Neolithic Reverse Engineering Surveying Toolkit
People in the Late Neolithic and Bronze Age were adept at surveying sites for the construction of Stone Circles and Henges. When they wanted to, their sites were accurately surveyed. However at other times, this did not seem to be important and the sites were designed by rule of thumb instead, i.e. by eye, dead reckoning and / or divide and conquer techniques. Their principal architectural concerns were Alignments (usually Solar or Outliers), Straight Lines, Circles, Ellipses, Flattened Circles and Ellipses, Compound Curved designs and usually Symmetry. We know this from looking at numerous surveys. The principle which guides us when trying to model ancient sites is usually called Occam's Razor, but the idea originally dates back to at least Aristotle. In its simplest form it says: The simplest solution is probably the correct one.
At Moel Ty Uchaf stone circle and at Egg-shaped sites, they seemed to be adept at Mirroring one side of the site onto the other across an Axis. This skill would also have been useful if they wanted to align an Ellipse on the Minor Axis as perhaps at Park Beck (the peg positions for an Ellipse lie on the Major Axis). As a ncessary part of the process they would have constructed the Major Axis as a Perpendicular to the Minor Axis using the some form of Mirroring.
NRest 1.09 uses modern Optimisation algorithms to generate Best Fit Circles, Best Fit Ellipses and Best Fit Lines from survey data. You may be familiar with Best Fit Lines drawn through a scatter of points. The Best Fit Line is calculated mechanically to minimise the discrepancies between the surveyed points and the modelled Line. Similarly we can generate Best Fit Circles and Best Fit Ellipses. This is only practically possible though the advent and ubiquity of modern computers and software.
Survey data from Blue and Green dots
NRest output from survey data (apart from the later Red line)
NRest allows multiple Layers of coordinates to be overlayed. Each Layer having its own configuration settings. So we can mix Best Fit Ellipses, Circles and Lines all on the same diagram. Ellipse and Circle centre points are shown. Ellipses can optionally include the Major and Minor Axes. Lines and Arcs of Circles can optionally include the axis of symmetry. Circular arcs can be extended to aid modelling. Normally I leave survey points on show, althouch they can be suppressed.
NRest Main Configuration File
Layer Configuration File
Typical Results from NRest
NRest describes the resultant modelled Ellipse in numbers, as well as plotting the model. The Optimisation algorithms provide a measure of the accuracy of the Fit in the form of the Root Mean Square Error (Rmse) for the model. It is this value that is minimised during the Best Fit process. This is converted into a percentage of the 'measured' distance involved when surveying, so that simple comparisons can be made between sites of different sizes and geometries. Typically the percentage comes in at about 2% or less.
Edin's Hall Ellipse
Major Axis is used as the measured distance. For a Circle, Major Axis contains the radius. For a Line, Major Axis contains the length of the Line from Start to End. For an Arc, Minor Axis contains the size of the Arc in degrees. For an Ellipse, Compass gives the orientation of the Major Axis (always assuming North is up). For an Arc, Compass gives the direction the Axis of Symmetry. For a Line, the direction of the Line.
Sample Workflow for Photoshop
Using NRest
While the modelling of the surveyed points is done independently by the algorithm, it is the surveyor who chooses which survey points to use. The human eye is adept at spotting circles and ellipses. The biggest issue tends to be, when an ellipse turns into a straight section, where does the last survey point on the ellipse belong? In addition, Best Fit Ellipses are remarkably adept at modelling short sections or surveys where there are few survey points. The process will happily inform you that the model is very accurate, but good accuracy alone is not a good guide. Poor accuracy indicates a poor model, but otherwise other factors also come into play. Guidelines for modelling an Ellipse to avoid some of these pitfalls:
If you follow these guidelines, it should save you from the worst excesses of Elliptomania. Similar guidelines apply to modelling Circles or Circular Sections. My two favourite sites so far are Edin's Hall for the completeness of the model / match and Park Beck for the unexpected alignment of the short axis with the internal avenue.
Edin's Hall
Park Beck
Modelling Moel Ty Uchaf (in feet)
Moel Ty Uchaf Tri-Flattened Circle SJ 056 372