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 Hanover, Geodetic Institute, Nienburger Straße 1, D-30167 Hanover,

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, +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, +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

1998