Media artists who work on animated movies and video games could have more control over their animations, thanks to a new technique developed by researchers at MIT (Massachusetts Institute of Technology). This novel approach uses mathematical functions called barycentric coordinates to define how 2D and 3D shapes can move and change shape.
Currently, many techniques for defining motion and shape of animated objects provide only a single choice for the barycentric coordinates, which might not always meet the artist’s vision. The new technique gives the artists more flexibility by allowing them to preview the deformation and choose the change in shape that best suits their preference.
The research team includes Ana Dodik, an MIT graduate student of electrical engineering and computer science (EECS), Oded Stein, an assistant professor at the University of Southern California’s Viterbi School of Engineering, Vincent Sitzmann, assistant professor of EECS at MIT, and Justin Solomon, associate professor of EECS at MIT. The researchers presented their work at the SIGGRAPH Asia conference.
The standard method for animating a 2D or 3D character involves creating a simpler framework, or “cage”, around the complex shape of the character. The animator then moves and deforms this cage to animate the character. The new method allows the animator to choose the amount of smoothness of the change in shape, and preview the animation before choosing which option they prefer.
To find the best possible solution, the team utilized a special type of neural network that could model the barycentric coordinates while automatically ensuring they meet all the necessary constraints, thus removing the artists’ need to consider the mathematical aspects.
The team’s innovative approach draws inspiration from August Möbius’s geometric calculations dating back to 1827. To apply this to modern, complex shapes, the team generated a network of overlapping virtual triangles that cover the shape. The neural network then combines these triangles to generate a smooth function that dictates the movement and shape-change of the figure.
This method allows artists to try different functions, make adjustments based on the final animation, and repeat until they achieve the desired effect. The researchers showcased how this method can result in natural-looking animations, such as a smoothly curving cat’s tail.
Funded by various institutions including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the U.S. National Science Foundation, the team plans to further enhance their neural network and aim to create an interactive interface. This would allow artists to make real-time amendments, making the animation process even more flexible and efficient.
