Researchers at MIT have developed a technique which provides an updated approach to creating animations and could deliver more control to artists. The technique uses mathematical functions known as barycentric coordinates, which dictate how 2D and 3D shapes interact with space, introducing possibilities for curvature and movement. Current techniques tend to offer limited flexibility, generally providing one option for barycentric coordinate functions for each animated character. However, the lead author of the paper, Ana Dodik, argued that artists need flexibility and control over final look, rather than only being concerned with the maths powering the animations.
This technology has the potential to be applied in various fields such as medical imaging, architectural design, virtual reality, and computer vision to aid robots in understanding how objects move in the real world. The research was undertaken by Dodik, an electrical engineering and computer science (EECS) graduate student, alongside Oded Stein, assistant professor at the University of Southern California’s Viterbi School of Engineering, Vincent Sitzmann, assistant professor of EECS, and Justin Solomon, an associate professor of EECS.
The team’s approach towards barycentric coordinates enabled artists to preview and select the smoothness energy that best suits their vision. They used a specific kind of neural network to model unknown barycentric coordinate functions. The network was built to understand how to output barycentric coordinate functions that comply with all constraints, freeing up artists to focus on the aesthetic rather than the mathematical challenges.
The team utilized triangular barycentric coordinates, which were easily computed and met all constraints. They then covered a shape with overlapping virtual triangles that linked triplets of points on the outside of the cage. The neural network learned how to blend the different coordinates to form a complex but smooth function.
Demonstrations of the method have shown that it can generate more organic animations than existing techniques, such as an animated cat’s tail that curves naturally when moving, as opposed to rigid movements informed by a cage’s vertices. Looking ahead, they aim to explore different strategies to accelerate the neural network, and potentially build it into an interactive interface for real-time iteration on animations.
