  We present a novel approach to the analysis of a full model of scalar
modulation instability (MI) by means of a simple geometrical description in the
power vs. frequency plane. This formulation allows to relate the shape of the
MI gain to any arbitrary dispersion profile of the medium. As a result, we
derive a straightforward explanation of the non-trivial dependence of the
cutoff power on high-order dispersion and obtain explicitly the power that
maximizes the gain. Our approach puts forth a powerful tool to synthesize a
desired MI gain with the potential application to a vast number of
parametric-amplification and supercontinuum-generation devices whose
functioning relies upon modulation instability.
