MIT researchers have developed a new method to improve the control animators have over their animated characters. The technique involves the use of a mathematical function called Barycentric coordinates, that defines how both 2D and 3D elements can be manipulated in space. Unlike other techniques, this allows for more flexibility and leeway for creatives.
An important aspect of this development is that it offers multiple choices for Barycentric coordinate functions for an animated character. This change means that artists are no longer limited to a single design for their characters but can mold their animations to better fit their creative vision without having to essentially start from scratch for each different look.
This method could have wider applications including medical imaging, virtual reality, architecture, and even helping robots understand how objects move. The effective development of this technique is rooted in the inclusion of artists perspectives about flexibility and desired end product aesthetic during the research process. The researchers acknowledged that artists typically aren’t concerned with the complex equations that underpin the function of the systems, but more so the outcome.
In animation, a common practice is to manipulate a ‘cage’, a simpler set of points connected by line segments, to move and deform a 2D or 3D character housed within it. The challenge with this is defining how the character moves when the cage is altered. The team utilized a neural network to model the uncertain Barycentric coordinate functions using multiple layers of interconnected nodes, thereby meeting all constraints.
Building on the work of German mathematician August Möbius, who introduced Barycentric coordinates in 1827, researchers adopted the use of overlapping virtual triangles, a simple and efficient method in compliance with all necessary constraints, to represent more complex shapes. The neural network then predicts how best to combine the Barycentric coordinates of the virtual triangles into more complicated, but smooth, functions.
This research provides artists with a system that allows them to adjust and modify animations until they eventually achieve the desired outcome. Through the neural network, creatives now have a spectrum of flexibility not previously available. The team hopes to build the ability to interactively tweak animations in real-time into future versions of this method, significantly enhancing the usability of their research. The research was funded by a range of organizations including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the Singapore Defense Science and Technology Agency.
