[metapost] Re: Intersections of NURBs

Larry Siebenmann laurent at math.toronto.edu
Wed Feb 2 19:29:02 CET 2005

Hi Laurence F,

 LF> In case anyone's wondering, the reason why points with the same
 > z-coordinate as Focus::position can't be projected is because this
 > would involve division by 0.  Objects consisting of points whose
 > z-coordinates are greater than 0 could be projected, but are generally
 > culled, because people don't see that way.

Projective (homogeneous) coordinates permit division by 0.
Projective transformations are bijective and everywhere defined.
The projective plane RP^2 was created to make that true!! Curiously
in certain circumstances we *can* see images that are located
behind us. This happens in Newtonian lens systems; the observer
does not realize the image is located behind her until she notices
that paralax has switched sign. This is a real memory; she was an
A-level highscool physics student in England writing up her optics
experiment.  Naturally her report was culled.  Naturally Galileo



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