NOTE SPECIAL TIME and PLACE:
January 26, Tuesday 12:00, Room 570, Education Building
Applying procedural representations to
problems in geometric computing
Lecturer : Iddo Hanniel
Lecturer homepage : http://sites.google.com/site/iddohan/
Affiliation : Solidworks Corp.
Abstract:
In
this talk I will present several problems I have been working on in geometric modeling,
computational geometry and computer graphics. The first problem is the construction,
under the exact computation paradigm, of arrangements of Bezier curves. The
second is the computation of Voronoi cells of free-form
curves and the third is the visualization of solid models using the graphics
processing unit (GPU).
The
common theme in these problems is that they contain geometric constructions, which
either cannot be represented using their standard geometric representation or
computing them is too expensive. Previous methods for attacking these problems typically
use approximations, either of the input or of the problematic geometric constructions.
Our methods, on the other hand, use procedural representations, which enable to
answer a set of queries that are sufficient for solving the problem at hand.
In
arrangements of Bezier curves, we represent intersection vertices with references
to intersecting curves, and to bounding polygons. This enables us to avoid the
prohibitive running times incurred by exact algebraic arithmetic.
In
the computation of Voronoi cells of free-form curves,
the bisector curves cannot be represented in standard (Bezier or B-spline) form. Instead we use a representation based on an
implicit function in the curves parametric domain combined with a mapping to
the Euclidean plane. Using this representation we can answer the queries
required to compute the lower envelope of the bisector distance functions and
thus compute the boundary of the Voronoi cell.
When
rendering solid models using the GPU, a common problem is the appearance of cracks
between faces in the model visualization. These are a result of the non-exact representation
of trimming curves in the model. Using a representation that stores references
to intersecting surfaces we are able to avoid these cracks and render a smooth
water tight model. This work is part of an ongoing project.
In
my talk, I will present the different problems and how applying procedural representations
helps in their computation. I will also present other problems for which I
believe applying such representations can be useful.
The
work described in this talk was done in collaboration with Gershon
Elber, Ron Wein, Kirk
Haller and others.