The Inner Curve of a Torus Viewed Obliquely

Shape and space, angle and circle properties, ...
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elendiastarman
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The Inner Curve of a Torus Viewed Obliquely

Post by elendiastarman » Mon Apr 19, 2010 4:36 pm

An orthographic rendering of a torus from a 45-degree angle is shown below:
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EDIT: Fixed

What is the curve seen on the inside? I'm sorta leaning towards ellipse, but I'm not entirely sure.
Last edited by elendiastarman on Mon Apr 19, 2010 5:23 pm, edited 1 time in total.
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genious999
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Re: The Inner Curve of a Torus Viewed Obliquely

Post by genious999 » Mon Apr 19, 2010 5:08 pm

Seems we don't have permission to view your image.

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elendiastarman
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Re: The Inner Curve of a Torus Viewed Obliquely

Post by elendiastarman » Mon Apr 19, 2010 5:20 pm

Whoops...I need to put it on a published page... -.-
EDIT: Fixed it.
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DjinnKahn
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Re: The Inner Curve of a Torus Viewed Obliquely

Post by DjinnKahn » Mon May 24, 2010 9:50 pm

I think if you continue to rotate the torus, the shape will be like a lemon, with two "sharp" points, which is clearly not an ellipse.

Hmm, actually I think there is a simpler way to get the same shape. Think of the torus as the shaped carved out by a sphere moving in a circle. When viewed obliquely, the circle appears as an ellipse. Now carve out a shaped with a sphere (circle) moving on this ellipse.

So, just draw an ellipse, and color all the points within a certain distance of the ellipse.

I guess this is the Minkowski sum of an ellipse outline and a circle?


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