UT Dallas computer scientists have developed a technique to create 3-D images that finds practical applications of a theory created by a famous mathematician.
This technique uses anisotropic triangles triangles with sides that vary in length depending on their direction to create 3-D "mesh" computer graphics of more accurate approximations of the shape of the original object, and in a shorter amount of time than current techniques. These types of images are used in movies, video games and computer modeling of various phenomena, such as the flow of water or air across the earth, the deformation and wrinkles of clothes on the human body, or in mechanical and other types of engineering designs. Researchers hope this technique will also lead to greater accuracy in models of human organs to more effectively treat human diseases, such as cancer.
"Anisotropic mesh can provide better simulation results for certain types of problems, for example, in fluid dynamics," said Dr. Xiaohu Guo, associate professor of computer science in the Erik Jonsson School of Engineering and Computer Science whose team created the technique.
The technique finds a practical application of the Nash embedding theorem, which was named after mathematician John Forbes Nash Jr., subject of the Hollywood movie A Beautiful Mind.
"The underlying mathematics we used to solve this problem is rigorous and beautiful," Guo said. "Finding a way to use the theory in a practical application will have great impact in the field."
The computer graphics field represents shapes in the virtual world through triangle mesh. Traditionally, it is believed that isotropic triangles where each side of the triangle has the same length regardless of direction are the best representation of shapes. However, the aggregate of these uniform triangles can create edges or bumps that are not on the original objects. Because triangle sides can differ in anisotrophic images, creatin
|Contact: LaKisha Ladson|
University of Texas at Dallas