Home         Site Map         Tutorial Material         Elements(1)         Elements(2)         Proscribed Ops        
        Absolutes(1)         Absolutes(2)         Absolutes(3)         Projection         Perspective        
 

A Note on “Parallel” versus “Central” Projection

According to Euclid, and, I suspect, to most people, absolute sizes do exist, and may be propagated by something called, “parallel projection”,

centproj

but,

if we accept the Caley/Klein proposal that

parallels are those co-planar lines that meet in a point at infinity
,

we see that
parallel projection is central projection still
—because it is projection from a point,
albeit at infinity.

So, in general, Projection of points by lines is Central,
with Parallel Projection just a special case of it.

Parallel projection is Central Projection from Infinity.

Geometries based on this speciality are called, “Affine”.


It appears to work for angular measure too.

halfprotract

   
Home         Site Map         Tutorial Material        Elements(1)         Elements(2)         Proscribed Ops        
        Absolutes(1)         Absolutes(2)         Absolutes(3)         Projection         Perspective