  Step-and-project is a popular way to simulate non-penetrated deformable
bodies in physically-based animation. First integrating the system in time
regardless of contacts and post resolving potential intersections practically
strike a good balance between plausibility and efficiency. However, existing
methods could be defective and unsafe when the time step is large, taking risks
of failures or demands of repetitive collision testing and resolving that
severely degrade performance. In this paper, we propose a novel two-way method
for fast and reliable continuous collision handling. Our method launches the
optimization at both ends of the intermediate time-integrated state and the
previous intersection-free state, progressively generating a piecewise-linear
path and finally reaching a feasible solution for the next time step.
Technically, our method interleaves between a forward step and a backward step
at a low cost, until the result is conditionally converged. Due to a set of
unified volume-based contact constraints, our method can flexibly and reliably
handle a variety of codimensional deformable bodies, including volumetric
bodies, cloth, hair and sand. The experiments show that our method is safe,
robust, physically faithful and numerically efficient, especially suitable for
large deformations or large time steps.
