Comp 236: Project Proposal

Comp 236: Course Project (Spring 2001)

Dynamic NURBS for String Motion Animation

By: Kelly Ward

[ Description | Goals | Previous Work and Novelty | References ]

First Update: March 7, 2001

Second Update: April 10, 2001

Final Report: May 10, 2001

Dynamic NURBS (NonUniform Rational B-Spline) or D-NURBS are a useful tool for modeling free-form shapes and curves. My goal for this project is to use D-NURBS to model "moving" curves, or it can be thought of as an animated model of the behavior of a string.

The use of NURBS in geometric design has many benefits including the ability to represent free-form curves, construct perspective views, and also create shapes such as conics and quadrics. D-NURBS allow a user to create physics-based models that can be changed or sculpted by the modeler by dynamically applying forces instead of relying on adjusting control points and weights. This ability can permit a more intuitive and predictable motion. A string is a very common and important object to model. It's motion or behavior can be used in countless number of places within modeling and animation (for example, modeling hair or a whip). There are many aspects to consider when modeling the motion of a string. The physical and geometrical constraints for the system have to be defined and the hard constraints that cannot be violated must be identified versus the soft constraints that have to be approximately fulfilled. The purpose of the project is to model the motion of a string as realistically as possible.

One of the main goals of the project will be to model a wave traveling or propagating across the string. In previous work, this has been done on a string that has two fixed endpoints (see previous work section). The next step will be to model this behavior on a string that has one fixed end and one free end. The challenges for these processes will be highly mathematical and physics-based. The wave travelling on the string will basically be a "moving curve."

Goals

Have one free end and one fixed end of the string - This proves to be challenging because if there is going to be physical accuracy it has been difficult to find the right set of equations so that the system is modeled accurately. Research has to be done to determine the best way to model this.
Three dimensional movement - As of now, the string with two fixed endpoints moves in two dimensions. Adding another dimension of movement will be especially desirable with a string with one free end and one fixed end.
Attach the string to a rigid body - As the rigid body moves, the string must move along with it. This behavior would be similar to hair; As a person moves his/her head, the hair must follow, but it still has it's own independent behavior.
Add more user interaction - This would allow the user to specify the motion of the string using either the mouse or keyboard. This simulation could imitate a person dragging a string across a table where the person is holding one end of the string and the rest of the string follows and moves and curves as the person specifies. As of now, with the two fixed endpoints, the user can create a wave and send it along the string. This ability can hopefully be extended to a string with one fixed endpoint and one free endpoint.
Demonstration - For the final demonstration I would like to be able to show the the use of the Dynamic NURBS in modelling hair or the behavior of a whip.

Previous Work and Novelty

Last semester I started my work on Dynamic NURBS for wave motion modeling for my

COMP 258 project

The work I had found in doing my research regarding Dynamic NURBS has been to use Dynamic NURBS to create specific shapes. The Dynamic NURBS allow users to interactively create these shapes in an intuitive manner. I have been using Dynamic NURBS instead to model a physically-based moving system. So, I had to integrate physics equations and real-world constraints into the Dynamic NURBS environment.

Extending the work as mentioned in the goals section will require continued work and research in this manner.

References

``Dynamic NURBS with Geometric Constraints for Interactive Sculpting,'' D. Terzopoulos and H. Qin, ACM Transactions on Graphics, 13(2): 103--136, 1994 (Special Issue on Interactive Sculpting).
``Dynamic Manipulation of Triangular B-Splines,'' H. Qin and D. Terzopoulos, Proceedings of Third Symposium on Solid Modeling and Applications (Solid Modeling'95), Salt Lake City, Utah, May, 1995, ACM Press, 351--360.