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On
Geometry and Optimization I
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Organizers:
Francisco Tovar & Marco Paluszny
Speakers:
Marco Paluszny, Jonnathan Otero,
& Miguel Martin-Landrove
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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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The graphical representation
of a parametric curve is a polygonal
made of many segments that might have
different lengths, because a uniform
partition of the domain of the curve,
does not guarantee that each segment
has the same length. Only in the case
that the curve is parameterized by
arc length one the approximating polygonal
consists of segments of approximately
equal length. A similar situation
occurs in when we display cyclides,
these surfaces are composed of circular
profiles and a uniform distribution
of points in the domain does not guarantee
that the circular profiles are evenly
distributed. The problem we address
is finding a distribution of the cyclide
domain such that the circular profiles
that define it are well distributed.
To achieve this two splines are built
that aproximate the inverse arc length
function and the bending energy of
the curve C(t), respectively, where
the curve C(t) allows for the control
the
spheres which define cyclide and its
circular profiles. |
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