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On
Geometry and Optimization I
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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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Marco
Paluszny
Path Splines with Envelope Conics |
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Jonnathan
Otero
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 consider the approximation
of planar regions by pairs of lemniscates
that are stitched together continuously.
Lemniscates are level curves of the
absolute value of an univariate complex
polynomial. We build orthogonal grids
on elongated regions with changing
width, such as riverbeds, 2D profiles
of arteries, sinuous roads using lemniscates
of
two foci. The use of low degree polynomials
gives some computational advantages
which are exploited in the implementation.
The main application is in the area
of numerical solution of PDE's and
computer aided geometric
design. We report on the results of
numerical experiments performed with
MATLAB® using data from the Orinoco
River and the Guajira Peninsula. In
this paper we compare the exact distance
between a point and a lemniscates
with the estimate we have used in
previous works. |
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