Faithful Real-Time Animation of Parametrized (Semi-) Algebraic Expressions via Cylindrical Algebraic Decomposition

Author:

Brown Christopher1,Kovács Zoltán2,Recio Tomás3

Affiliation:

1. US Naval Academy, Annapolis MD, United States

2. PHDL, Linz, Austria

3. Univ. Antonio de Nebrija, Madrid, Spain

Abstract

We present some current improvements, implemented in the software package GeoGebra Discovery, that combine symbolic computation and graphics algorithms to faithfully visualize (semi-)algebraic expressions. Our implementation allows fluid animation of set of (semi-)algebraic sets of dimension 1 in a desktop application or a web browser. We use the Tarski library to create a cylindrical algebraic decomposition of the input, and its plot2d command, which is processed further in GeoGebra Discovery, to provide the user with a familiar look and feel.

Publisher

Association for Computing Machinery (ACM)

Subject

Microbiology (medical),Immunology,Immunology and Allergy

Reference14 articles.

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3. Cylindrical Algebraic Decomposition II: An Adjacency Algorithm for the Plane

4. A polynomial-time algorithm for the topological type of a real algebraic curve;Arnon D. S.;Journal of Symbolic Computation,1988

5. P. Birklbauer and D. Drakulić . Implicit curves in GeoGebra 4 . The Second GeoGebra Conference, Hagenberg - Austria, August 28--30 2011 . P. Birklbauer and D. Drakulić. Implicit curves in GeoGebra 4. The Second GeoGebra Conference, Hagenberg - Austria, August 28--30 2011.

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