[metapost] re: Rovenskii
laurent at math.toronto.edu
Fri Feb 18 22:28:53 CET 2005
Laurence Finston LF and Taco Hoekwater TH write:
LF > I think it would be interesting to see if Knuth and
> Hobby's methods lend themselves to this extension.
TH > Not sure what methods you mean.
> The routine that finds control
> points based on tensions and curls?
The ".." and "..." operators concern curvature and
even *global curvature minimization*. I have not
seen that in any other graphics environment.
A 3-dim implemeention even just for curves
would involve curve torsion as well as curvature.
Something similar for surfaces would be much harder
We've been looking at mere affine invariants that are
fascinating mathematically but relatively easy. Also
physically, since they are directly visible to 'distant'
observers in dimension 3. A bezier curve viewed on a
tabletop by a distant observer is a bezier curve! But
curvature changes since is not an affine invariant; it's
hard to deal with in dim 2 and harder still in dimension
A full 3-dim metapost would be staggeringly difficult.
*But* I see no reason for hesitating to *start* with
affine bezier curves and surfaces in dimension 3. That's
foundational stuff and can be done well in any dimension.
Affine projection to dimension 2 is easy and useful --
except for occultation (as mentioned by LF), cf.
"overdraw" page 114 of mf book.
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