Abstract:
Projections are important properties of polyhedra and other 3D objects
due to its potential application in the field of computer graphics, object
reconstruction, machine vision, computational geometry and knot theory.
Niceness of projection refers to some structural and geometric properties
of the projection. Considerable amount of research work has been done
on different criteria of niceness. Some common criteria of niceness includes
maximizing (minimizing) the area of projection, maximizing (minimizing) the
volume of projection in arbitrary lower dimensions, minimizing the number
of crossing in the projection of 3D lines and generating silhouettes which
meet some predefined criteria. In this thesis, we have developed algorithms
such that the minimum visibility ratio of faces and edges of convex polyhedra
is maximized. For a particular view v of a polyhedron P, our algorithm runs
in O((ICI +Ivlllog(ICI +Ivll) time, where Ivl is the number of faces visible in
v and ICI is the size of the view cone of that view and both Ivl and ICI can
be much less than n, where n is the number of vertices of P. For all views
of P, our algorithm takes 0(n2Iogn) time. Moreover, we have extended our
algorithms to solve this problem for segments in 3D which takes O(nlogn)
time.
