A team of researchers from MIT has introduced a new technique that allows artists of animated movies and video games to have greater control over the movement of their animations. Their method is rooted in mathematical functions called barycentric coordinates, which define how 2D and 3D shapes move, bend and stretch. This level of dynamic flexibility enables artists to mold the movements of characters and objects in animation to fit their creative vision rather than having to adhere to a predetermined set of functional options. The technique is not just applicable in the field of animation, but in other sectors as well, including medical imaging, architecture, virtual reality, and computer vision for robots.
Animation artists traditionally leverage a technique where the complex shape of characters are enwrapped in a simpler set of points, linked by line segments or triangles, referred to as a cage. The movement of the character is tied to the modification of the cage and its resulting motion is defined by the design of a specific barycentric coordinate function.
The MIT research team aimed for a more inclusive method, allowing artists to choose from various smoothness energies that best suits their preference. A neural network was used to model the unknown barycentric coordinate functions, contributing to a flexible design. The constraints are directly integrated into the network to ensure legality and validity of the solutions.
Building on the work of German mathematician August Möbius in 1827, the researchers overlaid the shape with intersecting “virtual triangles”. These triangles enabled them to connect triplets of exterior points on the cage to help generate more complex, yet seamless, functions. The research team utilised the neural network to predict how to amalgamate the virtual triangles’ barycentric coordinates, thereby creating a smoother function.
This new technique not only allows artists to experiment with different functions, but also make real-time changes to increase flexibility in achieving desired movements in animations. The researchers demonstrated how their method could create more natural-looking animations, such as that of a smoothly-curving cat’s tail.
Future work from the team will focus on enhancing the speed of the neural network and developing an interactive interface for artists to iterate on animations in real time.
The research, funded by several organisations including the U.S. Army Research Office and Google Research Award, was presented at SIGGRAPH Asia and highlights a significant advancement in providing artists with more flexibility when creating animations, potentially transforming the animation industry.
