Pavel Emeliyanenko
ABSTRACT
A web application is presented to compute, plot, and interactively explore planar arrangements induced by algebraic plane curves of arbitrary degree. It produces accurate curve plots and reflects the exact topology for any arrangement, including degenerated cases. Various user interface features allow the interactive exploration of the arrangement structure. This makes the tool useful for demonstrative and educational purposes, especially as it runs without initial installation process.
- B. F. Caviness, J. R. Johnson (eds.): phQuantifier Elimination and Cylindrical Algebraic Decomposition, Texts and Monographs in Symbolic Computation. Springer, 1998.Google Scholar
Cross Ref
- A. Eigenwillig, M. Kerber: Exact and Efficient 2D-Arrangements of Arbitrary Algebraic Curves. In: phProc. of the Nineteenth Annual ACM-SIAM Symp. on Discrete Algorithms (SODA08), 2008 122--131. Google ScholarDigital Library
- A. Eigenwillig, M. Kerber, N. Wolpert: Fast and Exact Geometric Analysis of Real Algebraic Plane Curves. In: C. W. Brown (ed.) phProocedings of the 2007 International Symp. on Symbolic and Algebraic Computation (ISSAC 2007), 2007 151--158. Google ScholarDigital Library
- P. Emeliyanenko: phVisualization of Points and Segments of Real Algebraic Plane Curves. Mastercs thesis, Saarland University, 2007.Google Scholar
- F. Messine: Extension of Affine Arithmetic Application to Unconstrained Global Optimization. phJournal of Universal Computer Science (2002) 992--1015.Google Scholar
- R. Wein, E. Fogel, B. Zukerman, D. Halperin: '2D Arrangements'. In: CGAL-3.3 User and Reference Manual, 2007. URL http://www.cgal.org/Manual/3.3/doc_html/cgal_manual/Arrangement_2/Chapter_main.html.Google Scholar
Index Terms
- Visualizing and exploring planar algebraic arrangements: a web application
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