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MPI-INF D1 Publications :: Thesis :: Emeliyanenko, Pavel

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Thesis - Master's thesis | @MastersThesis | Masterarbeit

Author(s)*:Emeliyanenko, Pavel
BibTeX citekey*:Emel2007

Title, School
Title*:Visualization of Points and Segments of Real Algebraic Plane Curves
School:Universität des Saarlandes
Type of Thesis*:Master's thesis

Note, Abstract, Copyright
LaTeX Abstract:This thesis presents an exact and complete approach for visualization of segments and points of real plane algebraic curves given in implicit form $f(x,y) = 0$. A curve segment is a distinct curve branch consisting of regular points

only. Visualization of algebraic curves having self-intersection and isolated points constitutes the main challenge. Visualization of curve segments involves even more
difficulties since here we are faced with a problem of discriminating
different curve branches, which can pass arbitrary close to each other.
Our approach is robust and efficient (as shown by our benchmarks), it
combines the advantages both of curve tracking and
space subdivision methods and is able to correctly rasterize segments of
arbitrary-degree algebraic curves using double, multi-precision or exact rational arithmetic.

Keywords:Computational Geometry, Algebraic Geometry, EXACUS, Algorithms and Data Structures

Referees, Status, Dates
1. Referee:Kurt Mehlhorn
2. Referee:Nicola Wolpert
Supervisor:Eric Berberich, Michael Sagraloff
Date Kolloquium:13 February 2007

MPG Unit:Max-Planck-Institut für Informatik
MPG Subunit:Algorithms and Complexity Group
Audience:experts only
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BibTeX Entry:
AUTHOR = {Emeliyanenko, Pavel},
TITLE = {Visualization of Points and Segments of Real Algebraic Plane Curves},
SCHOOL = {Universit{\"a}t des Saarlandes},
YEAR = {2007},
TYPE = {Master's thesis}
MONTH = {February},

Entry last modified by Pavel Emeliyanenko, 02/28/2008
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Pavel Emeliyanenko
02/28/2007 01:52:48 PM

Pavel Emeliyanenko
Pavel Emeliyanenko

Edit Date
28/02/2007 13:56:31
28/02/2007 13:52:49