  Today's typical application of geometric morphometrics to a quantitative
comparison of organismal anatomies begins by standardizing samples of
homologously labelled point configurations for location, orientation, and
scale, and then renders the ensuing comparisons graphically by thin-plate
spline as applied to group averages, principal components, regression
predictions, or canonical variates. The scale-standardization step has recently
come under criticism as inappropriate, at least for growth studies. This essay
argues for a similar rethinking of the centering and rotation, and then the
replacement of the thin-plate spline interpolant of the resulting
configurations by a different strategy that leaves unexplained residuals at
every landmark individually in order to simplify the interpretation of the
displayed grid as a whole, the "transformation grid" that has been highlighted
as the true underlying topic ever since D'Arcy Thompson's exposition of 1917.
  For analyses of comparisons involving gradients at large geometric scale,
this paper argues for replacement of all the Procrustes conventions by a
version of my two-point registration of 1986 (originally Francis Galton's of
1907). The choice of the two points interacts with another non-Procrustes
concern, interpretability of the grid lines of a coordinate system deformed
according to a fitted polynomial trend rather than an interpolating thin-plate
spline.
  The paper works two examples using previously published cranial data; there
result new findings pertinent to the interpretation of both of these classic
data sets.
  A concluding discussion suggests that the current toolkit of geometric
morphometrics, centered on Procrustes shape coordinates and thin-plate splines,
is too restricted to suit many of the interpretive purposes of evolutionary and
developmental biology.
