Discrete vs Continuum

Posted on: Fri, 09/08/2006 - 00:17 By: dae

Ok, it's that time of the year again. ICRA07 is coming closer and closer. The clock is tick-tock and my own deadline and a promise to my dear professor that I will show him the full-baked paper is almost gone. (In fact, there is 49 minutes remaining at the time while I was writing this very sentence).

My new method just broke down this morning. After a careful consideration and a series of Lemma to be proven, I found out that there exists a case where my O(N) could not work. Ok, fine, I can change to O(N lg N) and the result is still cool, although less than it should be. A few minutes lates, I was hit by the fact that there still some more case that O(N lg N) could not save the day. It is pointless to do O(N^2) since another published method would be better.

I am down.

Until I met my advisor. He said that, why don't you do it in the continuous space.

Ok. I have to give some intro first. The core operation which is the main point of my work is to check whether cones achieve force closure. Nevermind what is force closure but concentrate on the cone. A cone is..... everybody know Cornetto?... The cone is exactly like the cone of cornetto. Mathematically, a cone can be expressed by quadratic equations. Normally, researchers in the field feel that cones are too hard to cope with and they usually linearize the cone into a regular pyramids, to get its linear description so that we can tackle it with a plethora of tools already exist in Linear.

I also thinking the same. That is my doom.

Since I am doom, then I consider the continuum as my last resort. I then changed my mode to continuous instead of discrete. Whala, the solution is found almost immediately, although a basic of solution. It looks very promising and I believe that it can be done. More work to do but my mood is much much better.

I always feel reluctant to work in the continuous space. I am not excel at Calculus. I prefer to tackle the N instead of X,Y,Z. Yesterday, while my old method still looked promising, I even sweared that I am very fond of discrete space, I won't step outside to the continuous space.

Shame on me. It is the continuous space that save my ass today.