Designer optical control of interactions in ultracold atomic gases has wide applications, from creating new quantum phases to modeling the physics of black holes. We demonstrate wide tunability and spatial control of interactions in a two-component cloud of ^{6}Li fermions, using electromagnetically induced transparency. With two control fields detuned ≃1.5 THz from atomic resonance, megahertz changes in the frequency of one optical beam tune the measured scattering length over the full range achieved by magnetic control, with negligible (10^{-6}) effect on the net optical confining potential. A 1D "sandwich" of resonantly and weakly interacting regions is imprinted on the trapped cloud and broadly manipulated with sub-MHz frequency changes. All of the data are in excellent agreement with our continuum-dressed state theoretical model of optical control, which includes both the spatial and momentum dependence of the scattering amplitude.