Fig. 5

Cross-section shapes of representative gingival margin (GM) and cemento-enamel junction (CEJ) profiles with “curvature combs” graphs of three maxillary teeth, i.e., right canine (a), left canine (b), and right first premolar (c). Visual inspection of cross-section profiles and “curvature comb” graphs depicts GM point as more distinct and easier to select than CEJ point. Visually perceived shape differences at CEJ points compared to GM points are larger despite the smaller differences in curvature values, i.e., − 0.32 mm^− 1 vs. − 0.98 mm^− 1 for CEJ points and − 3.11 mm^− 1 vs. − 7.03 mm^− 1 for GM points (a and b, respectively). It results from the mathematical definition of curvature as a ratio, i.e., an inverse radius (1/r), and human perception, which more easily distinguish between the straight line and a circle than between two circles with a small difference in radius. Interestingly, similar GM curvature values in a and c produce different shapes of curvature comb graphs (figure c “curvature comb” in coronal direction), which can be explained as an effect of root surface defect present in c