An innovative technique introduced by MIT researchers could offer greater control to artists who create animations for films and video games. The researchers’ method revolves around generating mathematical functions known as barycentric coordinates. These coordinates determine how 2D and 3D shapes can stretch, bend and move in space.
This new technique is distinctive in its flexibility. Many other techniques are inflexible, offering only a single option for the barycentric coordinate functions specific to an animated character. However, this tool allows artists to customise these functions, enabling them to better realise their conceptual vision without having to start from scratch for each new adjustment.
The technique also has implications beyond its applications in animation. It could be utilized in areas such as medical imaging, architecture, virtual reality, and even as a tool to enhance computer vision and help robots understand how objects move in the real world.
In terms of the technical process, artists animate a 2D or 3D character by surrounding the character with a simpler set of points connected by line segments or triangles, known as a cage. The artist can move and deform the character inside the cage by dragging these points. The primary technical challenge is determining how the character moves when the cage is adjusted. This process is governed by the barycentric coordinate functions, which can differ in their interpretation of ‘smoothness’.
Rather than following traditional approaches, the researchers utilized a neural network to model the unknown barycentric coordinate functions. The flexibility of neural networks makes them optimal for handling the mathematical aspects of the problem. With the constraints directly built into the network, the generated solutions are always valid.
To manage the complexity and constraints of the barycentric coordinates, the method revolves around overlapping virtual triangles that connect triplets of points on the cage’s exterior. The neural network then predicts how to combine these coordinates to create a complicated but smooth function.
This method allows the artist to test one function, observe the final animation, and tweak the parameters to generate varying motions until the desired animation quality is achieved.
The future plans for this technique include strategies to speed up the neural network and also to integrate this method into an interactive interface. This would allow an artist to conveniently adjust animations in real-time. The research was funded by several entities, including the U.S. Army Research Office, U.S. National Science Foundation, and the Amazon Science Hub.
