2003-09-25

WG4: Geometrical Investigations of Spatial Geodetic Problems

International Association of Geodesy
IAG Special Commission 4
Application of Geodesy to Engineering 
SC4 WG4: Geometrical Investigation of Spatial Geodetic Problems 

Chairman: Prof. Thomas Wunderlich, 
Department of Applied and Engineering Geodesy,
Vienna University of Technology,
Gusshausstrasse 27-29, A-1040 Wien, Austria 
Tel.: +43/1/58801-12844, Fax: +43/1/58801-12895,
E-mail: Thomas.Wunderlich@tuwien.ac.at

July 12, 1999

WG4 has been installed by Prof. Kahmen, who took over IAG-Spec.Commission 4 in 1995. The basic intention was to merge experts from the fields of geodesy and geometry in a capable team with the common interest in defining, studying and solving geometrical problems of geodetic origin and concern while simultanously improving the imaginative faculty.

During the past four years six active members, accompanied by a number of corresponding scientists inspired by the mission, dealt with a choice of present-day tasks listed by the chairman. In April 1998 at the occasion of the IAG Symposium on Geodesy for Geotechnical and Structural Engineering, the investigations’ results were presented in course of 11 lectures.

Active Members

A. Geiger 
ETH-Hönggerberg, Inst.for Geodesy and Photogrammetry, 
CH-8093 Zurich, Switzerland, 
Tel: +411/633 3244, Fax: +411/633 2661 
e-mail: alain.geiger@geod.ethz.ch

R. Heer
University of Hannover, Geodetic Institute, 
Nienburger Straße 1, D-30167 Hannover, Germany, 
Tel: +49511/762 4469, Fax: +49511/762 2468
e-mail: raini@gih.uni-hannover.de

H.Pottmann
Vienna Technical University, Institute of Geometry, 
Wiedner Hauptstraße 8,
A-1040 Vienna, Austria, 
Tel: +431/58801 11310,
e-mail: pottmann@geometrie.tuwien.ac.at
http: www.geometrie.tuwien.ac.at

W. Rath
Vienna Technical University, Institute of Geometry, 
Wiedner Hauptstraße 8,
A-1040 Vienna, Austria, 
Tel: +431/58801 11322, 
e-mail: rath@geometrie.tuwien.ac.at
http: www.geometrie.tuwien.ac.at

R.Santerre
University Laval, Dep. of Geomatics, 
Pavillon LouisJaques-Casault, G1K 7P4
Laval, Quebec, Canada, 
Tel: +1418/656 2294, Fax: +1418/656 7411 
e-mail: Rock.Santerre@scg.ulaval.ca

P. Savvaidis
University of Thessaloniki, Dep. of C.E., Lab. of Geodesy, Univ.Box. 465,
GR-54006 Saloniki, Greece, Tel: +3031/99 5724, Fax: +3031/99 6159 
e-mail: savvaidis@olymp.ccf.auth.gr

The agreed schedule of current geometrical problems in geodesy split up in two main areas: tasks related to complex geodetic measurement procedures and tasks related to pretentious functional and architectural design.

Regarding the first item, we stated that modern geodetic measurement techniques, sometimes based on novel measurement quantities (like e.g. pseudoranges in GPS), have their own specific geometrical properties. Research was needed to gain insight into the geometrical behaviour and to isolate optimum and minimum configurations. The investigations had to be accompanied by the development of instructive software to visualize the findings for training purposes.

As for the second matter, we observed that modern architectural designs, often in connection with precise prefab-manufacturing of plastic construction parts, demand geodetic conversion of the artistic idea into consistent geometric parameters and co-ordinates. Investigations were needed as an essential part of Total Quality Management on the major steps to the realization of the design, such as the geometrical elements, and on-site assemblage.

Evaluating the results, one feature became obvious above all: wherever a constructive dialogue between representatives of geometry and geodesy could be initiated, mutual inspiration seemed to conquer any challenge. This became most evident in Rath, 1998, which cleared up convincingly the kinematical background of oblique plumbing. It can be felt while reading Hoshen, 1995 and comparing the findings with the ideas cited in Wunderlich, 1998; positioning by means of pseudoranges seems to be left without any geometrical secrets from now on. Pottmann, 1998 gives a vivid example for the capabilities modern computer geometry disposes of when geodesy manages to put a clear question. Nevertheless, a considerable number of current geodetic problems were solved by scientists of one discipline only. The problems related to to the development of the Digital Field Map (Helm, 1998) where manual sketches on a pentop screen are to be converted into digital maps arouse great interest in geometry and will surely benefit from cooperation.

In conclusion, there is no denying the fact that - as geometrical problems in geodesy were the prime interest here - the input of geometry provided a decisive step forward. It is a pleasure to notice that it is the geometric party which does not hesitate to prolongate the prosperous alliance.

In the following the original schedule of problems offered to the members is given; those tasks which have been selected for treatment and of which the results have been published within the period 1995-1999 are printed in bold italics.

Schedule of Current Geometrical Problems in Geodesy

1. Complex geodetic measurement procedures

1.1. Terrestrial methods

Oblique plumbing with a theodolite

WUNDERLICH, Th. „Oblique plumbing with a theodolite", Proc. „Surveying of Large Bridge and Tunnel Projects", pp.169-180, Danish Road Directorate, Copenhagen, 1997

WUNDERLICH, Th. „Aplomado oblicuo con teodolito", Topografia y Cartografia, No.86, pp.20-29, Madrid, 1998

RATH, W. „Oblique Plumbing - The Kinematical Background", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.500-505, Culture and Congress Centre, Eisenstadt, 1998

Spatial resection (video theodolite/image processing,industrial measurement systems)

Robot calibration

HUSTY, M. „Abstandsprobleme zu windschiefen Geraden I", Sitzungsberichte d.

SACHS, H. Österr. Akademie d. Wissenschaften, Abt.II, Band 203, Springer,1995

HUSTY, M. „An algorithm for solving the direct kinematics of general Stewart- Gough-platforms", Mech. Mach. Theory, Vol.31, No.4, pp.365-380, Pergamon, 1996

KARGER, A. „On self-motions of a class of parallel manipulators", Proc. „Recent 

HUSTY, M. advances in robot kinematics", pp.339-348, Kluwer acad. publ., 1996

Rectification of field sketches (variable irregular scale)

HELM, F. „Geometrisierung und Rektifizierung manueller Skizzen", Zeitschrift für Vermessungswesen, Konrad Wittwer, Stuttgart, 1997

HELM, F. „Realisierung topologischer Kriterien bei der Rektifizierung manueller Skizzen", Zeitschrift für Vermessungswesen, Konrad Wittwer,Stuttgart, 1997

WUNDERLICH, Th. „Qualitätssicherung mittels Digitalem Feldplan", Wissenschaftliche Arbeiten der Fachrichtung Vermessungswesen der Universität Hannover, No.209, pp.229-239, Hannover,1996

HELM, F. „Geometrization and Rectification - Characteristics of the Digital Field Map", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.506-511, Culture and Congress Centre, Eisenstadt, 1998

WUNDERLICH, Th. „How Digital Sketches Convert to a Map", Proc. 3. Turkish- HELM, F. German Joint Geodetic Days, Istanbul Technical University, Istanbul, 1999

1.2. Satellite supported methods

1.2.1. Positioning and Navigation

Single point positioning (geometrical foundations & visualizations) - solutions based on pseudoranges and doppler shifts

HOSHEN, J. „From Apollonius to Newton to GPS", Proc. of the 51st annual meetingof the Institute of Navigation, pp.129-134, Alexandria, Virginia, 1995

Recognition and prevention of critical configurations (outage expulsion)

WUNDERLICH, Th. „A Strategic Alliance of Geodesy and Geometry", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.457-464, Culture and Congress Centre, Eisenstadt, 1998

Benefit from critical configurations - optimal positioning under influence of S.A. - improved navigation in urban canyons

HUSTY, M. „Abstandsprobleme zu windschiefen Geraden I", Sitzungsberichte d.

SACHS, H. Österr. Akademie d. Wissenschaften, Abt.II, Band 203, Springer,1995

1.2.2. Relative Positioning

Relevant DOP criteria for baseline evaluation

GOERRES, B.„Bestimmung von Höhenänderungen in regionalen Netzen mit dem Global Positioning System", Deutsche Geodätische Kommission, Reihe C, Heft Nr.461, Verlag des Instituts für Angewandte Geodäsie, Frankfurt am Main, 1996

RICHTER, B. „Konfigurationsabhängige Genauigkeitsfaktoren für GPS-Basislinien", diploma thesis, Vienna Technical University, 1999

Geometrical interpretation of double and triple differences

SANTERRE, R.„Geometrical Interpretation of GPS Positioning with Single, Double

GEIGER, A. and Triple Difference Carrier Phase Observations", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.500-505, Culture and Congress Centre, Eisenstadt, 1998

Campaign planning for distant observation points

BOULIANNE, M. „Floating lines and cones for use as a GPS mission planning SANTERRE, R. aid", Photogrammetric Engineering & Remote Sensing, GAGNON, P.A. Vol.62, No.3, pp.311-315, USA, 1996

NOLETTE, C.

Optimal representation of varying DOP-qualities in maps

KINDSGRAB, M. „Charting Areas of Constant GDOP for Urban GPS WALRAFF, C. Purposes",Proc. „Geodesy for Geotechnical and Structural Engineering", pp.471-476, Culture and Congress Centre, Eisenstadt, 1998

2. Pretentious functional and architectural designs

2.1. Functional designs

Optimal tiling (tesselation) for radom covers - Possible deformations of shell structures

SAVVAIDIS, P. „SECT3 - A Computer Program for the three-dimensional Representation of Structures Using an Industrial Measurement System", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.512-517, Culture and Congress Centre, Eisenstadt, 1998

WUNDERLICH, Th. „A Strategic Alliance of Geodesy and Geometry", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.457-464, Culture and Congress Centre, Eisenstadt, 1998

Definition and adjustment of a truncated conical shell from scattered points

KATRYCZ, W. „Zur Problematik ausgleichender Kegelflächen", diploma thesis, Abt. Ingenieurgeodäsie, TU Wien, 1997 

KATRYCZ, W. „Least Squares Treatment of Conical Surfaces", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.518-523, Culture and Congress Centre, Eisenstadt, 1998

2.2. Architectural designs

Best approximation of free-form connecting surfaces; smooth transition between geometrically pre-defined elements

GRAFAREND, E.W. „Map Projections of Project Surveying Objects and SYFFUS, R. Architectural Structures", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.489-499, Culture and Congress Centre, Eisenstadt, 1998

NITSCHKE, M. „Model of a Pipeline Axis Using Straight and Circular KNICKMEYER, Segments", Proc. „Geodesy for Geotechnical and Structural Engineering", pp.477-482, Culture and Congress Centre, Eisenstadt, 1998

POTTMANN, H. „Reconstruction of Kinematic Surfaces from Scattered Data", LEE, I.-K. Proc. „Geodesy for Geotechnical and Structural Engineering", RANDRUP, T. pp.483-488, Culture and Congress Centre, Eisenstadt, 1998

STIGLITZ, W. „Geometrische Umsetzung von Freihandentwürfen", diploma thesis, Abt. Ingenieurgeodäsie, TU Wien, 1997 

WUNDERLICH, Th. „Ein elliptischer Steg", Geowissenschaftliche Mitteilungen, No.50, Vienna Technical University, 1999 (in print)

Conversion algorithm for different geometrical descriptions of prefab plastic or wooden construction parts

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