Developing surfaces

Author

Shinagawa, Yoshihisa ; Kawamichi, R. ; Kunii, Tosiyasu L. ; Ohwada, Shigeru

Author_Institution

Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA

fYear

2002

fDate

6/24/1905 12:00:00 AM

Firstpage

253

Lastpage

260

Abstract

To transform a three-dimensional object or map texture to its surface, it is necessary to introduce a coordinate system. If the surface can be cut and developed, it is easy to identify each point on the surface with the coordinate values. According to a theory in topology, any closed polygonized two-dimensional surface can be represented by a canonical development. However, no efficient algorithm to actually develop a given surface has been presented, and the theory sounds abstract. This paper proposes a method to develop an arbitrary polygonized closed surface and to establish the correspondence between each point on the surface and a point on a regular polygon. Educational software is developed using the algorithm that visualizes the coordinate system by texture mapping or by allowing a user to paint on the surface

Keywords

computational geometry; courseware; data visualisation; image texture; solid modelling; topology; 3D object; closed polygonized two-dimensional surface; coordinate system; coordinate values; educational software; homology groups; regular polygon; solid modeling; surface development; texture mapping; three-dimensional object; topology; Application software; Cities and towns; Geometry; Paints; Robustness; Shape; Software algorithms; Surface texture; Topology; Visualization;

fLanguage

English

Publisher

ieee

Conference_Titel

Shape Modeling International, 2002. Proceedings

Conference_Location

Banff, Alta.

Print_ISBN

0-7695-1546-0

Type

conf

DOI

10.1109/SMI.2002.1003553

Filename

1003553