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On
Geometry and Optimization II
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Organizers:
Francisco Tovar & Marco Paluszny
Speakers:
Adriana Padron, Marianela Lentini,
& Mauricio Londao
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| Abstract
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Since early 2008, the
Laboratorio de Computacion Grafica
y Geometria Aplicada (CGGA) and the
Computacion Cientfica research group
of the Universidad Nacional de Colombia,
Sede Medellin have been collaborating
in a series of themes concerning geometry
and optimization with a strong emphasis
on applications. In this minisymposium
we will be presenting results concerning
the following topics:
- Using lemniscates to construct orthogonal
grids on meander-like regions
- Using envelopes of 1-parameter families
to construct path splines
- The Prony method in the detection
of tissue types in brain
- Construction of developable low
degree patches
- Models of molecular surfaces
- Distribution of circles along a
cyclide. |
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Adriana
Padron
Modeling of the Van Der Waals Surface
Using Triangular Patches |
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We study algorithms
for the design with developable surfaces,
namely the algorithm of Aumann and
the Pottmann projective algorithm.
In the latter, rational developable
surfaces are interpreted as Bezier
curves in the dual projective space.
We take an exhaustive look at the
developable polynomial patches of
degree 3, in the particular that the
base curve is a non planar cubic Bezier
curve and the generating curva is
quadratic. This last is done with
the intention of offering a "catalog"
of developable Bezier patches of degree
base curve 3 and quadratic generator.
The techniques discussed are implemented
in the design of developable surfaces
along cubic B-spline curves. |
