waanna.blogg.se - Dupin cyclide

Dupin cyclide how to#
Dupin cyclide manual#
Dupin cyclide code#

For a man to be a director of others, manual work has only a secondary importance it is his intellectual ability (force intellectuelle) that must put him in the top position, and it is in instruction such as that of the Conservatory of the Arts and Professions, that he must develop it.

It is to the director of workshops and factories that it is suitable to make, by means of geometry and applied mechanics, a special study of all the ways to economize the efforts of workers.

Charles Dupin (1808) in: Hacette (1813 86-87) as cited in Margaret Bradley, Charles Dupin (1784-1873) and His Influence on France, Cambria Press.

Endlessly occupied by a thousand different matters and constrained my state duties, it is the work of an engineer that I herewith present and not the fruit of the meditations of a savant.

I found myself obliged, through perhaps unique circumstances, to devote myself to my mathematical research, almost without help, advice or even books.

1.2 The Commercial Power of Great Britain, 1925.

1.1 A Tour Through the Naval and Military Establishments of Great Britain, 1822.

The change of radius is due to ax-cd instead of Rx. You already answered that: d(aka f) is then the minor radius, and a=b isĬomparing to the traditional torus equation: > it goes on to state that it's a ring cyclide if f > How can f be less than c if for a torus c=0 and f=r? > (unless of course f > 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. > In my quest to parameterize this, I found: > 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 Which has some useful information however, it's stated that: In my quest to parameterize this, I found: I'm sure I will have some fun playing with this new algebraic surface andįinding ways to harness it in some future scenes. Thank you as always, Jerome - and please thank your friends for me as well. Useful properties of the true Dupin cyclide. I found a very interesting paper by Langevin: "Geometry with two screens andĬomputational graphics" (2014) where he points out some very interesting and Normal torus, so I suppose that might not be inherent in the object. The large end always seems to be VERY largeĬompared to the smaller side, though IIRC, with certain values one can get a

Dupin cyclide how to#

I'm wondering how a, b, c, and d relate to the radii of the shape, and how to > It is, however, SLLLLlllllllllloooooooooooI had wondered / suspected / hoped that were the case. > I asked the other Internets about that, they had a round tuit left so I > got a nice answer.

> I hadn't gotten around to unraveling the implicit equation to fit the syntax for > a polynomial. > Le à 13:41, Bald Eagle a écrit : > I didn't have as much time as I would have liked to explore this, > but after fiddling with the Dupin cyclide in both isosurface (implicit) and > parametric form, I found the parameters to be highly unintuitive, the desired > shape very difficult to achieve and control, and the constraints on the > parameters too complex to be easily implemented. Dupin cylide and Faux-Dupin-cyclide object Proper radii for the fore and aft sections so as to be _just_ visible (1 pixel When placed at any distance from the camera will automatically calculate the The radii, position, and camera placement were all chosen to get that to workįurther work ought to yield a torus with a user-supplied major radius, which The x axis appears to be equally wide along both front and back. See how the toroid (left) has a variable minor radius, and when rotated around It will be fast enough to do what I want. Which is to be expected for a parametric, but probably with Ingo's slick method, It is, however, SLLLLllllllllllooooooooooowwwwwwww.

Dupin cyclide code#

Into the code I had for a normal parametric torus, and it gives me the desired So I home-cooked a formula for the minor radius of a torus, and patched that I hadn't gotten around to unraveling the implicit equation to fit the syntax for Parameters too complex to be easily implemented. Shape very difficult to achieve and control, and the constraints on the Parametric form, I found the parameters to be highly unintuitive, the desired I didn't have as much time as I would have liked to explore this,īut after fiddling with the Dupin cyclide in both isosurface (implicit) and POV-Ray : Newsgroups : : Faux Dupin Cyclide

POV-Ray: Newsgroups: : Faux Dupin Cyclide