PhD candidate Ryusuke Sugimoto and Professors Christopher Batty and Toshiya Hachisuka have won a best paper award at SCA 2022. The 21st ACM SIGGRAPH / Eurographics Symposium on Computer Animation took place virtually and in person this year at Durham University in the United Kingdom from September 13 to 15.
In their paper, “Surface-only dynamic deformables using a boundary element method,” the research team developed a novel method to simulate elastic objects using only computations that directly deform their surfaces. Importantly, the new method does not need to rely on complex volumetric calculations, which opens many interesting directions for further research in the field.
More about this award-winning research
Physical, dynamic simulation of elastic objects — what’s known as elastodynamics — is used widely in computer animation. Most simulation methods discretize an object into a volumetric mesh of tetrahedral or cubic elements. The simulation then processes both the surface of the object as well as its interior. But if a computer animator is concerned only with the visible motion of an object’s surface, complex calculations of its interior motion may not be needed.
“We developed a surface-only dynamic deformables simulation method suitable for computer animation,” says Ryusuke Sugimoto, a PhD candidate at the Cheriton School of Computer Science advised by Professors Christopher Batty and Toshiya Hachisuka. “As it’s a surface-only method, it does not need any volumetric discretization.”
The method builds on advances in what’s known as BEM, the boundary element method. BEM can solve partial differential equations while discretizing only the surface of the object.
“Although BEM is used for a few applications in computer animation, we are the first group to solve elastodynamics simulations using BEM in computer animation,” Ryusuke explains. “The thinking behind elastodynamics BEM is that we can express deformation at a point on the surface of an object by considering a superposition of elastic waves propagated from all surface points over time.”
This is achieved mathematically by solving a boundary integral equation for linear elasticity. This boundary integral equation is an integral over the object’s surface, so only the surface of an object needs to be discretized. This boundary integral equation for elastodynamics involves convolution over time to account for past motion, leading to a recursive matrix equation after discretization. However, simply employing BEM for elastodynamics would not result in a practical method.
“The first problem is that directly solving the boundary integral equation in a static frame results in artifacts because of the limitations of linear elasticity,” Ryusuke said. “We introduce a moving frame of reference and additional fictitious forces in BEM. This approach ensures that BEM only needs to look after the local deformations, which allow for large global translation and rotation and lead to better numerical stability.”
“The second problem is the cost associated with dense matrix construction and algebra,” Ryusuke continued. The team developed a compression method tailored to the dense matrices in BEM for elastodynamics. “Our compression method significantly reduces both the computational and memory storage costs by exploiting the smoothness of the integrands in the boundary integral equation.”
Last, the team developed a strategy to use BEM for simulating complex interactions of objects such as frictional contact.
“We incorporate a constraint enforcement strategy that enables frictional contact and domain decomposition to support more complex scenarios,” Ryusuke said. “Our method goes beyond a simple application of BEM to elastodynamics animation by tackling these three problems, and I am excited to see the further development of surface-only deformable simulations.”
To learn more about the award-winning research on which this article is based, please see Ryusuke Sugimoto, Christopher Batty, Toshiya Hachisuka. Surface-only dynamic deformables using a boundary element method. Computer Graphics Forum (Proceedings of the 21st ACM SIGGRAPH / Eurographics Symposium on Computer Animation), 2022, Volume 41 (2022), Number 8.