All Outputs (4)

On Hamilton's characteristic functions for reflection (2006)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2006). On Hamilton's characteristic functions for reflection. Bulletin - Irish Mathematical Society, 57, 29-40

Reflection in a translation invariant surface (2006)
Journal Article
surface. Mathematical Physics, Analysis and Geometry, 9(3), 225-231. https://doi.org/10.1007/s11040-007-9013-8

We prove that the focal set generated by the reflection of a point source off a translation invariant surface consists of two sets: a curve and a surface. The focal curve lies in the plane orthogonal to the symmetry direction containing the source, w... Read More about Reflection in a translation invariant surface.

Isolated umbilic points on surfaces in R^3 (2006)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2006). Isolated umbilic points on surfaces in R^3. Deltio tīs Ellīnikīs mathīmatikīs etaireias (1960), 51, 23-30

Reflection of a wave off a surface. (2006)
Journal Article
Klingenberg, W., & Guilfoyle, B. (2006). Reflection of a wave off a surface. Journal of Geometry, 84(1), 55-72. https://doi.org/10.1007/s00022-005-0022-0

Recent investigations of the space of oriented lines in R3R3 are applied to geometric optics. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecti... Read More about Reflection of a wave off a surface..