MPI-INF Logo
Publications

Thesis (Server    domino.mpi-inf.mpg.de)

Thesis

Master's thesis | @MastersThesis{Emel2007, ... | Masterarbeit

Emeliyanenko, Pavel

Visualization of Points and Segments of Real Algebraic Plane Curves

Universität des Saarlandes, February, 2007

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.

Computational Geometry, Algebraic Geometry, EXACUS, Algorithms and Data Structures
Kurt Mehlhorn
Nicola Wolpert
Eric Berberich, Michael Sagraloff
Completed
13
February
2007
Max-Planck-Institut für Informatik
Algorithms and Complexity Group
experts only
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:
@MASTERSTHESIS{Emel2007,
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
Hide details for Edit History (please click the blue arrow to see the details)Edit History (please click the blue arrow to see the details)

Editor(s)
Pavel Emeliyanenko
Created
02/28/2007 01:52:48 PM
Revision
1.
0.


Editor
Pavel Emeliyanenko
Pavel Emeliyanenko


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