Catenary curves

[tenochtitlanuk]

The shape of any free-hanging rope suspended from two points- not necessarily at the same height.

Basically a 'hyperbolic cos'.

Quick bit of fun to create the graphic below.

-

Code below..

Once I had the cosh( function, I felt ready to tackle Amazon's hanging cable problem... how far apart are the towers?


   nomainwin

   WindowWidth  =600
   WindowHeight =600

   open "Catenaries" for graphics_nsb as #wg

   #wg "trapclose quit"
   #wg "size 2 ; fill lightgray"

   for a =0.4 to 8 step 0.1
       #wg "up ; goto 0 0 ; down"

       s       =int( a /8 *256)
       col$    =str$( s) +" 50 " +str$( 255 -s)
       #wg "color "; col$

       for x =-6 to 6 step 0.05
           y       =a *cosh( x /a)
           #wg "goto "; 300 +50 *x; " "; 580 -50 *y
           oldX    =x
           oldY    =y
           scan
       next x

   next a

   #wg "getbmp scr 0 0 600 600"
   bmpsave "scr", "catenaryFamily2.bmp"

   wait

   function cosh( x)
       cosh =( 1 +exp( 0 -2 *x)) /( 2 * exp( 0 -x))
   end function

   sub quit h$
       close #wg
       end
   end sub



[Rod]

Aha, blended catenary fill. Cool.

[honkytonk]

nine meters
354,331 Inches ??

[tenochtitlanuk]

Sorry, no! There's a bit of a trick to the problem.. anyone else have the answer? ( No online cheating, of course..)

[tsh73]

trick indeed!
it just dawned on me, after reading this thread third time I think...

[tenochtitlanuk]

Nice 'playing with your mind' trick, isn't it!

Here's another catenary family graphic- coloured chain between two fixed points..

[Rod]

Shades of the new “Joker” symbolism in there.