Isometric Surfaces

I am having some trouble understanding this page. Although I believe I understand partial derivatives, and have worked with somewhat similar notation in the past, that does not mean that I understand all of the terms of these equations. Also, the two displayed surfaces do not seem to have the same topology (though that might be an artifact of the rendering -- where only part of each surface is displayed). And while I could perhaps go out and attempt to research this subject to attempt to fill in the blanks, I am not really clear on which of a broad variety of treatments I should be studying. I would appreciate more complete definitions here. -- Raul Miller 2008-09-03 14:34:25

... the surfaces can be viewed from the top for the purpose of visualization ...

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 'viewpoint 0.1 0 100'
pd y1;y2;y3
pd 'pdf'
pd 'show'

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 'viewpoint 0.1 0 100'
pd y1;y2;y3
pd 'pdf'
pd 'show'

Prev Page: Essays/Isometric Surfaces/Isometric Surfaces01