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Thread Subject:
Spiral Toroid

Subject: Spiral Toroid

From: James

Date: 16 Jun, 2010 02:30:33

Message: 1 of 4

Hi.
I am trying to create a model of a spiral contained within a toroid. The idea is that there is a continuous cylindrical spiral (cylinder diameter of 2) whose path is restricted to the inside of a 3D toroid (outer diameter of toroid being 150 with inner diameter of 50). The cylindrical spiral should be packed as closely as possible but be about 0.3 units from any surrounding rungs of the spiral. I appreciate any help you can provide.
Thanks.

Subject: Spiral Toroid

From: Roger Stafford

Date: 16 Jun, 2010 03:07:03

Message: 2 of 4

"James " <jeevans@ucdavis.edu> wrote in message <hv9d09$26g$1@fred.mathworks.com>...
> Hi.
> I am trying to create a model of a spiral contained within a toroid. The idea is that there is a continuous cylindrical spiral (cylinder diameter of 2) whose path is restricted to the inside of a 3D toroid (outer diameter of toroid being 150 with inner diameter of 50). The cylindrical spiral should be packed as closely as possible but be about 0.3 units from any surrounding rungs of the spiral. I appreciate any help you can provide.
> Thanks.

  I need for you to describe your model in greater detail and accuracy. You speak of a cylinder restricted to the inside of a toroid. However cylinders are usually understood to extend to infinity in two directions whereas toroids are bounded, so the notion of such confinement seems contradictory. Also it is not clear if you are trying to generate a one-dimensional curve, a two-dimensional surface, or a three-dimensional solid, with your "spiral". If it is a curve, what is the significance of specifying a two-inch diameter for the cylinder? Or is it a pseudo-cylinder, solid or surface, of two inch diameter snaking around inside the toroid? When making a complete circuit of the toroid, do you want the two ends of the spiral to meet in a continuous curve or surface?

  So you see, you have many questions to answer.

Roger Stafford

Subject: Spiral Toroid

From: James

Date: 16 Jun, 2010 06:26:04

Message: 3 of 4

Hi Roger,
Thanks for your quick reply. I will try to answer your outstanding questions clearly. I want to create a model of a 3D spiral in which the rungs of the spiral are closely packed and wrap around continuously in the overall shape of a toroid. Thus, my idea had been to somehow trace a path within the boundary of a 3D toroid. The path should have a 2 unit diameter as a pseudo-cylinder solid snaking around the inside of the toroid with a 150 unit outer diameter and 50 unit inner diameter. The two ends of the pseudo-cylinder do not need to be connected but the entire volume of the toroid should be occupied with a small space between each pseudo-cylindrical rung of 0.3 units. Please let me know if you need further clarification.
Thanks.


"Roger Stafford" <ellieandrogerxyzzy@mindspring.com.invalid> wrote in message <hv9f4n$cro$1@fred.mathworks.com>...
> "James " <jeevans@ucdavis.edu> wrote in message <hv9d09$26g$1@fred.mathworks.com>...
> > Hi.
> > I am trying to create a model of a spiral contained within a toroid. The idea is that there is a continuous cylindrical spiral (cylinder diameter of 2) whose path is restricted to the inside of a 3D toroid (outer diameter of toroid being 150 with inner diameter of 50). The cylindrical spiral should be packed as closely as possible but be about 0.3 units from any surrounding rungs of the spiral. I appreciate any help you can provide.
> > Thanks.
>
> I need for you to describe your model in greater detail and accuracy. You speak of a cylinder restricted to the inside of a toroid. However cylinders are usually understood to extend to infinity in two directions whereas toroids are bounded, so the notion of such confinement seems contradictory. Also it is not clear if you are trying to generate a one-dimensional curve, a two-dimensional surface, or a three-dimensional solid, with your "spiral". If it is a curve, what is the significance of specifying a two-inch diameter for the cylinder? Or is it a pseudo-cylinder, solid or surface, of two inch diameter snaking around inside the toroid? When making a complete circuit of the toroid, do you want the two ends of the spiral to meet in a continuous curve or surface?
>
> So you see, you have many questions to answer.
>
> Roger Stafford

Subject: Spiral Toroid

From: Jonathan Crider

Date: 27 Dec, 2010 21:07:20

Message: 4 of 4

James,

Did you have any luck with this problem? I am working on the same problem currently and could use any help you have to offer.

-Jonathan

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