Orbital-phased-resolved infrared spectra of Cygnus X-3 in outburst and quiescence, including tomographic analysis, are presented. We confirm the phasing of broad HeII and NV lines in quiescence, such that maximum blue shift corresponds to the X-ray minimum at phase = 0.00 +/- 0.04. In outburst, double-peaked HeI structures show a similar phasing with two significant differences: (a) although varying in relative strength, there is continuous line emission in blue and red peaks around the orbit, and (b) an absorption component, ~1/4 of an orbit out of phase with the emission features, is discerned. Doppler tomograms of the double-peaked profiles are consistent with a disk-wind geometry, rotating at velocities of 1000 km/s. Regrettably, the tomography algorithm will produce a similar ring structure from alternative line sources if contaminated by overlying P Cygni profiles. This is certainly the case in the strong 2.0587 micron HeI line, leading to an ambiguous solution for the nature of double-peaked emission. The absorption feature, detected 1/4 of an orbit out of phase with the emission features, is consistent with an origin in the He star wind and yields for the first time a plausible radial velocity curve for the system. We directly derive the mass function of the system, 0.027 M_sun. If we assume a neutron star accretor and adopt a high orbital inclination, i > 60 degrees, we obtain a mass range for the He star of 5 M_sun < M_WR < 11 M_sun. Alternatively if the compact object is a black hole, we estimate M_BH < 10 M_sun. We discuss the implications of these masses for the nature and size of the binary system.

Accepted for publication in ApJ main journal