Robert Z. Selden, Jr. November 1, 2019
The landmarking protocol developed for this project bears some visual similarities with the configuration used in the previous study (Selden Jr., Dockall, and Shafer 2018), as well as other two-dimensional geometric morphometric analyses (Buchanan and Collard 2010; Buchanan et al. 2011; Ragan and Buchanan 2018); however, it differs in some fundamental ways. The first and most obvious difference is that this is a three-dimensional study. The second is the method of landmark placement, where Geomagic Design X (Build Version 2019.0.2 [Build Number: 78]) was used to generate a spline around the periphery of each biface, and to populate the landmarks and equidistant semilandmarks in a replicable manner using mathematically-defined criteria.
knitr::include_graphics('images/figbev.png')
fig.cap="Gahagan biface 545 from the Gahagan Mound site, illustrating axial twisting. \\label{figbev}"The goal of this effort was to increase the precision and rigour of the study by including the z-dimension to capture those morphological characteristics associated with axial twisting that are introduced through the practice of bifacial beveling. This landmarking protocol represents an intermediate iteration between the previous 2D analysis (Selden Jr., Dockall, and Shafer 2018), and the forthcoming protocol that also includes semilandmarks placed on a series of equidistant cross-sections. The cross-sections increase the coverage of semilandmarks across the mesh topology, and provide for greater precision in the analysis of morphology for the whole object. The evolution of this landmarking protocol represents a concerted effort to better comprehend the vagaries of morphological similarities and differences among Gahagan bifaces. While true that some landmarking protocols can be—and often are—recycled as new specimens are added, this particular research programme endeavours to achieve ever-greater accuracy and precision in each analytical iteration.
Unlike the previous study, where the outline of each Gahagan biface was
projected onto a 2D plane, this effort enlists a spline extracted from
the surface geometry of the mesh using the extract contour curves
command, which is used to detect and extract 3D contour curves from
high-curvature areas of the mesh. In reverse-engineering, extract contour curves is regularly employed as the first step in building a
patch network that is used to create a surface. The extracted feature
curve is rendered as a spline, and follows the highest curvature
contours around the periphery of the lateral and basal edges, following
the highly variable sinuous edge morphology around the entirety of the
biface. The remainder of the landmarking protocol is based upon this
spline, which was subsequently split at four mathematically-defined
locations.
knitr::include_graphics('images/extractspline.png')
fig.cap="Spline extracted along the highest contours of the projectile. \\label{figspline}"A few definitions are warranted before proceeding. Reference geometries are used in the assistance of creating other features. These
include basic geometric entities, such as planes, vectors,
coordinates, points, and polygons. A reference point is a
virtual point and is used to mark a specific position on a model or in
3D space. A reference plane is a virtual plane that has a normal
direction and an infinite size. A reference plane is not a surface
body, and is used to create other features.
The characteristic points and tangents developed for this landmarking protocol were inspired by the work of Birkhoff (1933). The first landmark (LM1) is placed at the horizontal tangent on the tip of each Gahagan biface. The second and third splits (LM2 and LM3) occur at points of highest curvature, and LM2 is always split on the right side of the biface when oriented in 3D space following the alignment output of auto3dgm, which is illustrated in Figure 7a of the manuscript. To place the final landmark (LM4), a linear measurement was used to project a reference point equidistant between LM2 and LM3. The location of that point was leveraged in placing the reference plane used to cut the spline at the location of LM4.
The horizontal tangent is calculated by drawing a horizontal line
above the tip of the biface using the tangent as a common constraint,
and the horizontal as the independent constraint. To split the 3D
spline at the location of the horizontal tangent, a reference point
was inserted at the location of the tangent in the 2D sketch (light
blue point; below, left), followed by a reference plane (in white;
below, left and right) using the pick point and normal axis function
where the reference point (h-tangent) was used as the pick point,
and the Right plane as the normal axis (below, left). The 3D spline
was then cut at the location where the reference plane intersected
with the spline (below image, right).
knitr::include_graphics('images/lm1.png')
fig.cap="Identify horizontal tangent, insert reference point and reference plane (left). Use reference plane to cut spline at the location of the horizontal tangent (right). \\label{figlm1}"The point of highest curvature on either side of the basal edge was
calculated using the curvature function in the Accuracy Analyser. This
function displays the curvature flow as a continuous colour plot across
the area of the curve. In this instance, curvature is defined as the
amount by which a geometric shape deviates from being flat or straight
in the case of a line. The curvature is displayed in different colours
according to the local radius, and is calculated in only one direction
(U or V) along the curve. Using this tool, the two points of highest
curvature were located between the basal and lateral edges on either
side of each biface where the local radius measure was largest. The
alignment and orientation of each biface was dictated by the auto3dgm
output (see Figure 7a in the manuscript), and the landmarking protocol
follows the mesh orientation in that figure, where LM2 was always placed
on the right side of the basal edge, and LM3 on the left.
knitr::include_graphics('images/splinesplit1.png')
fig.cap="Identify points of hightest curvature (light blue) at left/right intersection of lateral and basal edges. \\label{figsplinesplitlr}"One additional landmark (LM4) was placed at the centre of the base. The
location of this landmark was identified by calculating the linear
distance between LM2 and LM3, and projecting a reference point
(ctrl-div; below) equidistant between the two. A reference plane was
added using the ctrl-div as the pick point, and the Right plane as the
normal axis. The spline was then split at the intersection of the
reference plane and the basal spline.
knitr::include_graphics('images/lm4.png')
fig.cap="Calculate linear distance between LM2 and LM3, insert reference plane coplanar to Right plane equidistant between LM2 and LM3, and use the reference plane to cut the spline. \\label{figlm4}"Through the preceding protocol, the initial spline was split into four discrete splines. These splines articulate with components of bifacial morphology that can be compartmentalised in the subsequent analyses (i.e., left/right [directional] asymmetry, blade/base morphological integration, etc.). The primary analytical gain achieved through this exercise is the requisite foundation needed to carry out replicable analyses of Gahagan biface morphology in three dimensions, further increasing the precision of the geometric morphometric analysis.
knitr::include_graphics('images/splinesplit-frbl.png')
fig.cap="Result of spline splits include four discrete splines, each articulating with a potential region of analytical interest. \\label{figsplinesplit-frbl}"Landmarks 1-4 were placed at the location of each spline split (blue points, below). Equidistant semilandmarks were then added to each of the four splines; 20 between LM1 and LM2, five between LM2 and LM4, five between LM4 and LM3, and 20 between LM3 and LM1.
knitr::include_graphics('images/lmslm-all.png')
fig.cap="3D spline with landmarks (blue) and equidistant semilandmarks (white) applied, with top, right, and front planes. Semilandmarks are renumbered in post. \\label{figlmslm-all}"Superficially, this constellation of landmarks and semilandmarks appears similar to those used in recent 2D studies. However, the rigourous protocol used in the application of landmarks and semilandmarks aids in capturing morphological variation that articulates with axial twisting introduced by knappers through the practice of beveling. Thus, this constellation of landmarks and semilandmarks provides for greater precision in the geometric morphometric analysis, marking a substantive advancement in those analytical protocols used to achieve a more complete and holistic analysis of Gahagan biface morphology.
knitr::include_graphics('images/figbevlm.png')
fig.cap="Mesh for Gahagan biface 545 from Gahagan Mound with landmarks and equidistant semilandmarks applied. \\label{figbevlm}"I extend my gratitude to Christian S. Hoggard and David K. Thulman for
their thoughtful comments and constructive criticisms on an earlier
draft of this landmarking protocol. The current iteration of the
landmarking protocol was developed using the digit3DLand package in R
(code available in this repository); however, the capacity to populate a
replicable suite of reference geometry across the sample in Geomagic
Design X made it a better option for the dynamic design process.
Definitions of reference geometries and Design X features described in
this protocol are paraphrased from the reference manual.
Birkhoff, George D. 1933. Aesthetic Measure. Cambridge: Harvard University Press.
Buchanan, Briggs, and Mark Collard. 2010. “A Geometric Morphometrics-Based Assessment of Blade Shape Differences among Paleoindian Projectile Point Types from Western North America.” Journal of Archaeological Science 37 (2): 350–59. https://doi.org/10.1016/j.jas.2009.09.047.
Buchanan, Briggs, Mark Collard, Marcus J. Hamilton, and Michael J. O’Brien. 2011. “Points and Prey: A Quantitative Test of the Hypothesis that Prey Size Influences early Paleoindian Projectile Point Form.” Journal of Archaeological Science 38 (4): 852–64. https://doi.org/10.1016/j.jas.2010.11.007.
Ragan, Kathryn, and Briggs Buchanan. 2018. “Assessing Collector Bias: A Geometric Morphometric Analysis of a Collection of Isolated Clovis Points from the Midcontinent.” Midcontinental Journal of Archaeology 43 (2): 91–111. https://doi.org/10.1080/01461109.2018.1426430.
Selden Jr., Robert Z., John E. Dockall, and Harry J. Shafer. 2018. “Lithic Morphological Organisation: Gahagan Bifaces from the Southern Caddo Area.” Digital Applications in Archaeology and Cultural Heritage 10: e00080. https://doi.org/10.1016/j.daach.2018.e00080.