Isometric Surfaces

1 Reference

'Tensor Analysis' by I. S. Sokolnikoff (Second Edition, 1964).

2 Software

NB. ... execute (ijx) ...

   9!:14 ''
j602/2008-03-03/16:45

3 First Fundamental Quadratic Form (ISS Section 53)

4 Isometric Surfaces (ISS Section 61)

4.1 S1

load 'plot'
load 'numeric'

u1=:steps 0 6 30
u2=:steps 0 2p1 30

p=:1

y1=:u1(%:@(*:@[+p*p"_)*/2&o.@])u2
y2=:u1(%:@(*:@[+p*p"_)*/1&o.@])u2
y3=:u1((p*_6&o.@(p%~%:@(*:@[+p*p"_)))*/$@]$1:)u2

pd 'type surface'
pd y1;y2;y3
pd 'pdf'
pd 'show'

4.2 S2

load 'plot'
load 'numeric'

u1=:steps 0 6 30
u2=:steps 0 2p1 30

p=:1

y1=:u1([*/2&o.@])u2
y2=:u1([*/1&o.@])u2
y3=:u1(($@[$1:)*/p*])u2

pd 'type surface'
pd y1;y2;y3
pd 'pdf'
pd 'show'