SIGGRAPH has to be the most prestigious conference for graphics research. While preparing for my talk last week, I came across this incredible resource for papers on the web. This is in many ways so much better than the official conference proceedings (links to the official homepages for example.)
My talk at the CUMC last week was well received. It so happened that it was scheduled on the last day — I got a chance to see some of the other presentations and assess the level of depth presented.
I was surprised to see that variational calculus and some analysis material is optional in the undergraduate curriculum, but we’ll debate that some other day…
The problem with conferences is that you tend to become mentally exhausted towards the end of four or five days of absorbing information non-stop.
Anyways, check out the outline of what I presented, geared towards a general audience. Someday, I’ll learn how to upload presentations…
Some random math facts that I came across last week.
The Special Euclidean group combines rotations and translations in Euclidean space. The SE group is an isometry, which means it preserves angles and distances.
In special relativity, the 4-vectors are three space variables and one time variable. Rotations in this space can be generalized to the Poincaré group. Instead of having sines and cosines in the rotation part as in SE, they have hyperbolic sines and cosines.
The norm of a vector is defined through its inner product:
which in special relativity is
A friend pointed out that the Lorentz transformation was only recently proved to be linear.
One of the most beautiful things I learnt in the last few weeks is the
connection between geodesics (shortest paths) and metrics in that
space. If 
is a geodesic path and 
is the
velocity of the path:
then the metric is defined by
Moreover, the path satisfies the Euler-Lagrange equation. This was first shown by Arnold in a hydrodynamical context, and subsequently borrowed by control systems and computer vision folks.
Two functions 
and 
were going in a
car. looked ahead and said, “Oh shit! There comes a
differential operator.” says with a smirk, “It can’t do
nothing to me!” On approaching the differential operator, it says
“Haha! I’m d/dy.”
As narrated to me by a random math major last week…