A new technique developed by researchers at MIT gives animators more control over their creations by generating mathematical functions that determine how 2D and 3D shapes can bend, stretch and move through space. These functions, called barycentric coordinates, provide enhanced flexibility as opposed to traditional methods that restrict artists to a single option for shape-motion functions. In consequence, artists can create animations that more accurately realise their creative intent without needing to concern themselves with the complicated mathematical aspects behind the technique.
The development of the technique, presented at the SIGGRAPH Asia conference, was spearheaded by Ana Dodik, a graduate student of electrical engineering and computer science, in collaboration with other researchers from MIT, the University of Southern California and the MIT Computer Science and Artificial Intelligence Laboratory. The researchers aim to use the technique in several other areas other than animation, such as medical imaging, virtual reality, architecture and robotics.
The traditional animation technique involves the use of a shape-cage, a simplified 2D or 3D outline consisting of interconnected points and triangles that can manipulate the enclosed character’s shape and positioning. The key technical issue here is determining how the character moves when the shape-cage is modified. This is resolved through barycentric coordinates developed from complex equations ensuring the smoothness of motion while minimising distortion.
MIT’s approach advocates flexibility in the design of barycentric coordinates. It enables artists to determine the mathematical representation of ‘smoothness’ that suits their creative idea, thereby offering them a larger say in crafting animations. This method also exploits the potentials of a unique type of neural network to generate barycentric coordinate functions that suit the constraints posed by complex 2D and 3D shapes.
This neural network, which functions as interconnected layers of nodes processing an input, outputs barycentric coordinate functions consistent with all constraints involved. As a result, artists are relieved from taking mathematical considerations into account. This makes it easier for them to conduct their creative process while being able to output an appealing animation.
The researchers used the concept of triangular barycentric coordinates to address the complexities of modern, non-triangular shape-cages. They proposed the creation of virtual triangles that extend across the cage’s exterior points to generate valid barycentric coordinate functions. These functions can then be integrated by the neural network to create a more intricate and smooth function.
The researchers also aim to expedite the neural network’s operation and integrate this method with an interactive platform enabling artists to rapidly modify and develop animations in real time. The research was funded by numerous organizations, including the U.S. Army Research Office, the U.S. National Science Foundation, and the MIT-IBM Watson AI Lab.
