Axl swMATH ID: 25792 Software Authors: Christoforou, Emmanouil; Mantzaflaris, Angelos; Mourrain, Bernard; Wintz, Julien Description: Axl, a geometric modeler for semi-algebraic shapes. We describe the algebraic-geometric modeling platform Axl, which provides tools for the manipulation, computation and visualisation of semi-algebraic models. This includes meshes, basic geometric objects such as spheres, cylinders, cones, ellipsoids, torus, piecewise polynomial parameterisations of curves, surfaces or volumes such as b-spline parameterisations, as well as algebraic curves and surfaces defined by polynomial equations. Moreover, Axl provides algorithms for processing these geometric representations, such as computing intersection loci (points, curves) of parametric models, singularities of algebraic curves or surfaces, certified topology of curves and surfaces, etc.{par}We present its main features and describe its generic extension mechanism, which allows one to define new data types and new processes on the data, which benefit from automatic visualisation and interaction facilities. The application capacities of the software are illustrated by short descriptions of plugins on algebraic curves and surfaces and on splines for isogeometric analysis. Homepage: http://axl.inria.fr Keywords: semi-algebraic model; isogeometric analysis; b-splines; algebraic surface; algebraic-geometric computation; generic programming Related Software: Voronoi; Julia; G+Smo; dtk; VTK; 3BA; ATAME; Francy; DiscreteZOO; libtropicon; Theoryguru; Polytop; IntegerSequences; HomotopyContinuation; Orbiter; Paramotopy; SageMath; Macaulay2 Cited in: 4 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Axl, a geometric modeler for semi-algebraic shapes. Zbl 1396.65028Christoforou, Emmanouil; Mantzaflaris, Angelos; Mourrain, Bernard; Wintz, Julien 2018 all top 5 Cited by 9 Authors 2 Mantzaflaris, Angelos 2 Mourrain, Bernard 1 Adamou, Ibrahim 1 Christoforou, Emmanouil 1 Davenport, James Harold 1 Kauers, Manuel 1 Labahn, George 1 Urban, Josef 1 Wintz, Julien Cited in 2 Serials 1 Lecture Notes in Computer Science 1 Mathematics in Computer Science Cited in 4 Fields 4 Numerical analysis (65-XX) 2 Computer science (68-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) Citations by Year