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Re: [help-3dldf] Re: button-hole problem

From: Laurence Finston
Subject: Re: [help-3dldf] Re: button-hole problem
Date: Sun, 24 Apr 2005 01:35:38 +0200
User-agent: IMHO/0.98.3+G (Webmail for Roxen)

L. Nobre G. wrote:

> The projection of a circle will not be an ellipse *only* when the circle
> touches (parabola) or crosses (hyperbola) the plan, parallel to
> the projection plan, containing Focus::position. Everything on this plan
> projects at infinty. This kind of projection is not computable. Avoid it.
> Forget it.

Thanks, that's very clear.

> Now, the center of the projected ellipse is the projection of the circle's
> center *only* when the circle is parallel to the projection plan and when
> the circle's center is on the line --Focus::position--Focus::direction--.

So is a perspective projection of a conic section always a conic section?  I
suppose it would be too good to be true if any transformation of a conic 
section would also be a conic section, but are there one or more classes of 
transformations for which this is true?  Shearing (an affine transformation)
can make an ellipse non-elliptical, but since it remains a closed curve, it is
neither a parabola or a hyperbola.  Is there a name for this kind of curve? 
And is there a  way of finding out _what_ curve the projection the projection
of a conic section is, i.e., finding an implicit or parametric equation to
describe it?  It's no problem to transform it to a convenient position and
then put it back where it was.  Have you solved these problems in FEATPOST?

Thank you very much again for all your help.


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