A new technique introduced by researchers from the Massachusetts Institute of Technology (MIT) could provide artists with enhanced control over their animated creations. This method uses mathematical functions known as barycentric coordinates, which define how 2D and 3D shapes can bend, stretch, and move through space. The procedure offers multiple options for barycentric coordinate functions, providing a flexibility that stands in contrast to existing methods.
The team behind this innovative method consists of Ana Dodik, lead author and graduate student specializing in electrical engineering and computer science; Oded Stein, Assistant Professor at the University of Southern California’s Viterbi School of Engineering; Vincent Sitzmann, Assistant Professor of EECS; and senior author Justin Solomon, an associate professor of EECS. Their research was discussed in depth at the recently-held SIGGRAPH Asia event.
Traditional animation methodologies involve encapsulating a complex character shape within a simpler set of connected points known as a cage. The challenge lies in determining how the character moves when the cage is altered, a motion dictated by the design of a particular barycentric coordinate function. However, the dimensions of the artistic concept of “smoothness” in mathematical terms can result in different functions. The new technique offers a generalized approach to enable artists to decide on or choose between smoothness energies that suit their preferences.
The system uses a special type of neural network to model the unknown barycentric coordinate functions. The neural network is capable of generating outputs that satisfy all the constraints, which are built into the network itself. By doing so, it minimizes concern about the mathematical aspects of the problem for artists.
The methodology also incorporates the concept of triangular barycentric coordinates, developed by German mathematician August Möbius in the 19th century, to accommodate the complex shapes encountered in modern animations. The team’s approach overlays the shape with virtual triangles connecting triplets of points on the edge of the cage. The neural network predicts how to combine the coordinates of virtual triangles to create a complicated yet fluid function, enabling artists to generate different types of movement until they achieve the desired result.
The technique has potential applications across a range of sectors including medical imaging, architecture, virtual reality, and computer vision to help robots understand how objects move in the real world. Looking ahead, the MIT team hopes to improve the speed of the neural network and integrate the technique into an interactive interface to allow artists to adjust animations in real-time. The development of this technology has been funded by several institutions including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the U.S. National Science Foundation, to name a few.
