CSCI 590 Directed Research

Progress Report 2

L-Systems Tree and its Animation

By Tanasai Sucontphunt

Date: 3/27/2003

 

Contents

 

1)     The 3D Tree Model

2)     What’s Next?

3)     Wind Force Effecting the Tree

 

 

      Last time, we created the 2D tree with its branches and leaves. In the mean time, we also finished the 2D tree with its thickness with different colors and its growth over time. See figure 1.

      For now, we already finished 3D tree modeling using the same approach on 2D except adding Quaternion to rotate the branches and leaves in 3D, and adding the camera setting to view the object dynamically. See Figure 2.

      We will skip the detail of how to create the 3D tree from 2D tree since it’s pretty much the same concept except the programming issues (which take a lot of time to finish).

     

 

     

 

Figure 1: 2D Plant Growth

 

 

           

             

 

Figure 2: 3D Tree in different view

 

 

 

            Now, our idea of creating the tree is changed from animating the growth of the plant to be simulating the realistic of the plant instead. The reason behind this is the simulation of realistic tree seems to be more useful than the growth of slowly growth plant.

            Thus, the next work we plan to do is developing the wind force effect on the tree.

 

 

(Physically-Based Wind Force effects on Tree Animation)

 

            The major work of this part is the simulation of wind force effecting on the constructed tree. The wind force using here is based on physical force model [1].

 

Physical Wind force Model

            Since the branches of tree will be fixed on their length and some holding positions, we have to apply the force only on their angle positions so that they are changing over time. Also, their must restore to their previous position after the blow [3].

            The changing will apply to each branch on the tree by altering their angles which are the rotation of θ along the z axis of the parent and the rotation of angle φ along the axis y of the child.

 

            The wind primitive is defined by an area of influence (disk (C, r)), a force vector F and a pulsation w.

 

 

 

 

 

We use the torque as the wind force effecting on the branch. The equation is

           

           

Next, we have to add the damping force as the joint force (a parent and children propagation force) which is

           

           

So, the final equation of torque is

           

 

So that we can get the changing of angle which is

           

           

 

            Then, we use standard Euler's method to compute the angle θ at time t+dt which is

 

 

            The angle φ will calculate the same way.

we have to skip their details for concise content. For more information, please consult [1].

 

Reference:

 

1)      An interactive forest, Thomas Di Giacomo, St´ ephane Capo, Franc¸ois Faure.

(http://w3imagis.imag.fr/~Thomas.Di-Giacomo/research/egwcas01/paper/html/)

 

2)      Animation based on the Interaction of L-systems with Vector Force Fields, Hansrudi Noser, Daniel Thalmann, Russell Turner.

 

3)      Modeling and Animation of Botanical Trees for Interactive Virtual Environments, Tatsumi Sakaguchi, Jun Ohya.