It is finally time to figure out where good and useful places are to measure. We’re going to be doing this twice, and use these points to show HOW orienting our mandible changes things.
Update: I’ve corrected the primary figure, below, indicating the various vertices separately (and avoiding “pincusionism”); these changes include the re-orientation of the mandible (I had used the posterior end of the articular glenoid, rather than the anterior end), the resizing of the box representing the mandibular aspect ratio, and the addition of a few vertices that I had forgotten to adjust for (I will eventually correct this in the figure above, as well). The figure is now the much larger working base image, so that anyone can have at it at slightly higher quality. The labels for the “points of interest” (formerly “measurement points,” which is redundant) have also been added. I have clarified the text in what was effectively non-explanation of the purpose and relation of aligned vertices.
The above image is a collection of three types of vertex, representing major morphological positions (light blue, Primary Vertices), indicated with letters without modification. These correspond to precise positions of the jaw, as are indicated by limits of bone along the vertical and horizontal axes. These positions can be found regardless of which orientation the jaw is in, or which view, and always affix to specific points on the bone itself. The jaw is shown in “standard” alignment, with the ventral-most margins of the jaw “balanced” horizontally.
a – anterior limit of anterodorsal end of dentary (excluding any dentition).
b – posterior limit of mandible, regardless of whichever bone we are measuring here is presented at this point (here, it is likely the surangular, although the fusion of the region may suggest instead it is the articular).
c – dorsal apex of the coronoid eminence OR the anteriormost point of insertion of the mAM [m. adductor mandibulae] group of muscles (on the lateral surface — I have not prepared a medial view to discuss the positional relationships of the lingual mPST [m. pseudotemporalis] group).
d – dorsal apex of the articular glenoid OR ventral nadir of the same [I am making a broad assumption of the median of the length of the glenoid as based on the "static" position of the quadrate and the glenoid, but these should roughly correspond to furthest ventral the quadrate (or corresponding cotylus, or the inverse as in the case of mammals) can sit on the glenoid. This should normally mean the most ventral position of the glenoid in any articulation, and thus "f" below, but I will get to that in a further post. Due to the nature of the articular, I can adjust this label to separate the two positions, but that is not necessary as in most archosaurian taxa these are generally in the same place and thus functionally identical].
e – anterior limit of the articular glenoid, ordinarily corresponding to the dorsal limit of the rostral articular wall of the articular or surangular bones.
f – posterior limit of the articular glenoid, again generally corresponding to a wall in typical “socketed” glenoids, although in some birds, most turtles, etc,. there is no wall per se.
g – posterior limit of the mandibular symphyseal articulation, regardless of whether the symphysis is fused.
h – ventral limit of the retroarticular process, or most distal point at which the m. depressor mandibulae (mDM) inserts on the retroarticular process.
i – dorsal limit of the external mandibular fenestra.
ii – ventral limit of the external mandibular fenestra.
j – anterior limit of the external mandibular fenestra.
jj – posterior limit of the external mandibular fenestra.
k – lateral limit of the retroarticular process.
l – lateral extent of the articular glenoid, including presence of the surangular forming the lateral wall of the glenoid.
m – medial extent of the articular glenoid, including presence of a wall of the articular, angular or prearticular forming the medial wall of the glenoid.
x – anterior limit of contact between mandible and maxilla.
Aligned Vertices (green) correspond to extensions along the vertical and horizontal axes (regardless of orientation of the jaw) to the bone limits. They are indicated, along with the Coordinated Vertices along the horizontal axis, with letters followed by a tilde (~) or double-tilde/approximate symbol (≈). Aligned vertices are determined to permit strict concordance of width and height/depth to the margins of the jaw, such as the approximate depth of the mandibular symphysis at its posterior extent, rather than the coordinated height, which follows the grey box (see below).
Coordinated Vertices will correspond to the bulk of the discussion in the next post, in which I use them to actually measure and produce the proportional qualities of the jaw at various alignments. These are indicated in red, and are oriented along the vertical and horizontal axes regardless of orientation, and thus do not follow the bone margins or surfaces. Above and below, I have shown these along the midline in dorsal view and along the anterior and ventral margins in lateral view. These form the primary purpose of indicating the grey box that represents the aspect ratio of the mandible in various views. They thus represent segments of this box in linear measurement. In lateral view, vertical coordinates are indicated with a circumflex (^) and horizontal coordinates with an asterisk (*). I should have indicated coordinate points in dorsal view with a third type of symbol, and thus reduced the confusion of the aligned points, and will correct this in time. [I have modified the file, but need to prepare it for upload, where I adjust the dorsal view midline coordinates to use single (') and double (") quotation marks (approximating single and double apostraphes, but a lot more elegant.] Relative orientation and inclination of the element in question can be thus explained merely by taking a fixed point and measuring the angle between a primary vertex and its coordinated counterpart. This is, actually, the second most important purpose for the vertex.
A fourth type of measurement point is indicated with dark blue, and represents the fourth box above, and labels corresponding to features (in italics), and are “points of interest.” These features represent morphological limits of the elements themselves (dentary, glenoid, external mandibular fenestra, etc.), and they have yet an additional system of measurements. Unlike the primary form of measurement, where I will segment the primary axes relative to the points described above, these follow the surface of the jaw, and will be described in further detail in the next post.
aane – anterior[most] angular extent.
adde – anterodorsal dentary [process] extent.
adsae – anterodorsal surangular [process] extent.
aemfe – anterior external mandibular fenestra extent.
avdane – anteroventral dentary-angular extent.
avsae – anteroventral surangular process extent.
dare – dorsal articular [glenoid] extent.
dcoe – dorsal coronoid [process] extent.
dde – dorsal[most] dentary extent.
demfe – dorsal external mandibular fenestra extent.
dmptfe – dorsal m. pterygoideus ventralis [externalis] fossa extent.
drare – Typo: should be “prare”, posterior retroarticular [process] extent.
pemfe – posterior external mandibular fenestra.
pvde – posteroventral dentary [process] extent.
pdde – posterodorsal dentary [process] extent.
psye – posterior symphysis extent.
saanc – surangular/angular [anteriormost] contact.
sp – sigmoid “peak.”
vare – ventral articular [glenoid] extent.
vde – ventral dentary extent.
vemde – ventral external mandibular fenestra extent.
vrare – ventral retroarticular [process] extent.
Currie, P. J., Godfrey, S. J. & Nessov, L. A. 1994. New caenagnathid (Dinosauria: Theropoda) specimens from the Upper Cretaceous of North America and Asia. Canadian Journal of Earth Sciences — Revue de Canadienne des Sciences de la Terre 30:2255-2272. [Published in 1994, dated 1993.]