From: leyfre@McRCIM.McGill.EDU (Frederic Leymarie)
Subject: Re: Developable Surface
Organization: McGill Research Center for Intelligent Machines, Montreal, Canada
Lines: 38


In article <C5x9xs.KHE@hkuxb.hku.hk>, h8902939@hkuxa.hku.hk (Abel) writes:
|> Hi netters,

|> 	I am currently doing some investigations on "Developable Surface".
|> Can anyone familiar with this topic give me some information or sources
|> which can allow me to find some infomation of developable surface?
|> 	Thanks for your help!

|> Abel
|> h8902939@hkuxa.hku.hk

A developable surface is s.t. you can lay it (or roll it) flat on the
plane (it may require you to give it a "cut" though...)

E.g., a cylinder, a cone, a plane (of course!) or any surface or patch
having vanishing Gaussian (intrinsic) curvature (i.e., with singular
Hessian, the matrix of 2nd derivatives for an adequate coordinate patch)
are "developable". In more technical words, a developable surface is
"locally isometric to a plane" at all points.


Think also of the sphere (or the earth) which in a non-developable:
whatever way(s) you cut it, you will not be able to lay flat any pieces
of it... (its intrinsic curvature is nowhere vanishing).

For more details on this look at any book on differential geometry
which treats surfaces (2D manifolds); e.g., M. do Carmo's book:

@Book{Carmo76Differential,
  author =      {do Carmo, Manfredo P.},
  title =       {Differential Geometry of Curves and Surfaces},
  year =        1976,
  publisher =   {Prentice-Hall},
  note =        {503 pages.}}

Enjoy!
-- 
Frederic Leymarie -- leyfre@mcrcim.mcgill.edu
McGill University, Electrical Eng. Dept., McRCIM,    |	Tel.: (514) 398-8236
3480 University St., Montreal, QC, CANADA, H3A 2A7.  |	FAX:  (514) 398-7348
