Wednesday, April 27, 2011

Basics and not so basic. Also, names are good.

I've decided to skip the additional research I have been doing while reading through A Unified Framework for Rigid Body Dynamics.  After reading about a certain subject, I would read about the same subject in the various programming books I own (Game Physics, Real-Time Collision Detection, etc.).  While this allowed me to gain a firmer understanding of the subject, I found that I would forget too much of the information by the time I got back to the thesis (or after learning the next subject).

Half of the day was spent in review for the most part.  I was reading through chapter 2, which covers essential areas of physics.  My experience with physics has been in 2D up till now, so I can't say that I didn't learn anything new though.  In particular, finding a useful definition of "tensor" was surprisingly difficult.  I eventually worked out that it is actually another way of saying array:  a "2nd-order tensor" means a 2D array like A[4][7], a "1st-order tensor" means a 1D array like A[20] and a "0-order tensor" is just a normal scalar.  It pretty much continues on like this with 3rd-order etc.

Another useful tid-bit I learned was that "skew-symmetric matrix" is another name for "cross-product matrix".  It might just be me, but I had some difficulty figuring out what a "cross-product matrix" was.  Performing a quick Google search now that I know this, the answer is more obvious...  Hindsight apparently is 20/20.

Chapter 2 also introduced the linear complementarity problem.  While familiar with the name (particularly as "LCP"), I don't have very much knowledge of what it actually is.  The introduction was very brief, but I came away from it being a little less scared of the ominous "LCP" which inevitably pops up when reading about physics simulation.

Chapter 3 was where things became really interesting for me.  I wish I had known about this book last year when I was researching physics simulation!  It's exactly what I was looking for: It discusses the different "modules" of a physics simulation, gives them names, and discusses some popular ways of using them (and gives them names as well).  The "Explicit Time Step Method" is pretty similar to what I have been thinking of using, so I will likely use that one.

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