An Analytic Solution to the Neugebauer Equations

For over 50 years the Neugebauer equations have provided a model for color reproduction in halftone screened images. But because the equations are nonlinear they have been solved either by analog computation or numerical digital techniques. Analytic approximation could be made only through severe simplifying assumptions. The equations originally described the printing with three inks (CMY) but can easily be extended to the case of a fourth black ink (CMYK) This appears to complicate the situation, making the equations even more nonlinear, increasing the number of equations , and making the problem non deterministic. However in one case [the case of full undercolor removal] the presence of a very good black can actually simplify the problem to the point where it admits an analytic solution. This paper begins with a review of color coordinate transforms as applied to additive color. These are then generalized to special cases of subtractive color. These are then generalized to special cases of subtractive color. This then provides a basis for determining dot areas which satisfy the Neugebauer equations for the case of full undercolor removal. The paper also presents a brief review of previous methods for the solution of the equations and comments on the inclusion of Yule Nielson. This paper begins with a review of color coordinate transforms as applied to additive color. These are then generalized to special cases of subtractive color. These are then generalized to special cases of subtractive color. This then provides a basis for determining dot areas which satisfy the Neugebauer equations for the case of full undercolor removal. The paper also presents a brief review of previous methods for the solution of the equations and comments on the inclusion of Yule Nielson.