6 citations · 23 across the 7 of their papers we have counts for
7 papers · 1 filter
Contact with circles and Euclidean invariants of smooth surfaces in R^3
Peter Giblin, Graham Reeve, Ricardo Uribe-Vargas
We investigate the vertex curve, that is the set of points in the hyperbolic region of a smooth surface in real 3-space at which there is a circle in the tangent plane having at le…
Equidistants for families of surfaces
Peter Giblin, Graham Reeve
For a smooth surface in this article contains local study of certain affine equidistants, that is loci of points at a fixed ratio between points of contact of parall…
Reflexion maps and geometry of surfaces in R^4
Peter Giblin, Stanislaw Janeczko, Maria Aparecida Soares Ruas
In this article we introduce new affinely invariant points---`special parabolic points'---on the parabolic set of a generic surface in real 4-space, associated with symmetries…
Geometry of isophote curves
Andre Diatta, Peter Giblin
In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This…
Pre-Symmetry Sets of 3D shapes
Andre Diatta, Peter J. Giblin
The investigation of 3D euclidean symmetry sets (SS) and medial axis is an important area, due in particular to their various important applications. The pre-symmetry set of a surf…
Level sets of functions and symmetry sets of smooth surface sections
Andre Diatta, Peter Giblin, Brendan Guilfoyle +1
We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of sur…