Transcript Measuring deformations of wheel
Measuring deformations of wheel produced ceramics using high resolution 3D reconstructions
Avshalom Karasik Hubert Mara, Robert Sablatnig, Ilan Sharon, Uzy Smilansky March 2005 Tomar, Portugal
Goals
• To learn about production technology of ceramics by studying its flaws and deformations.
• To try and use it to characterize workshops methods and production patterns.
Concept
• To introduce new investigation tool to the archaeological research which quantifies deformations of wheel-produced pottery, by combining two things: 1. Well-known mathematical theory.
2. High resolution 3D techniques.
Introduction
• Wheel-produced ceramics, are intended to be axially symmetric.
Introduction
• One profile section is usually used to represent the vessel morphology.
Introduction
• Their horizontal intersections by planes should be perfect circles.
100 50 0 -50 -100 80 60 40 20 0 -20 -40 -60 -80 -50 0 50 80 60 40 20 0 -20 -40 -60 -80 -80 -60 -40 -20 0 20 40 60 80
Introduction
• Their horizontal intersections by planes should be perfect circles.
100 50 0 -50 -100 80 60 40 20 0 -20 -40 -60 -80 -50 0 50 80 60 40 20 0 -20 -40 -60 -80 -80 -60 -40 -20 0 20 40 60 80
Introduction
• Ceramic objects may suffer deformations when still on the wheel, or during the drying and firing stages. • As a result the afore-mentioned sections will deviate from perfect circles.
• How to measure these deviations and what can it teach us as archaeologists is the subject of this talk.
Data acquisition
A mandatory requirement to this analysis is to have accurate 3D reconstructions of the objects.
We used Minolta VI-900 in collaboration with the PRIP group from the Technical University of Vienna.
Data acquisition
80 60 40 20 220 200 180 160 140 120 100 50 0 -50 -50 0 50 100 80 60 40 20 0 -20 -40 -60 -80 -100 -80 -60 -40 -20 0 20 40 60 80
Method
• Usually, these kind of convex curves are represented by the radius as a function of the angle, which is customary and convenient to analyze with the Fourier representation:
r
( )
R
0
n N
1 ˆ
n
cos
n
n N
1 ˆ
n
sin
n
• The coefficients are:
x n
1 2 2 0 cos
n
r
( )
d
;
n
1 2 2 0 sin
n
r
( )
d
Method
• The n’th deformation parameter and associated phase are defined by:
r n
x
ˆ
n
2
y
ˆ
n
2 ;
n
arcsin
x
ˆ
n r n
Method
• This representation is applicable only for convex or star-like shapes where the radii intersect with the curve only once.
• Nevertheless, by taking the radius as a function of the
arc-length
any close curve can be described in an unambiguous way.
r
(
s
)
Method
• The new Fourier coefficients can be simply calculated by changing the integration variable so that: ˆ
n
1 2 0
L
cos
n
(
s
)
r
(
s
)
d
ds ds
;
y
ˆ
n
1 2 0
L
sin
n
(
s
)
r
(
s
)
d
ds ds
.
• This coincides with the definition above for convex curves.
• Again, the deformation parameters are:
r n
x
ˆ
n
2
y
ˆ
n
2 ;
n
arcsin
x
ˆ
n r n
Method
• • The deformation parameters are determined in an unambiguous way when we choose the origin such that the coefficients and vanish. • The parameter is the mean radius, and it serves to set the scale (size) of the section. • The first non trivial coefficients or (
r
2 , 2 2 the ellipse which fits the curve best 2
r
2
r
0 the tilt angle of the main axes of the ellipsoid relative to the coordinate axes.
a.
Method
0.012
100 50 0 -50 -100 -60 -30 0 mm 30 60 r n r 0 0.008
0.004
b.
smaller section larger section 0 2 4 n 6 8 10
Test case
• Two contemporary but traditionally produced wheel-made jugs from the market of Vienna were scanned by the 3D scanner.
Test case
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Test case
0.012
r n r 0 0.009
0.006
Left jug Right jug 0.003
0 1 2 3 4 5 n 6 7 8 9 10 n
Test case
Neck Shoulder Body Base
Neck Shoulder Body Base
Test case
0.04
r n r 0 0.02
Neck Left jug Right jug 0.04
r r n 0 0.02
Shoulder Left jug Right jug 0.04
r n r 0 0.02
0 2 4 n 6 Body 8 10 Left jug Right jug 0.04
r r n 0 0 2 4 n 6 Base 8 10 Left jug Right jug 0.02
0 2 4 n 6 8 10 0 2 4 n 6 8 10
Test case
Top view of the neck: Blue – measured radii points Red – best fitted circle -10 -20 -30 -40 -50 20 10 0 50 40 30 -20 0 20 -10 -20 -30 -40 -50 20 10 0 50 40 30 axis of mirror symme try -20 0 20
Conclusions
We introduced new quantitative tool which measures minute deformations and differences between ceramic vessels that could hardly be traced by eye.
We propose these measures as relevant archaeologically to provide technical information on the production process and workshop skills, and may be for the identification of potters hand marks.