Researchers at MIT have developed a new technique that gives animators greater control over their designs in animated films and video games. This method uses mathematical functions, known as barycentric coordinates, to define how 2D and 3D forms can bend, stretch and move in space. Animators, therefore, have the option to choose functions that fit their vision for an animated object or character.
Traditionally, animation techniques offer only a recommended set of barycentric coordinate functions for an animated character. This can cause inflexibility as artists cannot easily adapt the functions to achieve different aesthetics. Therefore, if an animator desires to try a slightly different look, they are forced to begin again with a new approach.
Ana Dodik, lead author of the project’s research paper, emphasized the importance of flexibility in artistic applications, hence the necessity for a more versatile option for barycentric coordinate functions beyond traditional methods. The new technique is also being considered for use in fields like medical imaging, virtual reality, and computer vision.
Dodik—an electrical engineering and computer science graduate—is part of the team responsible for the research alongside Assistant Professors Oded Stein and Vincent Sitzmann as well as the senior author and Associate Professor Justin Solomon. The team presented their research at SIGGRAPH Asia.
The new procedure allows artists to customize or select the ‘smoothness energies’ that are most desirable for any given form. Using a neural network, the team’s system models the unknown barycentric coordinate functions, successfully creating solutions that are always valid and satisfying all the constraints. This process enables artists to design captivating coordinates without concerning themselves with mathematical details.
The team established these groundbreaking methods by using triangular barycentric coordinates – a creation of German mathematician August Möbius in 1827— in combination with a neural network predicting how to compile these coordinates to form a more complex function.
With this technique, artists can test various functions, observe the resulting animations, and alter the coordinates to create different motions until they have a final product that aligns with their vision. For instance, they can create a cat’s tail animation that moves naturally instead of moving rigidly.
Moving forward, the researchers aim to enhance the process by developing strategies to speed up the neural network, as well as integrate the method into an interface that facilitates real-time animation iteration. The research project was boosted by funding from multiple institutions, including the U.S. Army Research Office, the U.S. National Science Foundation, and Amazon Science Hub, among others.
