Original scientific paper

Shade Lines of Curved Surfaces - Linear Approach to Involution of Conjugate Tangents at Points of Translation Surfaces

Daniel Lordick ; Institute of Geometry, Dresden University of Technology, Dresden, Germany

Abstract

In KoG 6 we introduced a global approach to the tangents of the shade lines of curved surfaces. The constructions are made by using an accompanying ruled surface along the shade line. In this paper the method is expanded to translation surfaces. In that way we get a linear access to the involution of conjugate tangents in those points of a surface where the curvature at two conjugate tangents is given. At the end of the paper a helical surface with circular cross section is handled as translation surface, which leads to additional elegant constructions for the tangents of its shade line. For more details on the general subject see [4].

Keywords

curved surface; Dupin-indicatrix; ruled surface; shades and shadows

Hrčak ID:

3707

URI

https://hrcak.srce.hr/3707

Publication date:

17.2.2005.

Article data in other languages: croatian german

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