MIT researchers have introduced a new technique that will give artists more control over their animations. This method generates mathematical functions, called barycentric coordinates, that allow artists to bend, stretch, and move 2D and 3D shapes as they see fit. This could be useful for animated movies, video games, medical imaging, architecture, virtual reality, computer vision, and robotics. The researchers, Ana Dodik and others, say their technique provides artists with the flexibility and control they desire when animating characters. The team used a special type of neural network to model the barycentric coordinate functions, which allows artists to easily iterate on animations in real time. This project was funded by various organizations and companies including the US Army, US Air Force, National Science Foundation, and more.
This Generalized Approach is Modern and Groundbreaking for Design and Visualization
The researchers sought a general approach that allows artists to have a say in designing or choosing among smoothness energies for any shape. Then the artist could preview the deformation and choose the smoothness energy that looks the best to their taste. The barycentric coordinates that make this all possible were first introduced nearly 200 years ago by the German mathematician August Möbius. The researchers’ method covers a shape with overlapping virtual triangles that connect triplets of points on the outside of the cage. They then used a special type of neural network to model the unknown barycentric coordinate functions.
Virtual Triangles and the Practical Perspective
The researchers drew on the triangular barycentric coordinates Möbius introduced nearly 200 years ago. These triangular coordinates are simple to compute and satisfy all the necessary constraints, but modern cages are much more complex than triangles. The researchers pioneered on a method that would cover a shape with overlapping virtual triangles that connect triplets of points on the outside of the cage. Each virtual triangle defines a valid barycentric coordinate function. Using their method, an artist could try one function, look at the final animation, and then tweak the coordinates to generate different motions until they arrive at an animation that looks the way they want. From a practical perspective, the researchers believe the biggest impact is that neural networks give you a lot of flexibility that you didn’t previously have. They also demonstrated how their method could generate more natural-looking animations than other approaches. They want to try different strategies to accelerate the neural network and build this method into an interactive interface. This research product is funded by various organizations and companies including the US Army, US Air Force, and National Science Foundation.