Month: September 2016

XPBD: Position-Based Simulation of Compliant Constrained Dynamics

Miles Macklin, Matthias Muller, Nuttapong Chentanez

We address the long-standing problem of iteration count and time step dependent constraint stiffness in position-based dynamics (PBD). We introduce a simple extension to PBD that allows it to accurately and efficiently simulate arbitrary elastic and dissipative energy potentials in an implicit manner. In addition, our method provides constraint force estimates, making it applicable to a wider range of applications, such those requiring haptic user-feedback. We compare our algorithm to more expensive non-linear solvers and find it produces visually similar results while maintaining the simplicity and robustness of the PBD method.

XPBD: Position-Based Simulation of Compliant Constrained Dynamics

A Robust Method to Extract the Rotational Part of Deformations

Matthias Muller, Jan Bender, Nuttapong Chentanez, Miles Macklin

We present a novel algorithm to extract the rotational part of an arbitrary 3×3 matrix. This problem lies at the core of two popular simulation methods in computer graphics, the co-rotational Finite Element Method and Shape Matching techniques. In contrast to the traditional method based on polar decomposition, degenerate configurations and inversions are handled robustly and do not have to be treated in a special way. In addition, our method can be implemented with only a few lines of code without branches which makes it particularly well suited for GPU-based applications. We demonstrate the robustness, coherence and efficiency of our method by comparing it to stabilized polar decomposition in several simulation scenarios.

A Robust Method to Extract the Rotational Part of Deformations