Axl, a Geometric Modeler for Semi-algebraic Shapes

  • Emmanouil ChristoforouEmail author
  • Angelos Mantzaflaris
  • Bernard Mourrain
  • Julien Wintz
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10931)


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.

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.


Semi-algebraic model Isogeometric analysis b-splines Algebraic surface Algebraic-geometric computation Generic programming 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Emmanouil Christoforou
    • 1
    • 2
    Email author
  • Angelos Mantzaflaris
    • 3
  • Bernard Mourrain
    • 1
  • Julien Wintz
    • 1
  1. 1.Inria Sophia Antipolis - MéditerranéeSophia AntipolisFrance
  2. 2.National and Kapodistrian University of AthensAthensGreece
  3. 3.Johannes Kepler UniversityLinzAustria

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