Faithful real-time animation of parametrized (semi-)algebraic expressions via cylindrical algebraic decomposition

摘要

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.