Le 17/05/2017 à 19:05, Bald Eagle a écrit :
> In my quest to parameterize this, I found:
> 
> http://or.nsfc.gov.cn/bitstream/00001903-5/173475/1/1000009340012.pdf
> 
> Which has some useful information; however, it's stated that:
> 
> a,b > 0 and c,f >= 0 are constants.
> it goes on to state that it's a ring cyclide if f < c < a.
> 
> How can f be less than c if for a torus c=0 and f=r?
> (unless of course f < 0)...

when c=0, the sign of f( aka d) is irrelevant

(x^2+y^2+z^2+b^2-d^2)^2-4*(a*x-c*d)^2-4*b^2*y^2=0

> 
> it's a normal torus if a=b=R,  c=0,  and f=r
> 
> 
> Currently in the process of expanding the polynomial and grouping to see how a&b
> behave when equal, eliminating the c terms, and seeing how f affects the minor
> radii of the Dupin cyclide.
> 

you already answered that: d(aka f) is then the minor radius, and a=b is
the major radius.

Comparing to the traditional torus equation:

(x^2+y^2+z^2+R^2-r^2)^2-4R^2(x^2+y^2) = 0

the change of radius is due to ax-cd instead of Rx.

Notice that b <= a, and they should be positive, yet c is amongst the
two roots of c^2 = a^2-b^2.

the sign of b is irrelevant, but the sign of a can have an impact with
the sign of c.

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