Differential Geometry and Geometric Structures
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I3809-N32: Geometric shape generation

Joint Project between Austria (FWF) and Japan (JSPS)

FWF - Austrian Science Fund

JSPS - Japan Society for the Promotion of Science

Project leader (Austria): Udo Hertrich-Jeromin
Project leader (Japan): Miyuki Koiso
Funding period: 1 Apr 2018 - 31 Mar 2020 (approved 5 Mar 2018)

Fields: Mathematics, Arts; Areas: Differential geometry, Integrable systems, Discrete differential geometry, Geometric design methods


Semi-discrete principal net Semi-discrete principal net,
smoothed by channel surfaces
(Fig: M Lara Miro)

Abstract. Explicit classification results and representation formulae are at the core of the differential geometry of curves and surfaces - they serve to generate geometric shapes (curves or surfaces) with certain prescribed properties: for example, the classical Weierstrass representation formulae serve to generate any surface that (locally) minimizes area out of simple data. Other shape generation methods include "transformations", which transform a given shape of a certain class into another such shape, while preserving its key properties.

While such "shape generation methods" are designed to produce curves or surfaces of a particular kind out of suitable input data, it is often difficult to control other features of the generated shape by the input data - deep knowledge about the particular shapes and the generation process are required.

These shape generation methods play an important role in geometry, not just for the production of interesting shapes for design or ilustration purposes, but also to obtain a better understanding of the structure of the investigated shapes. In particular, the properties of transformations are essential for describing facetted or panelled surfaces that display similar properties as the corresponding smooth surfaces.

In this project we aim to investigate different methods to generate shapes, in particular:

  • the interrelations between different shape generation methods;
  • the related discretizations and, hence, discretizations of the shape generation methods;
  • the applicability and scope of these shape generation methods in theory and generative art and design.

By interlinking these different aspects of shape generation we hope and expect to gain new insight and to establish new interesting methods for the geometric generation of shapes, for their use in theory as well as for their application in art or design.


Summer/Autumn school
- Fukuoka 10-14 Sep 2018
- Vienna 1-5 Oct 2018


Birgit Slama (Secretary)

Shintaro Akamine (JP)
Joseph Cho (JP)
Yuta Hatakeyama (JP)
Udo Hertrich-Jeromin (AT)
Yoshiki Jikumaru (JP)
Kenji Kajiwara (JP)
Miyuki Koiso (JP)
Maria Lara Miro (AT)
Hyeongki Park (JP)
Denis Polly (AT)
Florian Rist (AT)
Wayne Rossman (JP)
Masaaki Umehara (JP)
Kotaro Yamada (JP)


FWF - Austrian Science Fund
JSPS - Japan Society for the Promotion of Science
TUW - Vienna University of Technology
JASEC - Japan-Austria Science Exchange Centre
DMG - Institute of Discrete Mathematics and Geometry

(W3C) Last modified on Sat 05 May 2018, 18:36:42 CEST