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

From: Laurence Finston
Subject: [help-3dldf] Re: [metafont] Re: button-hole problem
Date: Sat, 23 Apr 2005 13:30:21 +0200 (MEST)

On Sat, 23 Apr 2005, Peter Vanroose wrote:

> No, circles can indeed project as a parabola or a hyperbola.
> Take the following example:
> - project onto a horizontal plane.

What does horizontal mean in this context?  The way I do perspective
projection implies that the plane of projection is always perpendicular to
the line from `Focus::position' to `Focus::direction', which are both
`Points'.  I have also implemented parallel projection onto the x-y, x-z,
and z-y planes, but it isn't clear to me that the projections of circles
wouldn't be ellipses, except for the cases where they are circles (which
are also ellipses, of course) or straight lines (which could be termed
degenerate ellipses, I suppose).

> - place a circle vertically with its lowest L point on that plane.
> - take as projection "eye" point P any point which is at the same
> height above the plane as the highest point H of the circle.
> In this case the projection is a parabola, with its top in L and its
> axis parallel to the line PH.
> If you want a hyperbola, move the eye point P a bit down (towards the
> projection plane). If you want an ellipse, move P upward.

Thank you very much.  I'll try this out as soon as I get a chance.


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