Simple Size and Shape Variables: Shape Coordinates - Geometric Morphometrics for Biologists - page 51

SC x and SC y are the “shape coordinates” of landmark C (which from now on we will
simply call C xy ). This relatively simple set of operations will be important when we com-
pare the shapes of two triangles.
Comparing Shapes of Two Triangles
To compare the shape of two triangles, we apply the operations outlined above to
both of them and calculate the shape coordinates of landmark C. That is, we assign the
coordinates (0, 0) to landmark A in both triangles, and we assign the coordinates (1, 0)
to landmark B in both triangles ( Figure 3.2B ). As a result, the difference between the two
triangles is entirely represented by the difference in the location of the third vertex, land-
mark C. We can now draw both triangles on the same coordinate system ( Figure 3.2C ).
While there are programs to do these calculations, they are easily done in any spread-
sheet or statistical program that manipulates formulae. As an exercise, take the following
three pairs of coordinates for points of a triangle (in the format produced by a common
digitizing program), compute the shape coordinates, and draw the triangle. For the
FIGURE 3.2 Two triangles whose shape difference
is the subject of investigation. (A) The two triangles as
initially recorded; (B) the same two triangles after being
translated, rotated and rescaled by the two-point regis-
tration; (C) the same two triangles, superimposed.