Researchers from MIT have developed a technique that provides animation artists greater flexibility and control over their characters. Their approach generates mathematical functions known as barycentric coordinates which define how 2D and 3D shapes can bend, stretch, and move. This change allows artists to choose functions that best suit their vision for their characters, offering flexibility that was lacking in previous methods.
In the past, animators would need to start over with a new approach for every minor change they wanted to make, but this new technique allows them to modify and create more natural-looking animations without worrying about the mathematical details. Artists don’t concern themselves with the algorithms, rather they care about adapting the appearance of their final product.
Beyond its artistic uses, the technique could also be beneficial in fields such as medical imaging, architecture, virtual reality and robotics. The particular advantage of this method is that it allows artists to consider the smoothness of the animation according to their own taste, offering them the opportunity to preview the deformation and select their preferred smoothness energy.
One of the key problems to address was how the character reacts when the cage – a simpler set of connected points and lines that surrounds the complex character shape – is modified. This is determined by the design of a specific barycentric coordinate function. Using a neural network to model the unknown barycentric coordinate functions, the team’s network architecture was built to output functions that satisfy all constraints. It enabled artists to design barycentric coordinates without fretting over the mathematical constraints.
To do this, the team drew from the triangular barycentric coordinates introduced by German mathematician August Möbius in 1827. They covered the shape with overlapping virtual triangles connecting triplets of points on the outside of the cage. The barycentric coordinate functions from each of these virtual triangles were then combined using the neural network to create a smoother, more complex function.
The team has managed to demonstrate their method’s ability to create more natural-looking animations like a smoothly curving cat tail. They now aim to speed up the neural network’s operations and integrate their method into an interactive interface that would allow artists to experiment with animations in real-time. The research was backed by various entities including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the U.S. National Science Foundation.
