Axl, a geometric modeler for semi-algebraic shapes

Abstract : 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 pa-rameterisations, 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. 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.
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Contributor : Bernard Mourrain <>
Submitted on : Wednesday, July 25, 2018 - 12:21:53 PM
Last modification on : Thursday, February 7, 2019 - 2:38:08 PM
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Emmanouil Christoforou, Angelos Mantzaflaris, Bernard Mourrain, Julien Wintz. Axl, a geometric modeler for semi-algebraic shapes. ICMS 2018 - 6th International Conference on Mathematical Software, Jul 2018, Notre Dame, United States. pp.128-136, ⟨10.1007/978-3-319-96418-8_16⟩. ⟨hal-01848546⟩



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