## Posts

Showing posts from March, 2010

### Thoughts on shape casting

I implemented a different type of shape casting yesterday. The most common way, to my knowledge at least, is to do it with conservative advancement:
1) Run the GJK algorithm to find closest point to the origin in configuration space 2) Use the distance and angle to compute a safe estimate to move (cast) the configuration space object towards the origin, in the cast direction. 3) Repeat until below a certain threshold, or the direction to the origin is pointing away from the cast direction (in which case it is a miss).
Even though this is an iterative method, relying of GJK, which in itself is iterative, this is actually pretty fast, because it converges quickly, like two or three iterations and you can benefit from warmstarting GJK with the simplex from the previous iteration.
However, there is a completely different method, which I thought I came up with, but after googling it for a while it seems Jay Stelly has mentioned similar methods before across the Bullet and MollyRocket forums. Th…

### Greetings from the inside!

So after spending a few weeks outside the CSO, I got around to step inside and experiment with a number of different penetration distance algorithms this week. However, I failed to come up with an alteriative to EPA that can actually guarantee a global minimum separation. These are the ones I tried:
1) Use MPR to raycast the inside of the CSO in a direction estimated by the geometric center of the CSO, use the resulting normal and iterate until convergence. This works in 95% of all cases and is really fast. The downside is that there is no way to guarantee or measure if this really is the global minimum.
2) Same method as in 1) but use multiple search directions. I was for a while under the impression that two local minima had to be at least 90 degrees apart, so casting six rays should be safe (of which three can be optimized away). This works in 99% of all cases, but there is still that annoying one percent where it finds a local minima.
3) Same method as in 1) but trace the edges of th…

### Trapped in configuration space

I've spent the last couple of weeks tinkering with GJK and ended up rewriting it from scratch. Ever since I saw Casey's video about SAT-GJK a couple of years ago I've wanted to try it, so I finally did. Now Casey's video only deals with binary overlap status, not closest points, but it was relatively easily to extend his approach and even do a linear sweep operation. I especially like how his method does not include any divisions or square roots, which makes it very robust. I must add though that it's not straightforward to get a robust implementation that works on both polyhedra and quadric objects. Especially the termination criteria needed a lot of attention.

I knew from the beginning that decent visualization tools would be required to pull off a new GJK implementation, and it's certainly not trivial to visualize all the information needed. There are the two objects, the configuration space object, the simplex which comes in four flavors, normals, closest po…