// _IonicVolute script by Brian McMillin March 30, 2016

// This script is based upon the paper by Denise Andrey and Mirko Galli, specifically

// their equation derived from work by Dürer (1525), Giullaume Philandrier (1544).

//

http://link.springer.com/article/10.1007%2Fs00004-004-0017-4#/page-1
//

http://www.springerlink.com/content/r61qh2354m56qt31/fulltext.pdf
//

http://www.emis.ams.org/journals/NNJ/AndGal.html
//

http://www.c4dcafe.com/ipb/forums/topic/59105-ionic-volute/
// There are good pictures of the Ionic Volute's here:

//

https://en.wikipedia.org/wiki/Ionic_order
// This is a 2D script, with z = 0.0.

// The "eye" circle has a diameter of one unit, and is placed at x,y coordinate (0,0).

// The "inner side" of the spiral begins at the top of the eye, at (0, 0.5). (The angle here is PI/2.)

// The spiral is made up of 3 whorls, and the "inner side" of the top of the spiral is at (0, 4.5).

// (note that b = 4.5 units is a fixed value in this script).

// The "inner side" of the bottom of the spiral is at (0, -3.5), but this will change

// if aValue is changed.(aValue = +3.5 units).

// (It is up to the user to model the "outer side" of the spiral, which may be done by

// doing a few sweeps, etc. The user can also scale the spiral with MoI.)

// Polar coordinates are used, which consist of an angle alpha, and a radius r.

// The equation is r = r(alpha) = 3.5 * tan(beta + ((alpha - PI/2)/(whorls*2*PI)) * (gamma - beta))

// The number of turns is whorls, which defaults to integer 3, as per sample Ionic Volutes.

// Angle alpha ranges from PI/2 to (whorls*2*PI + 1)/2, which is 13*PI/2 for 3 whorls.

//

// gamma = arctan(b/a) = arctan(4.5/3.5).

// beta = arctan(0.5/a) = arctan(0.5/3.5).

// Polar coordinates are converted to (x,y,z) using x = r*cos(alpha) and y = r*sin(alpha), with z = 0.

I'll modify the ArchimedeanSpirals script with the above formulas, to make the Volute script. But it is too late tonight to finish :-)

- Brian

So the volute appears to be Ionic, rather than Corinthian.