Axl
swMATH ID:  25792 
Software Authors:  Christoforou, Emmanouil; Mantzaflaris, Angelos; Mourrain, Bernard; Wintz, Julien 
Description:  Axl, a geometric modeler for semialgebraic shapes. We describe the algebraicgeometric modeling platform Axl, which provides tools for the manipulation, computation and visualisation of semialgebraic models. This includes meshes, basic geometric objects such as spheres, cylinders, cones, ellipsoids, torus, piecewise polynomial parameterisations of curves, surfaces or volumes such as bspline 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:  semialgebraic model; isogeometric analysis; bsplines; algebraic surface; algebraicgeometric 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 semialgebraic shapes. Zbl 1396.65028 Christoforou, Emmanouil; Mantzaflaris, Angelos; Mourrain, Bernard; Wintz, Julien 
2018

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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 (65XX) 
2  Computer science (68XX) 
1  General and overarching topics; collections (00XX) 
1  Algebraic geometry (14XX) 