FIGURE 10. Valve reflections and the measurement of semilandmark mean coordinates. An initial orientation of a valve after centering and rotation is presented in the upper left panel. The valve face was divided into 4 Cartesian quadrants (I–IV) based on the intersection of the apical and transapical axes. Landmarks and semilandmarks were numbered 1–40 starting at the center of the valve apex (y = 0) on the left and proceeding clockwise, independently of rotations, i.e. landmark 9's (yellow dot) position was preserved. Three combinations of reflections are shown: transapical axis only (lower left), apical axis only (upper right), and both transapical and apical axes (lower right). Point (semilandmark) 9 in the original configuration was about 40% of the distance along the mantle's upper margin between the valve ends; this position was always the 9th point digitized when starting at the left end and proceeding clockwise. If the valve had been reflected about the transapical axis, then point 13 would have been in the semilandmark 9 position; if it had been apically reflected, then point 33 would have been in the semilandmark 9 position; and, if it had been reflected about both axes, then point 29 would have been in the semilandmark 9 position. The mean coordinates (mean x and y) of semilandmark 9 was the average of the 4 points which could possibly occupy semilandmark position 9 after reflection. The same process was applied to the calculation of the mean coordinates of all other semilandmarks. The mean x,y coordinates of the landmarks and semilandmarks for each specimen were used in the geometric morphometric analysis. Blue arrows indicate reflections about axes; yellow arrows show translocation of a semilandmark to digitizing position 9.

Published as part of Edgar, Robert K., Saleh, Amal I. & Edgar, Stacy M., 2015, A morphometric diagnosis using continuous characters of Pinnunavis edkuensis, sp. nov. (Bacillariophyta: Bacillariophyceae), a brackish-marine species from Egypt, pp. 1-56 in Phytotaxa 212 (1) on page 8, DOI: 10.11646/phytotaxa.212.1.1, http://zenodo.org/record/13642672