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

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