The analysis of Balmer-dominated emission in supernova remnants is potentially a very powerful way to derive information on the shock structure , on the physical conditions of the ambient medium and on the cosmic-ray acceleration efficiency . However , the outcome of models developed in plane-parallel geometry is usually not easily comparable with the data , since they often come from regions with rather a complex geometry . We present here a general scheme to disentangle physical and geometrical effects in the data interpretation , which is especially powerful when the transition zone of the shock is spatially resolved and the spectral resolution is high enough to allow a detailed investigation of spatial changes of the line profile . We then apply this technique to re-analyze very high quality data of a region along the northwestern limb of the remnant of SN 1006 . We show how some observed features , previously interpreted only in terms of spatial variations of physical quantities , naturally arise from geometrical effects . With these effects under control , we derive new constraints on physical quantities in the analyzed region , like the ambient density ( in the range 0.03– 0.1 { cm ^ { -3 } } ) , the upstream neutral fraction ( more likely in the range 0.01–0.1 ) , the level of face-on surface brightness variations ( with factors up to \sim 3 ) and the typical scale lengths related to such variations ( \sog 0.1 { pc } , corresponding to angular scales \sog 10 { arcsec } ) .