INTRODUCING 3D VISION AND COMPUTER GRAPHICS TO

ARCHAEOLOGICAL WORKFLOW

An Applicable Framework

Hubert Mara

PIN - Servizi Didattici e Scientiﬁci per l’Universit`a di Firenze, VAST-Labratory, Piazza Ciardi 25, 59100 Prato, Italy

Andreas Monitzer

Vienna University of Technology, Institute of Computer Graphics and Algorithms

Favoritenstrasse 9/186, 1040 Vienna, Austria

Julian St¨ottinger

Vienna University of Technology, Institute for Computer Aided Automation

Pattern Recognition and Image Processing Group, Favoritenstr 9/183-2, 1040 Vienna, Austria

Keywords:

3D Computer Vision, Bi-Directional Reﬂectance Distribution Function (BRDF), Rotational Axis, Cultural

Heritage, Archaeology.

Abstract:

Cataloging drawings of ancient vessels and sherds is still the most time consuming task in the typical archae-

ological workﬂow. The properties of these ﬁndings like proﬁle, volume, and wall thickness have always been

estimated and drawn by hand. Through archiving, classifying and exhibiting these ancient artifacts we wish

to gather as precise information as possible. Within seconds, today’s 3D-scanners provide surface meshes of

ancient vessels which are more precise than any manual estimation which may take up to several hours.

We propose a semi-automated, applicable framework for dealing with large 3D-meshes of ancient ﬁndings

from scanning the vessels for publication. In this interactive environment we estimate the axis of vessels,

estimate their proﬁle lines and render real time visualizations using state-of-the-art 3D-hardware techniques.

The results can be printed in their real size for direct use in archaeological literature. Further, these methods

will give the ability to publish 3D-meshes of ancient vessels for archaeological research.

Recent extended tests have been carried out on archaeological sites in Peru and Austria. These experiments

showed under real life circumstances the improvement of using this system in both precision and time efﬁ-

ciency.

1 INTRODUCTION

Motivated by the requirments of archaeologists we

are developing a system for automated documentation

of their ﬁnds. Beside (large) remains of architecture

the most common ﬁnds on archaeological excavations

are (small) objects of the daily live. These small ob-

jects are typically tens of thousands of fragments of

ceramics (sherds), because ceramics have been used

and preserved for thousands of years. Therefore doc-

mentation of sherds is one of the important tasks

for archaeology, because sherds represent information

about population movements, inter-regional contacts,

production context, and technical or functional con-

straints (archaeometry (Leute, 1987)).

Until present day documentation is done by man-

ually drawing a horizontal cross- section of the ori-

entated sherds and a side-view of the ceramic. The

horizontal cross-section is called proﬁle (line). Fur-

thermore the proﬁle line is also the longest elongation

around the wall of a ceramic. Therefore it is estimated

the maximum height of a ceramic. An example for

such a manual drawing is shown in Figure 1. While

the right-hand-side of this Figure shows the Proﬁle,

the left-hand-side shows a front view of the sherd as

it would appear without any traces of wear, dirt or any

other dis-coloration of long-time-storage.

Therefore we have identiﬁed two major tasks to

305

Mara H., Monitzer A. and Stöttinger J. (2008).

INTRODUCING 3D VISION AND COMPUTER GRAPHICS TO ARCHAEOLOGICAL WORKFLOW - An Applicable Framework.

In Proceedings of the Third International Conference on Computer Vision Theory and Applications, pages 305-312

DOI: 10.5220/0001082603050312

 SciTePress

(a) (b)

Figure 1: (a) Photo of a real sherd and (b) its manual draw-

ing showing the proﬁle line.

be performed after 3D-acquisition of ceramics shown

in the next Section. The ﬁrst task is the estimation of

the proﬁle line shown in Section 3. Then we show

a method for rendering the surface of acquired 3D-

models adopted for archaeological publication in Sec-

tion 4. In Section 5 we show results of our experi-

ments applied to synthetic and real objects of excava-

tions in Peru and Austria. Finally a conclusion and an

outlook is given in Section 6.

2 DATA ACQUISITION

Depending on the skills of a craftsperson a manual

drawing as shown in Figure 1 is done in 10 to 15 min-

utes for simple sherds. Regarding the vast numbers

of sherds a large amount of working time on an ex-

cavation is spent on manual drawings. Therefore we

are developing an automated system for acquisition of

sherds and estimation of the proﬁle-line. The acquisi-

tion is done by using a 3D-Scanner based on the prin-

ciple of structured light (Cosmas et al., 2001) using a

Konica-Minolta Vi-900 or Vi-9i shown in Figure 2.

(a) (b)

Figure 2: In-situ setup of the 3D-scanner (a) consisting of a

Laser, a CCD camera and a rotational plate for acquisiton of

(b) e.g. a NASCA sherd found in the Valley of Palpa, Peru.

The rotational plate shown in Figure 2 is typically

used for acquisition of unbroken ceramics for auto-

mated registration using ICP (Besl and McKay, 1992;

Chen and Medioni, 1992; Rusinkiewicz and Levoy,

2001). In case of sherds, plates and other small ob-

jects either a model based approach (Kampel and Sab-

latnig, 2003) or a well deﬁned frame (Mara, 2006)

also acting as holding device can be used. Further-

more this frame is used to increase the performance

of our system by acquiring severall sherds at once,

as the 3D-Scanner requires ﬁxed amounts of volume.

Background objects and noise are removed either us-

ing their color (black/white) or by their size and/or

location (Mara, 2006).

For testing the Proﬁle estimation in the next sec-

tion and for further interdisciplinary research to an-

swer further archaeological questions we acquired

severall hundred unbroken vessels and sherds in Aus-

tria (Lettner et al., 2006; Mara et al., 2007) and

Peru (Mara and Sablatnig, 2007).

3 ORIENTATION & PROFILE

ESTIMATION

Regardless if we are using a digital or manual sys-

tem, the orientation of a sherd is the essential part of

the estimation of the proﬁle line as every further anal-

ysis (Leute, 1987) relies on it. Therefore this section

shows how orientation is carried out by the estimation

of the axis of rotation.

The oldest and most popular approach to orienta-

tion is the manual method used by archaeologists for

several decades. This manual approach is based on

the production process of ceramics, because ceram-

ics have been produced on potters wheels (rotational

plates) for thousands of years. Therefore ceramics

have a axis of rotation, which is also called the axis

of symmetry. This axis of rotation is also present for

fragments of ceramics (sherds). Our method is in-

spired by a variation of the manual orientation, which

is related to (Melero et al., 2003), because we also use

the ﬁtting of circle templates for the estimation of the

axis. In contrast to (Melero et al., 2003) our method

can be carried out both semi-automatically and auto-

matically. Other related methods are (Willis, 2004)

and (Orriols, 2004), which focus more on reconstruc-

tion of a complete, but broken object than on orienta-

tion of single fragments. Fitting of circle templates is

done similiar to the manual method of archaeolgists.

Therefore circles are ﬁt into the inside of a sherd un-

til the circle templates are concentric and their cen-

ters are aligned along the axis of rotation. This is

achieved by ﬁtting circle templates into the intersec-

tion between the sherd and sets of parallel planes. Fig-

ure 3a shows such circle templates and other tools to

orient a sherd. Figure 3b shows a Proﬁlkamm which

is used to transfer the proﬁle line to paper.

For the semi-automatic method these planes are

aligned parallel to the XY-plane. The sherds have

to be in upright position with an angular error less

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

306

(a) (b)

Figure 3: Tools for drawing a proﬁle line: (a) pens, scale

paper, lead-wire, ruler and sliding calliper, (b) Proﬁlkamm.

than 20°towards and sidewards of the axis of rota-

tion. The distance (radii) towards the axis of rotation

is then estimated automatically. For the fully auto-

mated estimation of the axis the upright position is

found in two stages: The ﬁrst stage is the ﬁtting of

circles into intersections of sets of parallel planes or-

thogonal to the balancing plane of the inner side of

the sherd. The normal vectors of the set of parallel

planes having a minimum deviation of circle centers

are aligned within the plane of symmetry. Figure 5

shows the inner side of a sherd with parallel intersec-

tions and a hypothesis for the axis of rotation (nor-

mal vector of the parallel planes). In the second stage

this set of planes is rotated around the normal vector

of the plane of symmetry until the minimum point of

the deviation of the circle centers is found. The nor-

mal vector of the planes having this minimum point is

used to transform the sherd into the upright position

for the ﬁnal estimation of the axis, which is identical

to the axis estimation of the semi-automatic method.

As all these methods typically exist as matlab pro-

totypes, which requires a license and computer ex-

pert skills for handling, we decided to implement

the estimation of the proﬁle line using open source

technologies. Therefore we choose to implement our

methods using Qt© (Trademark of Trolltech in Nor-

way and other countries), which allows us to provide

our framework for all actual major operating systems.

Figure 5 shows a screenshot of our framework called

ArchiCut. The next section shows how we achive a

surface based rendering typically used together with

the proﬁle line within archaeological publications.

4 RENDERING CERAMICS FOR

ARCHAEOLOGICAL

DOCUMENTATION

Having the proﬁle-line automatically estimated as

shown in the previous section, we achived to render

the most important part for archaeological documen-

tation of ceramics. Considering Figure 3b we have

seen that archaeolgists add another important infor-

mation about the ceramics: a side- view of the ce-

ramic showing its surface, which is as important as

the shape of the proﬁle line, because the roughness

and color of the surface leads to the manufacturing

process and the ingridients of the clay.

Having a digital camera as part of the 3D-Scanner

it is possible to acquire a still image or render the

3D-Modell with the texture acquired by the camera

for the side-view of a ceramic. As simple this solu-

tion is for well-preserved ﬁnds - as unpracticable it is

for archaeological documentation for the majority of

sherds, because they are in general partially or com-

pletly discolored due to erosion. Therefore archae-

ologist generally favor a drawing over a still image

or a photo-realistic rendering, because the drawings

has a certain amount of abstraction showing the ob-

ject with its original color. Furthermore, not every

3D-Scanner includes a camera capable of acquiring

texture in color.

Therefore we require a simple and versatile con-

cept to render the surface which does not include the

colour information provided by some 3D scanners.

It has to be simple, because having no texture re-

quires a manual adjustment of reﬂectance parameters

as templates for different ceramic surfaces. This has

to be done by an archaeologist in an fast and intu-

itive way. Versatility is required, because we may

also take into account the use of the na¨ıve approach

of measuring the reﬂectance of an existing material

using a spectrometer and a robotic arm-setup that al-

lows to freely move a spotlight and the spectrometer

around the sample, and store them in an matrix. Such

a device is called a ”gonioreﬂectometer” (Foo, 1997).

Even by such a na¨ıve approach storing the reﬂectance

parameters in very limited space, while still giving an

adequate appearance of many materials, such as vel-

vet or lacquer can be achieved.

Suitable approaches to our problem, not limited

to a certain domain are: The mathematical approach

using a separable decomposition (Kautz and Mc-

Cool, 1999), the phenomenological approach using

the Lafortune BRDF (Lafortune et al., 1997) and the

physically-based approach using the Cook-Torrance

reﬂectance model (Torrance and Sparrow, 1967). An

example for a limited domain is the Binn-Phong re-

ﬂection, which is only used for rendering metals.

The rendering of the 3D data was supposed to

take advantage of current graphics cards and to run

predominantly on these dedicated graphics processors

(GPUs). Because it could be done with minimal mod-

iﬁcations to the prior source code and it is supported

by all current hardware we choose to use the Graph-

INTRODUCING 3D VISION AND COMPUTER GRAPHICS TO ARCHAEOLOGICAL WORKFLOW - An Applicable

Framework

307

(a) (b) (c) (d)

Figure 4: (a) Axes used for the ﬁrst estimation of the rotational axis. These axes are deﬁned by the masspoint and the

balancing plane. (b) First Axis from (a) deﬁned by the ﬁrst eigen-vector of the balancing plane. (c) Axis deﬁned by the

second eigen-vector of the balancing plane. (d) Axis from (a) deﬁned by the about 130° rotated ﬁrst eigen-vector of the

balancing plane.

Figure 5: Screenshots ArchiCut - Left: Ceramics intersected through rotational axis. Right: Estimated Proﬁle Line.

ics Library Shading Language (GLSL) programming

language which is built into OpenGL 2.0. Taking

this into account, we chose to include the Lafor-

tune Bi-Directional Reﬂectance Distribution Function

(BRDF) to our existing system done purely in GLSL.

Shaders were added to graphics cards, because the

previous static rendering model (now called ﬁxed-

function pipeline) became more and more complex

with each revision, in order to add rendering fea-

tures like shadows or shading models. These features

were implemented using a proprietary vendor-speciﬁc

bytecode language. In order to allow more freedom

to the graphics programmer, an open speciﬁcation for

shaders was created, extending the ﬂexibility of the

graphics card.

In the beginning, these shaders did not allow loops

or conditions, since the graphics processor is a spe-

cialized stream-based processor, which allows it to

be much faster at tasks that can be mapped to these

constraints, compared to generic central processing

units used in desktop computers. Beginning in shader

model 3, loops and conditions were added at a great

speed penalty.

4.1 Programming Shaders

GLSL (Shreiner et al., 2006) is designed in a similar

way to all other high level shading languages avail-

able – namely, Microsoft’s High Level Shader Lan-

guage (HLSL) (Gray, 2003) and NVIDIA’s Cg (Fer-

nando and Kilgard, 2003). It is based on the C pro-

gramming language, allowing software developers to

leverage existing knowledge about it.

Shaders in the shader model 3 are are structured

into two separate parts, a vertex shader and a fragment

shader.

1. A vertex shader is responsible for transforming

the vertices of the triangles sent to the GPU from

the world space to the view space. It can move

vertices, but it cannot add or drop them. Its main

function is run once per vertex.

2. A fragment shader is responsible for deﬁning the

color of a fragment after the rasterization step.

A fragment (in respect to the shader) can be de-

scribed as a “potential pixel” on the screen. It

might get culled after the shader is run, but if that

doesn’t happen, it is directly written to a pixel in

the frame buffer. This allows using arbitrary shad-

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

308

ing, and is the location where the Lafortune BRDF

used in this paper has to be implemented. It is run

once per fragment, so it is important to keep this

shader as simple as possible.

4.2 The Lafortune Shader

(Lafortune et al., 1997) demonstrates that an even ap-

proach simpler than (Kautz and McCool, 1999) can be

used to adequately approximate a BRDF. Basically a

BRDF reﬂectance function is a combination of mul-

tiple so-called “Phong Lobes” – or vice versa: The

representation known as Phong reﬂection model is ac-

tually a simple but limited BRDF. Mathematically, the

reﬂectance function can be represented as

(

) = ρ

∑

i=1

s,i









o,x

o,y

o,z

















i,x

i,y

i,z









where ρ

is the diffuse reﬂectance (texture), M is

the number of Phong Lobes, and ρ

s,i

, C

, n de-

scribe the Lobe shape. So, considering that ρ rep-

resents colored information, the amount of memory

required is M ∗ 7 + 3 per surface. This small require-

ment enables storing a separate BRDF for each UV-

coordinate of the object (using two additional tex-

tures per lobe). The results of this technique named

“Spatial BRDF” (SBRDF) is demonstrated in images

available on

http://sbrdf.cs.unc.edu

(McAllis-

ter, 2004) (checked 26.Sept., 2007), where more in-

formation is also presented.

The lobe shape described by C

, C

and n

can be interpreted as follows: The C-parameters de-

ﬁne the location of the reﬂection peak using a three-

dimensional vector. n describes the spread of the

highlight created by this lobe. Usually, only up to

three lobes are necessary for visually pleasing result.

The ray tracer “pbrt” described in (Pharr and

Humphreys, 2004) also implements the Lafor-

tune BRDF (non-spatially). However, it allows spec-

ifying one BRDF per primary color, allowing a more

realistic reﬂectance behavior, for the price of tripling

the storage requirements. (Marschner et al., 1999) de-

scribes how to create primary-color-separatedBRDFs

by using a laserline scanner and a video camera.

The pseudocode used for calculating a fragment’s

color is shown in Listing 1. The algorithm’s complex-

ity is O(n· m), where n is the number of lights and m

is the number of lobes.

Note that the implementation calculates the BRDF

for the three primary colors separately, in order to fur-

ther enhance realism and be able to integrate the ex-

ample materials used in (Pharr and Humphreys, 2004)

(not shown in the pseudo code).

Listing 1: Pseudocode for the fragment shader.

void main ( ) {

normalize normal v e c t o r

c a l c u l a t e and normalize view v e ct o r . . .

based on t he normal v e c t o r and . . .

the p o s i t i o n of the fragment in . . .

world space

fragment color = base color of the . . .

fragment der ived from the vertex color

for every l i g h t {

l i g h t d i r e c t i o n = normalized . . .

l i g h t po s i t i o n

add d i f f u s e color t o fragment color

/ / d i f f u s e = l i g h t c o l o r

. . .

/ / object ’ s d i f f u s e c o l o r

. . .

/ / (N . l i g h t d i r e c t i o n )

i f ( fragment i s v i s i b l e from the . . .

viewer and l i gh t source i s . . .

v i s ib l e from the fragment ) {

uv = pointw ise m u l t i p l i c a t i o n . . .

of the view v e c t o r and the . . .

l i g h t d i r e c t i o n

for every l a f o r t u n e lobe {

add the lobe r e f l e c t i o n to the . . .

fragment c ol o r s e p a r a t e l y f o r . . .

each primary color

/ / r e f l e c ti o n = l i g h t color

. . .

/ / ( ( Cx , Cy , Cz ) . uv )\ ˆ n

}

The values Cx, Cy, Cz and n used for the lobes are

speciﬁc to the material used and stored in a separate

XML ﬁle (Bray et al., 2006) shipped with the appli-

cation, which allows adding, removing and changing

the presets without requiring a recompile of the ap-

plication. The demo materials used were blue paint,

brushed metal, clay, felt, primer and skin (see Fig-

ure 6).

4.3 Image Creation

The second part required for publications is the cre-

ation of an image based on the rendered image. A

screenshot would not be sufﬁcient for this, because

the typical screen resolution of 100 dots per inch is

too low, at least 300 dots per inch (preferably more

than 600 dots per inch) are required for printed mate-

rial. Thus, a more sophisticated approach is required.

The OpenGL extension called “Framebuffer Ob-

jects” allows replacing the screen’s framebuffer with

a texture-based one. This texture is not limited by the

screen dimension, and thus can be any size up to the

INTRODUCING 3D VISION AND COMPUTER GRAPHICS TO ARCHAEOLOGICAL WORKFLOW - An Applicable

Framework

309

(a) (b) (c) (d) (e) (f)

Figure 6: The demo materials rendered using the Lafortune Shader. From left to right: blue paint, brushed metal, clay, felt,

primer and skin.

maximum texture size allowed by the graphics card

(currently, this is 8192 × 8192 pixels). After render-

ing into this texture, it can be copied from the graph-

ics memory to the main memory, encoded in an image

format like PNG or TIFF, and saved to the disk.

The ﬁrst implementation created a 8192 × 8192

texture, and rendered into it. As mentioned earlier,

the real dimension of the object is known (per con-

vention, laserline scanners use a millimeter unit scale

for their data ﬁles), since orthographic projection is

used. So, the resolution is stored into the ﬁle, if the

format supports that metadata. However, this results

in unequal horizontal and vertical resolutions if the

object isn’t square, or phrased differently, non-square

pixels. Tests revealed that many graphics processing

applications including Adobe Photoshop (which is the

post-processingapplication used by the archeologists)

cannot handle non-square pixel graphic ﬁles. Thus, a

second revision was created, that scales portrait ob-

jects to a height of 8192 pixels while setting the width

according to the vertical resolution, and vice-versa for

landscape objects. This reduces the resolution in one

dimension slightly, but is still sufﬁcient for the objects

usually scanned by the archeologists. Due to the ﬁxed

size of 8192 pixels, the actual resolution of the image

depends on the object’s physical size.

5 RESULTS

For a ﬁrst glance of results of our transdisciplianry

work in cooperation with archaeologists, we could

directly answer their questions for objective/precise

and rapid documentation. This means for examples:

we are the ﬁrst to publish new volume of the Cor-

pus Vasorum Antiquorum (CVA) – a very well estab-

lished book series in classic archaeology for a cen-

tury (Pottier, 1923) – using 3D-acquisition and our

proposed methods. This work includes digital proﬁle

lines with side/top-views as shown in this paper. Ad-

ditionally unwrappings of textured surface including

multispectral readings (Mara et al., 2007) and volume

estimations were conducted. We could also decrease

the costs for acquisition as less working time was re-

quired. Furthermore the risk for damaging this high-

value objects was minimized, as 3D-acquistion using

optical means takes only a few seconds and requires a

minimum of (in-situ) handling the objects.

Another recent example are the results for the ves-

sels excavated in the Valley of Palpa, Peru. In this re-

gion the wheel was not invented and therefore the as-

sumption of an rotational axis for ceramics may not be

valid either. Allthough we could determine axis and

planes of symmetry giving the archaeologists qual-

ity features for further classiﬁcation. Furthermore we

could unwrap and enhance the pictoral information of

the painted vessels (Mara and Sablatnig, 2007).

The ﬁnal result of our work is the collection of

methods as application framework called ArchiCut,

which completly relies on Open-Source to achive

transparency and cost-effectivness of the archaeolgi-

cal workﬂow. A screenshot of the User-Interface is

shown in Figure 5, while Figure 7a shows the com-

bined result for the proﬁle line and a scaled side-view

render as clay, while Figure 7b shows a typically im-

proper rendering - as 3D-scanners may not acquire

correct reﬂectance nor any texture nor colour infor-

mation at all. As there already exists software for

editing 3D-data, we choose to implement an import

function using human- readable ASCII ﬁles (Wave-

front .OBJ). Furthermore data can be directly ac-

quired from Polyworks, InnovMetric Software Inc. –

a commonly used 3D- editing software – to increase

the performance of the workﬂow.

VISAPP 2008 - International Conference on Computer Vision Theory and Applications

310

(a) (b)

Figure 7: Rendering of the proﬁle line and the matching

side-view: (a) Arbitrary surface properties giving the im-

pression of a glaced pot. (b) Clay rendering reassambling a

clean and synthetic, but realistic impression.

6 CONCLUSIONS AND

OUTLOOK

Concluding and summarizing this paper, we are able

to show the application of 3D Vision and Computer

Graphics to archaeology within very different re-

search ﬁelds: From South American (”prehistoric”)

to Roman ﬁndings and for small fragments up to

complete large objects. While 3D-acquisition can

already be done by off-the-shelf products, for post-

processing like noise removal and registration there

exist a vast amount of algorithms. Although there

is still much space for improvment, state-of-the-art

methods already suit archeolgist’s purposes as we

showed in large scale experiments. The main part

of this publication concerns with the orientation of

non-industrialized objects and their fragments, which

are supposed to be rotational symmetrical. There-

fore we could show a method for orientation based

on disturbed symmetry to estimate the proﬁle line –

the most important part of archaeological documen-

tation of ceramics. Followed by real-time-rendering

of the objects surface adopted for archaeolgical docu-

mentation, which requires high-resolutionfor printing

and spatial information for further research. This in-

formation is merged with the proﬁle line to complete

the documentation. Furthermore the surface proper-

ties can easily be adopted and stored as templates as

the real texture is either not acquired by certain types

of 3D-scanners or it merely contains noise – typically

dirt.

Future work will be the integration of novel meth-

ods into our framework, which are currently under on-

going development. These methods concern the pro-

cessing, (pattern) recognition and rendering of dec-

orated surfaces. Furthermore we will investigate to-

wards symmetry analysis, which e.g. lead to answers

about other important archaeological questions about

manufacturing processes and quality features for dif-

fernt types of ceramics and their classiﬁcation.

Beside all the previously mentonied improve-

ments of methods another important – conceptual –

work has begun to ensure the intellectual integrity, re-

liability, transparency, documentation, standards, sus-

tainability and accessibility of the information gath-

ered by the increasing use of 3D-scanners. Other-

wise we will face the problems shown in (Ogleby,

2007). Therefore we are adopting The London Char-

ter (Beacham et al., 2006), which will be a future

standard for the use of 3D- Vision and Computer

Graphics within Cultural Heritage.

ACKNOWLEDGEMENTS

We would like thank the following institutes

for granting access to their objects: Deutsches

Arch

aologisches Institut, Bonn, Germany

(

http://www.dainst.org/abteilung 272 de

.html

); Kunsthistorisches Museum, Vienna, Austria

(

http://www.khm.at

); the Austrian Bundes-

denkmalamt (

http://www.bda.at

); the Institute

for Studies of Ancient Culture, Austrian Academy

of Sciences (

http://www.oeaw.ac.at/antike

)

and the Duwe 3D AG (

http://www.duwe-3d.de

Germany for their support regarding InnovMetric

Polyworks (

http://www.innovmetric.com

). All

URLs checked 26.Sept., 2007. This work was par-

tially supported by the Austrian Science Foundation

(FWF) under grant SESAME (P17189-N04), and the

European Union Network of Excellence MUSCLE

(FP6-507752).

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