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

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.