Academic Facets: News and Views from Spatial's University Community

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Academic life across the world is frantic at the moment;with a series of looming paper deadlines and the inevitable, all consuming,efforts to get results or algorithms into a publishable form.

The conference season runs roughly from May through to late Octoberand as a consequence most of the CAD/CAM/Geometric Modelling meetings all havepaper submission deadlines within a few weeks of each other. For example:

January paper deadlines have passed for;

• Product Life Cycle Modelling http://www.plm09.org/ 

 

• The Mathematics Of Surfaces http://www.ima.org.uk/Conferences/13_maths_of_surfaces_09.htm

 

February offers the chance to submit to ;

• ASME 2009 International Design Engineering TechnicalConferences (IDETC) & Computers and Information in Engineering Conference(CIE): http://www.asmeconferences.org/idetc09/  : Papers by February 27th

……and March 16th is the deadline for (arguablythe leading conference for this area) the

• ACM/SIAM Symposium on “Geometric andPhysical Modelling”: http://www.siam.org/meetings/gdspm09/ 

It is not inconceivable that there are research groupssubmitting works to two, or even three, of these events. And no matter how hardyou try to avoid it, paper writing expands to fill the time available.  Noses to the grindstone for the next few weeks.

One small diversion from this endless round of hacking oftext, started before Christmas when the inverse kinematic equations used of oneof my students were criticised by a colleague. He pointed out, quite rightly(with hindsight), that an implementation using atan2 would be much more stablethan the arccos and arcsin functions currently being uses. To be honest I’dforgotten what a useful function atan2 was.

As everyone who has ever tried to calculate an angle fromgeometric data has learnt by bitter experience the range of values an inversetrig function can return is limited to only a fraction of the 360 degreespossible (so arcsin returns values between [-90 to +90 degrees], arccos [0 to180] and atan’s range is [-90 to 90]).  Butuniquely amongst inverse trig functions atan2 can return values between [-180,  +180] degrees ( http://en.wikipedia.org/wiki/Atan2 ). 

So atan2 can potentially provide a much more general angle calculationfunction; see, for example, the discussion of atan2’s application forcalculating the angle between two vectors at:

http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925

In fact, I think, whoeveradded the original atan2 function to the Fortran maths library had near genius levels of foresight and made the 20th century’s only contribution trigonometry (the general view that not much has happened with trigonometry since the eighteenth century; http://www.math.rutgers.edu/~mjraman/History_Of_Trig.pdf)! 

Indeed the motivation for defining atan2 appears to be so closely linked to computer graphics that I started wondering if CAD could take any credit for its invention. Perhaps Ivan Sutherland’s Sketchpad program (http://en.wikipedia.org/wiki/Sketchpad)had been implemented in Fortran?

This lead to some idle time spent Googling "CAD histories" on the net. Although I came tono conclusion about the origins of atan2 I did find David Weisberg’s ebook on the history of CAD ( http://www.cadhistory.net/ ) that provides a fascinating account of the (frequentlyincestuous) origins of the CAD industry we know today.

Naturally I turned first to the ACIS references in Chapters 2 (page 13) and 2, which  reminded me that at some point in 2009 ACISwill be 20 years old (version 1.0 was released in 1989). But exactly when in 1989 is unclear. I emailed one of the people involved in the early days of ACIS (who checked with a handful of others). No one could recall the exact release date although there was a general feeling it was later in the year (e.g. September ish).….perhaps there is still a version 1.0 manual sitting on a shelf somewhere that could fix the date? It would be nice to know .... we could have a cake!  

Lastly I have also been divertedfrom paper writing by the appearance in the popular media a novel shape calleda  'Gömböc'  that is claimed to be the most “self-righting”object ever manufactured. Interestingly none of the media reports I have seen mentioned that the shape is a child of CAD/CAM technology (i.e. defined by mathematics,represented by 3D modelling and created by rapid prototyping). See   http://www.2objet.ch/Misc/TestPage/TechnologyMathematicallyProven/tabid/380/Default.aspx

Expensive to buy (www.gomboc-shop.com)at the moment, but I’m sure an open source version (with STL file) will appear shortly! 

Message Edited by Jonathan_Corney on 02-15-2009 09:00 PM