Tree Animation

To describe a virtual tree and its motion is a long run topic in the computer graphics filed. The research for shaping a tree is well done by the previous result and there are some mature theories to backup it. We have accepted the methods that are made of fractal and stochastic technology to create virtual trees for our system. For the shaping is not the major task in our system, we can use some shaped trees that are created by others systems to motivate it in a virtual environment.Though the research for the tree shaping is matured, the research for the motion of the tree is on the stage of very beginning. This paper summarizes the experience of the previous work, builds a better system and pushes the direction to move toward. There are three major drawbacks of all the work for the tree animations. The first, no work has created a precise physical model. There are many phenomena that can be explained by the physical law, but be substituted by some stochastic functions. Therefore, the right results cannot be presented. As to this problem, we designed a more reasonable model with a complex pendulum model. Since the complex pendulum model is more precise than the traditional single pendulum model, the analysis of the model is difficult. We resolve it in a numerical way. The second, most of the previous works cannot satisfy the interactive, realizing and real-time request at the same time even though in the single pendulum assumption. Now we increase the complexity of the model so that satisfying the three requests is a real challenge to our system. We choose the numerical method with implicit integration to solve the system. The numerical method makes the system easy to interact and the implicit integration makes the computation convergent quickly. Then to make the system quick enough, we abandon the traditional way to solve the complex pendulum based on the energy, and use a new way based on the force analysis to make the simplification of the computation possible. At the same time, we design a new way to make the tree shape adjust with the distant between the tree and the viewer, called Level of Detail (LOD) and a new way to simplify the computation of the tree's motion, called progressive motion. With such design, we can simplify the computation when the viewer is moving away from the tree. Then the cost of the computation to the roam in the virtual system decreases. The tree shape LOD is brought out by the previous work and we design a total new way to approach it and the concept of the progressive motion is created in this paper first time. We developthe simplification from the shape to the motion. Our system can be called real-time with 20 f/s and can be controlled by the user without any confine and any sense of time-lapse based on the technologies presented above. The last, most of the previous systems cannot provide the tree related animation, such as the branch broken and the leave flying. The tree animation is related to a virtual environment. If the moving object is only the tree itself, the animation cannot be felt realized by the user. So we describe such related physical phenomena with some simply physical theory and realize them with the animation of the tree. With some simplification, we can make them little influence in the computation efficiency. In the system, some other technology, such as the pre-computation of the vertex and making the computation more convergent with adjusting the damping coefficient, are also included to make the system more successful.We have provided the contrast between our system and one typical previous system to show the improvement and the contribution of our work. At last, we bring out some shortcomings of our system and discuss the possible solutions to show the way to promote our system furthermore.