I think ink traps often look pretty good and I wonder if
- they are really designed to serve an optimal purpose, which can be modelled as given a shape
d(S,I(S'))is minimized, where
Iis the ink spreading function, which models how ink spreading alters the shape in the transfer to paper, and
dis some appropriate distance functions, like integral of the symmetric distance, and
- if the answer to this is yes, what computational methods can be used to solve this optimization problem numerically?
My first intuition was that ink spreading could be modeled by looking for a shape whose area is
a times the area of
S, for some
a>=1, which contains all the points in
S and whose boundary length is minimized (clearly
a=1 reduces to the identity). But I guess the algorithm for ink traps described above would then only insert holes, because closing holes is a very efficient way of reducing boundary length.
Other (simpler) ideas for ink spreading include morphological closing (which I think produces no interesting results) or taking the union of all lines
L whose endpoints lie in
S and whose length is smaller or equal to some constant
a=0 reduces to the identity).