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

[L. Nobre G.]

On Sun, 24 Apr 2005, Laurence Finston wrote:

> So is a perspective projection of a conic section always a conic section?

A physicist like me would say "allways".

> 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?

Ellipse.

> 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?

Of course: project six points and solve ax2+by2+cxy+dx+ey+f=0.

> It's no problem to transform it to a convenient position and
> then put it back where it was.

I think that adequate transformations (using symetry, eigen axis) may
reduce the number of projected points to three...

> Have you solved these problems in FEATPOST?

"Yes". I project 32 points and then construct a cyclic path with them.

> Thank you very much again for all your help.

But be "carefull" out there

Lu\'{\i}s Nobre Gon\c{c}alves - http://matagalatlante.org