Early English Toothed Ornament
Chris Heath 
How to construct Early English toothed (English Gothic dogtooth) ornamentation using geometry.
Inspired by the drawing of a dogtooth ornamental band (below) by Patrick Webb, I wanted to see if it can be constructed geometrically. Obviously, it is geometric in its construction, and Patrick's drawing reveals some interesting arcs. The trick with this design was to locate the centres of these arcs using geometry.
By the way, Patrick Webb is a heritage and ornamental plasterer who teaches Gothic architectural design for La Table Ronde de l’Architecture’s Bruges Summer School of Architecture & Crafts in Belgium. Patrick is currently matriculated at Le Centre de Formation Dans le Metiers de l'Artisinat in Fez, Morocco for the study of traditional Islamic design and Gebs, gypsum plaster carving. I'd like to thank Patrick for introducing me to this toothed ornament and for clarifying a number of points relating to this design.
Observations
The first thing I noticed was that the curves of the star ornament (below-left) where the centre of the arc (Point A) is easy to locate is different to the Early English design on the right. The star design on the left was used in Norman architecture; an example from Romsey is illustrated below.
The centre of the arc (Point B) in the toothed design is offset and the radius is slightly longer than for the arc centred on Point a. In addition, neither the location of the centres b and c, nor their associated radii are obvious.
Geometric Construction of the Toothed Ornament.
Below are the steps that can be followed to reproduce the toothed ornament. If you can draw the initial square accurately, the steps, left-to-right from top-left to bottom-right should be easy enough to follow.
Analysis - The Root-Two Proportion
Drawing squares within circles and circles within squares establishes a proportional relationship between the radii of each consecutive circle as shown below. Radius b is used to set the location of the circle of radius f. Radius g is used to set the centre of the designs major arc.
Radii a/b = b/c = c/d = d/e = e/f = f/g = √2
Research
Getting this far wasn't difficult. However, I wanted to model the dogtooth in 3D. This required some research because where I live (Napier, New Zealand), there is no Early English architecture.
The images I found online did not provide enough detail, so I had to raid my library of old books which are currently in storage. I like to scour second book stores for old books on architecture in the hope they come in useful one day.
The book I found turned out to be exactly what I needed. It is a 5th edition book published in 1848 called "An Attempt to Discriminate the Styles of Architecture in England from the Conquest to the Reformation" by Thomas Rickman, F.S.A. All the scanned engravings featured below are from Rickman's book.
So now we are at this point, it's time to learn some history. For that I'm going to include an extract from the book that summarises the four styles of English Architecture so we can see when in history, the toothed ornament came to be. These four styles are:
- Norman Style
- Early English
- Decorated English
- Perpendicular Style
Norman Style
"1st, the Norman style, which prevailed to the end of the reign of Henry II., in 1189; distinguished by its arches being generally semicircular; though sometimes pointed, with bold and rude ornaments. This style seems to have commenced before the Conquest, but we have no remains really known to be more than a very few years older." Rickman
Early English Style
"2nd, the Early English style, reaching to the end of the reign of Edward I., in 1307'; distinguished by pointed arches, and long narrow windows, without mullions; and a peculiar ornament, which, from its resemblance to the teeth of a shark, we shall hereafter call the toothed ornament." Rickman
Decorated English Style
"3rd, Decorated English, reaching to the end of the reign of Edward III., in 1377, and perhaps from ten to fifteen years longer. This style is distinguished by its large windows, which have pointed arches divided by mullions and the tracery in flowing lines [or] forming circles, arches, and other figures, not running perpendicularly; its ornaments numerous, and very delicately carved." Rickman
Perpendicular English Style
"This is the last style, and appears to have been in use, though much debased, even as far as to 1630 or 1640, but only in additions." Rickman
Toothed Ornament
The 'toothed' ornament resembles the teeth of a shark and is a feature of the Early English style. It is also referred to as 'dogtooth', presumably because. of its resemblance to dogfish teeth.
The following picture shows the toothed ornament used on two church fonts.
Recreating a Toothed Arch in 3D
The following image was created by tracing the cross-section of the molding in Rickman's book, modelling the tooth, applying arrays to the teeth to arrange them into bands, and applying bend modifiers to the moldings and teeth to approximate the curve of an arch.
"English" vs "Gothic"
It's clear from Rickman that there is a distinction between the bold simpler English buildings when compared to the Continental buildings called Gothic. The Early English style was largely influenced by, and evolved out of the Norman style.
"A careful examination of a great number of Norman buildings will also lead to the conclusion – that the style was constantly assuming a lighter character, and that gradation is so gentle into the Early English, that it is difficult in some buildings, to class them, so much have they of both styles." Rickman
Elliptical Approach
Since publishing the information above, Frank Beckmann from the Cheetah 3D community provided an alternative approach to laying out the toothed ornament using an ellipse.
One thing that Frank pointed out with my approach, was that by shifting the major arc's centre, the points of adjacent toothed ornaments will not come into contact at the tips and the arc will curve outside of the square within which it is drawn. The following picture shows how the arc sweeps from the tip outside the square, before sweeping back into the square.
To ensure the arc stays within the square, Frank stretches the circles to form ellipses as shown below.
There is one more alternative approach, and that is to use an oval instead of an ellipse.
It's difficult to know the actual approach used by Early English stonemasons. The differences in the methods described above are very small. Chances are it will be the most practicable method that was used. Thank you to Frank Beckmann for his contribution to this post.
Categories: Architecture, Dynamic Symmetry, Geometric Progression