Researchers at the Massachusetts Institute of Technology (MIT) have developed a technique that enables digital artists more versatility in how they move their animations of 2D and 3D shapes. Traditionally, artists had limited choices when it came to defining movements using mathematical functions known as barycentric coordinates.
The researchers suggest that existing solutions are rigid and despite the different look, a character might require they all use the same functions, limiting the artist’s control over the final outcome.
“Artists care about flexibility and the look of their final product. They don’t care about the partial differential equations your algorithm solves behind the scenes,” says Ana Dodik, lead author of a paper on this technique, adding that this new approach allows artists to select the functions that best fit their desired look.
In addition to its artistic applications, this unique technique could be instrumental in fields such as medical imaging, architecture, virtual reality, robots’ computer vision, and more.
When animating a 2D or 3D character, artists surround the complex shape of the character with a simple set of points connected by line segments or triangles, called a cage. The artist then moves these points to shift and alter the figure within the cage. One key issue is to ascertain how the character moves when the cage is adjusted; this motion is determined by the design of a specific barycentric coordinate function.
The research team’s unique approach provides artists the liberty to design or choose among smoothness energies for any shape. The artist can then preview the deformation and choose the preferred smoothness energy accordingly.
However, the design of barycentric coordinates is complicated. The calculations become especially disorderly when the cage isn’t a triangle. For complex shapes, each barycentric coordinate must meet a set of restrictions while ensuring smoothness.
In an innovative move, the researchers used a neural network to model the unknown barycentric coordinate functions. Unlike conventional uses of neural networks, this project uses them primarily for mathematical purposes. Artists can create interesting barycentric coordinates without worrying about the math behind it due to the constraints being built directly into the network.
Creating a mathematical bridge between modern cages and triangular coordinates — an idea almost two centuries old — the team’s method covers a shape with overlapping virtual triangles connecting triplets of points on the outer cage.
The neural network assists in predicting how to combine the virtual triangles’ barycentric coordinates to form a complicated but smooth function. This function enables artists to try one function, view the final animation, and adjust the coordinates to generate different motions until the desired effect is achieved.
Their method also demonstrated how their technique could generate more realistic animations, such as a smoothly moving cat’s tail instead of a rigid one.
The team has future plans to accelerate the neural network and develop an interactive interface to permit artists to easily iterate on animations in real time. The research is sponsored by several international science, defence and technology organisations.
