A team of MIT researchers has developed a new technique that gives animators greater control over their creations in video games and animated films. Their method uses mathematical functions known as barycentric coordinates, which determine how 2D and 3D shapes can bend, stretch, and move within a given space. This offers a significant improvement to previous techniques, which offered only a singular option for how an animated character can move.
Often, researchers work to solve artistic problems without consulting artists, disregarding the creativity inherent to such tasks. This innovation ensures artists can maintain greater flexibility and control over the eventual look of their creations. The method has broad applicability across industries such as medical imaging, architecture, virtual reality and computer vision for robotics.
The research was executed by a collaborative team of graduate students and professors across the field of Electrical Engineering and Computer Science, including MIT CSAIL’s Scene Representation Group and the USC Viterbi School of Engineering. Their work was presented at SIGGRAPH Asia.
In animation, artists traditionally would create a ‘cage’ of line segments or connected points around their character or object, then manipulate the points to animate the form within. Barycentric coordinate functions determine how these forms will move when their ‘cage’ is modified. The MIT research provides a more flexible approach, enabling artists to select from various types of “smoothness energies” to best fits their desired outcomes, allowing them to design different motions for more natural-looking animations.
The researchers used a sophisticated type of neural network to model the barycentric coordinate functions. This neural network can output functions which satisfy all constraints, making it easier for artists to design coordinates without considering complicated mathematical problems.
Simplifying the handling of barycentric coordinates, which date back to August Möbius in the 19th century, was not without its challenges. Creating these coordinates for complex ‘cages’ is a complex process, requiring each coordinate to meet stringent constraints along integrated mathematical smoothness.
The team resolved this by overlaying given shapes with barycentric coordinate-based virtual triangles, creating smooth and valid functions for complex shapes. The neural network utilised by the researchers combines the virtual triangles’ coordinates to generate a more complex, smoother function.
This new approach revolutionizes the animation process, granting artists the ability to iterate their animations in real-time, retain a high degree of flexibility, and generate more natural-looking results. In the future, the MIT team is looking to accelerate the neural network and build an interactive interface for this method, while exploring funding from a range of sources including the U.S. Army Research Office, the CSAIL Systems that Learn Program, and the Singapore Defense Science and Technology Agency among others.
