From: QueeneMUSE (QueeneMUSE@aol.com)
Date: Sat Dec 13 1997 - 07:37:56 MST
Forwarding this for those who constantly mutter that art is a totally
"subjective" thing, and who act as if artists need to be housewives or hippie-
ass ninnies who should stay out of the science reading rooms
attached mail follows:
I figured some of the Rhizomers might find this discussion
interesting. NURBS are Non-Uniform Rational B-Splines and
they allow artists/industrial designers/architects/etc. to
build smooth objects inside the PC. Anyways, this discussion
started because most NURBS programs convert the 100% smooth
NURBS surfaces to (flat) polygons for rendering. Yet
some programs avoid this by subdividing the NURBS surfaces
beyond/below the size of a pixel. Generally the polygon
method is faster and looks just as nice for most purposes,
BUT there are those in the world who feel it is necessary to
have *ideal* 100% mathematically smooth surfaces on their PC's ;)
Graeme Bailey wrote:
>
> There are some interesting points in this discussion
> relating to the difference between maths and real life entities
> like real surfaces, which in actuality are composed
> not of mathematical points, not even atoms, but molecules.
>
> My point is just that often the ability to calculate
> must have some common sense attached to the
> number of decimal places being considered...?
>
> Engineering tolerances are designed to allow for surface
> irregularities, real enough even for apparently smooth
> surfaces like bores and pistons...
> Yet without some surface imperfections, the surfaces
> will be too smooth to function properly?
>
> In my experience the human eye starts to lose the ability
> to distinguish individual black dots when they are about 400 dpi,
> and so there is a real gap between visual smoothness
> say from above 500 dpi
> and engineering smoothness say from above
> 1000 to 10,000 'bumps' per inch
>
> Light itself bombs out at a magnification of say 2000,
> ( I tried to look at coloured paint particles and found them
> to be just below the 'graininess' of light itself,
> ie beyond the optical microscope's range...
>
> when you think about it, this is necessarily <grin>
> for the paint particles to modify the light to produce colours....
>
> Under the microscope, skin is composed of lots of translucent
> semi-clear fluid-filled 'domes', quite different in appearance
> to the effect at normal viewpoints
>
> The graininess of the individual crystal lattices of steel are
> of the order of cubes with iron atoms spaced at maybe a few angstrom
> units apart (what? a couple of thousand millionths of a metre?)
> and far beneath the range of light...
>
> Yet thinking in millimeters, the angstrom unit is what?
> about the tenth place of decimals...
>
> At 11:16 PM 12/10/97 +0100, you wrote:
> >Pierce wrote:
> <...>
> >> Is it possible to directly render NURBS surfaces without the Meshing?
> >> Is the raw 'horsepower' of the endusers CPU the main reason why this is
> >> not done, or has no one figured out a means of doing so yet?
> >
> >Out of the empty I'd say the NURBS is a mathematical definition of space
> >and has infinitely many points on it.<...>and rendering would take
> infinitely long.
>
> >To avoid that, you set a margin of wished resolution
> >and all of the mathematically spoken infinitely many points being within
> >a single point of your wished resolution of rendering form a <...>surface,
> >and that is the polygon, which makes a mesh.
> <...>
> >Its all polygons, there is no curve in real life, it's all
> >approximation.
> >Even the molecules of, say steel, form polygons.
> >All curves in real life are projections on material, which has
> >limitations.
> <..>
> >
> --
> Graeme <gbailey@iig.com.au>
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