Pure Maths Colloquium: Shining light on surfaces
14 March 2011 17:15 in CM221
A smooth surface in 3-space viewed from a particular direction has an 'apparent contour' or 'profile' generated by points on the surface where the viewline grazes (is tangent to) the surface. As the view direction changes, the profile changes in general in a limited number of ways. When the surface is also illuminated from another direction there will be 'shade curves' where the light rays graze the surface, and perhaps cast shadows thrown by these shade curves elsewhere on the surface. The surface may also be piecewise-smooth, perhaps two smooth surfaces meeting along a common boundary, called a 'crease' or three surfaces meeting in a 'corner'. The various features, creases, shade curves, cast shadows, profiles, and perhaps others, interact in a limited number of ways as we change viewpoint. These ways can be found by methods of singularity theory, and I shall explain the connexion between the 'physical' problem and an abstract version of it amenable to singularity theory classification, and give examples to show how passing from 'abstract' to 'real' further limits the possibilities, as well as causing headaches for the classification process. I shall not assume knowledge of singularity theory. The work is
joint with Jim Damon and formerly with postdoc Gareth Haslinger.
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