Propagations from a space curve in three space with indicatrix a surface

Journal of Singularities
volume 6 (2012), 131-145
Proceedings of the Workshop on Singularities in Geometry and Applications, Będlewo, 5 – 21 May 2011

Received: 2 March 2012. Received in revised form: 8 July 2012.

DOI: 10.5427/jsing.2012.6k

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Abstract:

Generic singularities of rays emanating from a space curve in R^3 in all directions with the rate determined by an indicatrix (independent of the point in R^3) defined by a surface are classified. Similarly rays emanating from surface defined by an indicatrix given by a curve are also considered. Some applications to control theory are indicated.

Keywords:

affine equidistants, boundary singularity, caustic, control system, indicatrix, Minkowski set, singularity

Mathematical Subject Classification:

58K05, 58K40, 53A15