Researchers at MIT have developed a technique that could allow animators to have greater control over their characters. The method uses mathematical functions known as barycentric coordinates, which define how 2D and 3D shapes can bend, stretch, and move through space. This technique could provide artists with more flexibility in their animations, unlike previous techniques that often provided only a single option for the barycentric coordinate functions for certain characters.
The team’s methods even have applications beyond the animation industry, potentially being useful in areas such as medical imaging, architecture, virtual reality, and in computer vision to help robots understand how objects move in the real world. The research was a collaborative effort, involving experts from MIT and the University of Southern California’s Viterbi School of Engineering.
A typical method in both 2D and 3D animation involves surrounding a character with a simpler set of points, called a cage, from which the animator can manipulate movement and deformation. Barycentric coordinate functions dictate this movement. While traditional techniques often limit the smoothness of these movements, the MIT researchers’ approach allows artists to choose the smoothness energy that suits their particular artistic vision.
In contrast to earlier work, the team used a neural network to model the unknown barycentric coordinate functions. This allowed all constraints to be built directly into the system, freeing artists from dealing with the mathematical aspects of animation and focusing instead on the artistic aspects.
Drawing on mathematical concepts that are nearly two centuries old, the researchers applied overlapping virtual triangles that connect triplets of points on a cage. The neural network then predicts how to combine these virtual triangles’ barycentric coordinates to make a complex, smooth function.
This method liberates artists by allowing them to experiment with different functions, alter the coordinates, and play around with the animation until it aligns with their artistic vision. A significant advantage of using neural networks is the flexibility it provides to the artists.
The researchers demonstrated that their technique could produce more natural-looking animations, such as a cat’s tail smoothly curving as it moves. In the future, the team hopes to accelerate the use of the neural network, turn their method into an interactive platform for artists, and to make improvements in real-time animation. This project received funding from several institutions, including the U.S Army Research Office, U.S. Air Force Office of Scientific Research, and the MIT-IBM Watson AI Lab.
