A new technique introduced by MIT researchers promises artists greater control over the animations of heroes and villains in animated movies and video games. The method generates barycentric coordinates – mathematical functions that define how 2D and 3D shapes can move, bend, and stretch in space. This allows an artist to shape the motion of a character to fit their creative vision.
Other techniques usually offer a single barycentric coordinate function for a specific animated character, limiting an artist’s ability to create a different look without starting from the beginning. The new technique offers a more flexible range of coordinate function choices, depending on the artist’s particular vision for an animation.
Ana Dodik, lead author of the paper, emphasized that the focus was to give artists more flexibility and control over their final product. The technique could also be used in other areas like medical imaging, architecture, virtual reality and computer vision, helping robots analyze how real-world objects move.
Artists animate characters by surrounding complex shapes with a simpler set of connected points or triangles known as a cage. Modifying this cage allows deformation of the character inside. The technique to determine how the character moves when the cage is changed is complex, but the MIT researchers wanted to allow artists to choose or design their own smoothness energies. The artist can then preview the deformation and select the energy pattern that they find aesthetically pleasing.
The team diverged from traditional methods and used a special type of neural network to model unknown barycentric coordinate functions. The network processes the input using many layers of interconnected nodes, allowing for output of functions that satisfy all required constraints.
This process helps artists design appealing barycentric coordinates without having to concern themselves with their mathematical aspects. The researchers relied on triangular barycentric coordinates to simplify computations. The modern cages are more complex than simple triangles and are therefore overlaid with virtual triangles connecting triplets of points on the cage’s outside.
To combine the virtual triangles, a neural network is used that predicts how to blend the coordinates to create a more intricate yet smooth function. The technique was demonstrated by the researchers by creating smoother animations than previous methods, featuring a cat’s tail that curves smoothly instead of folding near the cage’s vertices rigidly.
In the future, the researchers plan to develop strategies to speed up the neural network and incorporate the method into an interactive interface that will allow artists to easily iterate on animations in real-time. The research was partially funded by many sponsors including the U.S. Army Research Office, the U.S. Air Force Office of Scientific Research, and the U.S. National Science Foundation among others.
