Talk:Level-set method

message: Both of Osher's and Sethian's books (given in the references section) give level set function values as negative inside the curve and positive outside.  Osher does so explicitly on page 5 (a circle shown with phi < 0 inside and phi > 0 outside) whereas Sethian's plots on page 8 do so implicitly.  I would argue that their sign convention trumps whatever was used as the basis for this article, but I don't want to be the one who has to recreate all of the pretty graphs if a change is made. WokYai 17:56, 16 October 2007 (UTC)
replies: text: Indeed. Changing Oleg's matlab script that generated the picture should not be so hard. Jmath666 (talk) 19:29, 29 November 2009 (UTC)
thread_title:  Sign convention? 

message: The level set method [...] is a numerical technique for tracking interfaces and shapes.
*what is meant with tracking?
*What is an interface?
Thanks, --Abdull (talk) 21:33, 2 July 2008 (UTC)
replies: text: An interface is a boundary between things. Tracking, means following the interface as it moves. Oleg Alexandrov (talk) 03:58, 3 July 2008 (UTC)
thread_title:  Missing definitions 

message: As a side note, for those encountering "level sets" for the first time, the choice of symbols might be challenging. Given that this article needs to distinguish less than ten different entities, is there really a need to stretch over two different alphabets and so many different type style combinations?  It would be helpful to indicate how much of this variation is intended to convey something important, and how much is simply sticking to convention.
For example, what is the significance of using greek letters, and these particular greek letters, in this example? Are they reandomly chosen, or does their particular choice, and type style, signify something that's important to understand? Why upper-case greek non-italic for one function, and lower-case greek script italic for the other function? Or perhaps it's just customary, and if so that could be explained.  I point out that if readers didn't already know that the phi symbol used here happens to be a rather "scripty" version of the italic and lower-case phi, they would not figure it out from wikipedia page:
http://en.wikipedia.org/wiki/Greek_letters_used_in_mathematics,_science,_and_engineering
... and lacking that knowledge would find it difficult to even verbalize what they were reading. 
Gwideman (talk) 04:57, 29 November 2009 (UTC)
replies: text: It is customary. Upper case \Gamma is the common notation for a curve or the boundary of a domain in numerical analysis and PDEs. \Gamma is not a function, which is perhaps why it is not lowercase. Lowercase \phi, \varphi, or \psi for the level set function happens to be the notation used by all the references (as well as all the level set papers I can remember). No particular reason. It could be any other symbol, really. Well, not quite in an applied paper where this methods gets used... there is a lot of notation that has an established meaning and you want to avoid those otherwise it turns counterintuitive. For example, x, y, z are coordinates... f is right-hand-side... u,v are usually velocities... a, b, c are coefficients...  \alpha, \beta, \gamma are usually coefficients too... \delta, \epsilon are something small... and so on. So pretty soon not much is left. I am sorry if the use of a greek letter looks like a hindrance. I do not think the particular choice of font (scripty or not) matters, that's just how it happens be here. Jmath666 (talk) 05:49, 29 November 2009 (UTC)
thread_title: Comment on symbols and type styles