Digital BW, The Print

Hi everyone,
I'm curious what kind of Math is behind curves blending process? - Specifically if I want mathematically build smooth transition between let's say Black, Light Black and Light Light Black inks - what kind of variables are necessary (I assume density and Lab values) - and what equations to use to build the curves? I've had hard time finding any info online - if anyone can point me to a right direction or share this info it would greatly appreciated

Thank you very much in advance

Eugene

The classic theory of density & color blending of printed inks is given by the Neugebauer equations. A Google search will give you plenty of sources.

Good luck,

Joost
  

--- In DigitalBlackandWhiteThePrint@yahoogroups.com, "Ev K" <evko1@...> wrote:

>
> Hi everyone,
> I'm curious what kind of Math is behind curves blending process? - Specifically if I want mathematically build smooth transition between let's say Black, Light Black and Light Light Black inks - what kind of variables are necessary (I assume density and Lab values) - and what equations to use to build the curves? I've had hard time finding any info online - if anyone can point me to a right direction or share this info it would greatly appreciated
> 
> Thank you very much in advance
> 
> Eugene
>

--- In DigitalBlackandWhiteThePrint@yahoogroups.com, "horstenj" <j.h.j.h@...> wrote:
>
> The classic theory of density & color blending of printed inks is given by the Neugebauer equations. A Google search will give you plenty of sources.
> 

I guess I should have added a bit to save you some time. 

The Neugebauer equations themselves are actually very simple. GIVEN 1) a dot distribution, 2) ink color/densities, 3) color/densities of comined inks the resulting color/density can be computed in a straightforward way. However, in practice that is of very little use as one is usually interested in the inverse problem: what should the dot distribution be to achieve a certain color/density? Now that is still a nonlinear problem that can be solved, either numerically or by approximation. 

But that's still not of much use for profiling/curve creation. I'm not familiar with the mathematics of color profiling but I've spent some time on how to compute an "optimal" BW multi-gray curve. I tried to approach it as a numerical nonlinear constrained optimization problem. At a certain point I gave up. The problem appeared ill-defined to me without a clear objective optimum. There's just quite a bit of "art" in curve creation as opposed to "science".

I'm still sure I could have gotten further but just lost the urge to spend more time on it.

Joost

"Ev K" <evko1@...> wrote:

> I'm curious what kind of Math is behind curves blending process? ...

"horstenj" <j.h.j.h@...> wrote:

> The classic theory of density & color blending of printed inks is given by the Neugebauer equations. ...
> 
> But that's still not of much use for profiling/curve creation. ...



Being a pragmatist, I have found it easier to download and buy a copy of QuadToneRip <http://www.quadtonerip.com/html/QTRoverview.html> and use the Curve Creator to make the curves. If you look at the graphs of the curves it creates you'll see some interesting things Roy has done that make his partitioning a bit better than what I have been able to do just by hand with other rips.  I think Epson also has excellent crossovers, but they don't show a graph of what they've done. 

I don't think in terms of equations, but visually the graphs in QTR are very informative.

One thing I do that I think improves a single QTR partitioning curve is to use a secondary partitioning progression using one of the "toner" channels.  So, for example, I have 5 different dilutions/densities of Eboni in my 7800.  There is a "gray" set of curves that has 3 inks, and there is a "toner" that uses 2 inks.  Both the light inks are light enough to be in the highlights.  The work is divided between the 2 partitioning sets.  So, the ink limits are cut in half for each.  The overlapping helps hide the crossovers and makes the profile smoother and more tolerant of the inevitable inconsistencies that might throw off a profile.

Paul
www.PaulRoark.com