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ROY_NUZZO
12-08-2013, 05:23 PM
Long ago (when Amiga's were out there hammering away at electronic art) I got one of the companies that had the killer app to make a secret change that drove folks wild (according to their feed back). This was a best kept secret. All those programs are gone so we can reveal.

It was this observation: There are no Bezier's in nature. Yup they lend to math and are easy and everywhere, but nothing real looks like them. Also true for NER (nearly equi-rippel Bessel). Artists use FRENCH curves and they use them to better approximate real viewing of CATENARY curves which are EVERYWHERE, hanging blowing strings, the line of a rowboat face on, clothes & telegraph lines, the shape of gear cogs (THOSE ARE CATENARY, catenary shapes do not slide as they rotate so gears don't wear if the shape is catenary).. like phi (1.618...) catenaries are everywhere because they are what gravity dictates, what friction demands, and what the eye somehow wants to see. Use those other shapes and - mmmmmm - ehhh.. doesn't quite do it.

The SECRET was that the secret splines were using catenary math and then fitting with Bezier's after the fact. (created the curve with catenary then saved as best fit Bezier approximation). Swirl functions and whorls also used catenary.

The point? We need a catenary curve based tool set because that is what is out there. Everywhere you look. And look closely at anything that turns and nudges or drives something else.

-rmn

meshpig
12-09-2013, 01:01 AM
Bezier was a Car designer at Renault so it's not surprising; why though would a Catenary system look anymore "natural"? There are no straight lines in Nature either... :)

Sensei
12-09-2013, 05:38 AM
LightWave doesn't have native Bezier nor B-Spline curves.
It has only Catmull-Rom curves (curve passes through the all control points).


catenaries are everywhere because they are what gravity dictates,

3d apps have no forced which axis is pointing to the center of Earth.
One curve you might want to be straight in XZ, and bend in Y, so it's like Catenary.
But other time you want straight in XY and bend in Z, or reverse, or bend in the all axis.

meshpig
12-11-2013, 03:27 AM
I'm always thinking 3D has it's own semiological "naturalism". Like how sometimes a scene view looks by far more interesting than a render view.

ROY_NUZZO
12-11-2013, 06:16 AM
Well we don't need French curves as the 3D perspective is inherent in what we do. So building the original true to life means 'How does life do it?"

The easiest description is a suspended CHAIN. Each link is suspended to the one before and supports the next. So - stepwise - what does physics do? (Basic calculus) with gravity as the main player, a catenary is the shape (sought my mathematicians of old) gravity gives to anything flexible. That's a lot of stuff. Wind does something similar. Also when wheel rolls on wheel if they don't slip there is little wear. But cogs increase ability to impart rotational force. The cogs then slip on one another. They wear. But if the cogs are catenary based on gear radius, the cogs ROLL on one another.

In the neck, the C2 vertebra has a protrusion (odontoid) that engages the atlas (head & neck motion control). Look closely - a catenary. What is often seen as ball & socket motion is if you look closer two catenary saddles (saddle joints) engaging one another.

Want to slip through water with low friction then overlap those planks in a least friction max strength way. Guess.

So even people supporting other people in athletic chains will approach catenary shapes.

So SOME of us (not everybody) could use a spline that seeks a catenary for making shapes that are closer to reality with

jeric_synergy
12-11-2013, 10:19 AM
OK, interesting, but on a practical level how do we use this info? Can we construct a faux-catenary and match the curves we DO have to them (iow, fake it)??? And how does one construct a catenary curve? Do we just need one that we spiin around and scale or what?

ROY_NUZZO
12-12-2013, 08:04 PM
Well it isn't easy to fake, hence the request. Many famous have tried simple shape solutions (hyper & parabolic sections etc.). Nope. It works best as calculus with the differential steps set to match needs (close for rope, and link size for chains etc). Right now it means using something real to image and tracing as a viewport background. If a simple spline pulled from A to B with the desired number of steps or intervals (chain links ?) and direction of gravity (where 'down' lives, or parallel to wind), then easy - connect two points.

If you put your hands palms together as if praying then slowly separate the palms while keeping fingers touching at the tips, you get a pretty good approximation when you see that shape that looks like real gear cogs.