Well that was my point really. The claim is that better results are provided than 4D (i.e., time-parameterized) intersection tests, to which I must raise an eyebrow. Perhaps the claim is for a closer estimate of the TOI...Erwin Coumans wrote: The main unknown of their approach is how they 'estimate' the first time of impact, rathern then what to do with this time.
Given a scenario where a closed-form solution does exist (e.g., translation w/o rotation or rotation w/o translation) its doubtful that there exists a faster method that provides more accurate results than simply performing the calculations for the exact solution.Erwin Coumans wrote: I guess they either subdivide the timestep until there are no large 'gaps' in the motion or they use an iterative approach like the pure linear version of raycasting against the Minkowski sum (Gino van den Bergen) or the angular extension (described in my draft).
That said, I'm interested in what kind of motions objects can simultaneously undergo in the situations they do handle, and what makes their method so fast/accurate. I'm sure its very interesting, to all of us here. Given that it is stated to not handle extreme rotations, it sounds like the performance relies on some rather unsafe assumptions on the bounds of motion. Such assumptions as could be enforced perhaps by subdividing timesteps...? Just my thoughts, without specific knowledge of the intersection tests used.
My work focuses on the many-body problem mostly, though I've been looking into more object-pair intersection tests lately, to make a more complete system all my own. Initially I worked with spheres, but that lasted only until I came upon Dave Eberly's Wild Magic code. I've debugged, optimized, and extended some of the collision detection code. I've provided it all to Eberly and some has been added to the main code base. The portions I use handle triangle meshes as well as numerous bounding volumes of course. TOI is calculated by solving for closed form solutions to intersections between translating objects, using hierarchies for efficient traversal of the geometry. I'd like to look into point-set and other implicit surfaces though, if anyone can suggest good collision detection papers on them.[/url]Erwin Coumans wrote: Dan, what method do you use to estimate or calculate the first time of impact? And which shapes do you support?