An orthographic rendering of a torus from a 45degree angle is shown below:
EDIT: Fixed
What is the curve seen on the inside? I'm sorta leaning towards ellipse, but I'm not entirely sure.
The Inner Curve of a Torus Viewed Obliquely
 elendiastarman
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 Joined: Sat Dec 22, 2007 8:15 pm
The Inner Curve of a Torus Viewed Obliquely
Last edited by elendiastarman on Mon Apr 19, 2010 5:23 pm, edited 1 time in total.
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58209749445923078164062862089986280348253421170679...?
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?

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Re: The Inner Curve of a Torus Viewed Obliquely
Seems we don't have permission to view your image.
 elendiastarman
 Posts: 410
 Joined: Sat Dec 22, 2007 8:15 pm
Re: The Inner Curve of a Torus Viewed Obliquely
Whoops...I need to put it on a published page... .
EDIT: Fixed it.
EDIT: Fixed it.
Want some
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?
3.14159265358979323846264338327950288419716939937510
58209749445923078164062862089986280348253421170679...?
Re: The Inner Curve of a Torus Viewed Obliquely
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?
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?