Artists behind animated movies and video games may soon have greater control over their animations through a new technique devised by researchers at the Massachusetts Institute of Technology (MIT). The approach employs barycentric coordinates, mathematical functions that articulate how 2D and 3D figures can be manipulated through space.
Existing solutions are often limited, providing a single set of barycentric coordinate functions for each character. These may or may not be ideally suited to each animation. Any alterations to the desired look require a complete overhaul with a new method. Flexibility is crucial for artists. They aren’t typically concerned with the complex workings behind the scenes, focusing primarily on the final aesthetic of their product.
The team’s technique could serve a range of additional applications, including in fields such as medical imaging, virtual reality, architecture, and computer vision, which can help robots understand how objects maneuver in the physical world.
Animation artists often use a ‘cage’ comprised of straightforward points connected through lines or triangles, to wrap the complex shape of a character. The artist can then manipulate these points to move the character. How the character moves as the cage changes is determined by the specific design of a barycentric coordinate function.
Methods traditionally use complex equations to uncover cage-based movements that are ultra-smooth, avoiding any unusual alterations that might happen in the shape. However, there are various interpretations of how an artist’s concept of “smoothness” translates mathematically, each leading to a different configuration of barycentric coordinate functions.
The MIT team aimed to gain a broad perspective that grants artists the flexibility to define or select among smoothness energies for any shape. This enables the artist to preview the deformation and choose the smoothness energy that best suits their style.
The researchers’ method places overlapping virtual triangles onto a shape that connect multiples of points on the cage’s exterior. Each virtual triangle represents a valid barycentric coordinate function. The challenge comes in combining these. This is where the neural network is applied, predicting how to amalgamate the virtual triangles’ barycentric coordinates to form a more intricate, but smooth function.
Using this approach, an artist can experiment with one function, assess the final animation, then adjust the coordinates to create different movements until they find an animation that fulfils their vision.
The researchers demonstrated how their method could deliver more realistic animations than other approaches, creating animations like a cat’s tail that moves fluidly instead of stiffly.
Further research aims to test various strategies for accelerating the neural network. Other goals include developing this method into an interactive interface, allowing an artist to easily fine-tune animations in real time. The research was funded by a number of organizations, including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the U.S. National Science Foundation.
