a wall) and cylinder column (for a utility pole) can be specified. When we detect a collision, we decide the contact point using a cantilever model. After decided the shape of a tree, the rendering is done using POV-Ray. 4. ENVIRONMENTAL FACTORS 4.1 Collision with Other Branches, and Amount of the Sunshine Received We find the collision with other branches and calculate the amount of sunshine received by putting spheres that approximate collections of leaves on the branching points. When a sphere contacts with other spheres, the growth of the branch is stopped because it means a collision with other branches. The effect of this process is shown in Fig. 3. In this figure, the difference can Fig. 2 Flow of our algorithm. be seen in the crowded area. Growth of some branches is stopped because of the collision with other branches. Fig. 3 Generated tree models with (left) and without (right) the collision detection with other branches. We calculate the amount of sunshine received by casting rays from the branching point to the light sources and judge whether the rays intersect with other spheres or not. By judging with every light source, we decide the amount of sunshine received at the branching point. The influence of sunshine is expressed by reflecting the amount of sunshine to the length of the branches growing from the point. The effect of this process can be seen in Fig. 4.

3 Fig. 4 The affect of sunshine. The left model considers the amount of sunshine received for each branch; the right model does not. Some branches of the left model have been trimmed in the crowded area. 4.2 Heliotropism The heliotropism is the property of trees to direct the branch toward the sun. In this paper, the heliotropism is applied on the middle point of a branch to represent the bend of branches. We change the branch's growth direction a little bit toward the most intense light source among the light sources whose light reaches the point. To realize that, we modify the growth direction vector u to u by rotating small angle θ along a direction that is perpendicular to u and the light source direction s (Fig. 5). In this computation, we considered the light source which gives the largest amount of sunshine to this branch only. The effect of this process can be seen in Fig. 6. Fig. 6 Generated tree model with (left) and without (right) heliotropism. We assume that the sun is on the left side. Fig. 7 Branches avoiding obstacles. 5.1 Avoidance of a Rectangular Parallelepiped When a branch contacts with a rectangular parallelepiped, it grows up along the surface. Therefore we keep the parallel component to the surface in the direction of the growth, and change the perpendicular component toward the direction along the surface. We show the affect of this process in Fig. 8. Fig. 5 Model for heliotropism. 5. AVOIDANCE OF OBSTACLES The shape of a real tree that contacts with obstacle objects is shown in Fig. 7. From this figure, we can observe that the branches collided with obstacles continue to grow with bending their direction. We simulate this using cantilever model to decide the amount of bending. We deal a rectangular parallelepiped and a cylinder column as obstacle objects. Fig. 8 Generated tree models with (left) and without (right) collision handling with rectangular parallelepiped obstacle. In the right model, the growth of a bramch is stopped when it touches to an obstacle. 5.2 Avoidance of a Cylinder Column Fig. 9 shows a real tree that collides to a cylinder object. In case of avoidance of a cylinder column, the direction of the growth depends on

4 candidate contact points and comparing the angle to the maximum bending angle at each point (Fig. 11). The effect of this obstacle avoiding algorithm is shown in Fig. 12. Fig. 9 A tree colliding to a utility pole. the elasticity of the branch (Fig. 10). Therefore we must decide the contact point with the column. Fig. 11 Determination of bending angle. Fig. 10 Affect of elasticity to the position of contact point. Left figures shows a hard branch, and right figure is a soft branch. We decide the contact point using the knowledge of material and mechanics and regard branches as cantilever beams. A cantilever beam is a beam whose one end is fixed and the load is put on another end. The maximum bending angle is given by i max σ = E max l d i max σ max is the allowable bending stress, E where is Young modulus, I is the distance from the fixed edge and d is the diameter of the beam. Because both σ max and E are decided depending on the material, i max is proportional to the length of the beam and is inversely proportional to the diameter of the beam. We decide the contact point by moving the Fig. 12 The effect of cylinder pole avoidance algorithm. The left column figures use the algorithm; the right column figures just stop growth when collide to an obstacle. View points are in East direction (top figures), and in Northeast direction (bottom figures). 6. RESULTS We show a ginkgo model colliding to obstacles in Figs. 13 and 14. From Fig. 14, it is observed that our method can create a tree model that is suitable in the environment. The computation time is summarized in Table 1. We used a PC with Pentium M 1.70GHz and 512MByte memory. OS is Windows XP professional. We used POV-ray 3.6 for the rendering.

5 Fig. 13 A ginkgo model avoiding a cylinder pole. Recursion depths are 3 (top) and 4 (bottom) for the tree model generation. Table 1. Computation time for the situation shown in Fig. 14. Rec. Depth Modeling Rendering sec 18.6 sec sec 89.1 sec 7. DISCUSSION We proposed a method for automatic creation of tree models adapting to the environment. We considered the collision with other branches, the amount of sunshine received, heliotropism, and the avoidance of obstacle objects as the environmental factors. This method makes it easy to create tree models in various scenes. We still have some problems that should be solved. Fig. 14 A ginkgo model avoiding two obstacles. Recursion depths are 3 (top) and 4 (bottom) for the tree model generation. First, there are other factors that influence the structure of the trees, for example the soil, the root. We have to study the plant ecology and find the relationship between these environmental factors and the structure of the trees. Second, we dealt only a rectangular parallelepiped and a cylinder column as obstacle objects. There are other obstacles in real world. We need to establish the system that can deal them collectively. Finally, we need to use the parameters of the real tree in the modeling of a tree. In this paper, the length of a branch is proportional to the amount of sunshine received. But in real world, a branch would be stopped when the amount of sunshine received is smaller than the specific value. We have to find the function of the length of the branch and the amount of sunshine received.

6 ACKNOWLEDGMENTS This work is supported in part by a Grant in Aid for the 21st Century Center of Excellence from the Ministry of Education, Culture, Sport, Science and Technology in Japan. REFERENCES [1] Aristid Lindenmayer, Mathematical Models for Cellular Interaction in Development, Part I and part II, J. Theoretical Biology, Vol.18, pp , [2] Aristid Lindenmayer, Przemyslaw Prusinkiewicz, The Algorithmic Beauty of Plants, Springer-Verlag, New York, [3] Oliver Deussen, Pat Hanrahan, Bernd Lintermann, Rodomir Mech, Matt Pharr, Przemyslaw Prusinkiewicz, Realistic Modeling and Rendering of Plant Ecosystem, SIGGRAPH 98 Proceedings, pp , [4] Radmir Mech, Przemyslaw Prusinkiewicz, Visual Models of Plants Interacting with Their Environment, SIGGRAPH 96 Proceedings, pp , [5] Katsuhiko Onishi, Shoichi Hasuike, Yoshifumi Kitamura, Fumio Kishino, Interactive Modeling of Trees by Using Growth Simulation, Proc. ACM Symp. Virtual Reality Software and Technology, pp.66-72, 2003.