Researchers from the Massachusetts Institute of Technology (MIT) have introduced a technique that could provide artists working on animated movies and video games greater control over their creations. The method employs mathematical functions known as barycentric coordinates, enabling 2D and 3D shapes to move, stretch, and bend in space according to an artist’s vision.
The new method is more flexible than previous techniques, which usually provided a single option for the barycentric coordinate functions for a specific animated character. If an artist aimed for a different look, they often had to start from scratch with a novel approach. “Artists want flexibility and to ensure their final product looks great. They aren’t concerned about the complex equations your algorithm solves,” says Ana Dodik, the lead author of a paper explaining the technique.
The technique could also find use in fields such as medical imaging, architecture, virtual reality, and even computer vision, acting as a tool for robots discerning how objects move in real life. The research team comprised Oded Stein from the University of Southern California’s Viterbi School of Engineering, Vincent Sitzmann, an assistant professor at MIT, and senior author Justin Solomon from MIT. The research was presented at SIGGRAPH Asia.
To animate a 2D or 3D character, artists typically encase the complex shape within a set of simpler points known as a cage, where the line segments or triangles connect. The movement of the character is determined by modifying this cage, using specifically designed barycentric coordinate functions.
However, the various forms of “smoothness” in art translate to diverse sets of barycentric coordinate functions mathematically. Therefore, the MIT researchers aimed to create a generalized approach allowing artists to select among smoothness energies for any shape. An artist can then preview the deformation and select the smoothness energy best suited to their vision.
The researchers utilized a special neural network to model the barycentric coordinate functions. The network architecture ensures that the created barycentric coordinate functions satisfy all constraints. This approach helps artists without requiring them to worry about the mathematical aspects.
Their method uses overlapping virtual triangles that connect triplets of points on the cage’s exterior to cover a shape. The neural network predicts how to combine these virtual triangles’ barycentric coordinates into a more complex, smooth function. This allows an artist to experiment with different functions and tweak the coordinates to create a desired animation.
In the future, the researchers aim to speed up the neural network and develop an interactive interface that would let artists easily modify animations in real time. The research was funded by several entities such as the U.S. Army Research Office and the National Science Foundation.
