These are two C++ libraries for symbolic, numeric and graphical manipulations in non-Euclidean geometry. There is GUI which allows to interact with these libraries by mouse clicks.

On a dipper level the first library Cycle implements basic operations on cycles (quadrics) through FSCc construction. The second library Figure operates on ensembles of cycles connected by Moebius-invariant relations, e.g. orthogonality.

Both libraries are based on the Clifford algebra capacities of the GiNaC computer algebra system (http://ginac.de). Besides C++ libraries there is a Python wrapper, which can be used in interactive mode (https://codeocean.com/capsule/7952650/).

Both libraries work in arbitrary dimensions and signatures of metric. Additionally, there are some 2D/3D-specific routines including a visualisation to PostScript files through Asymptote (http://asymptote.sourcefourge.net) software. The source is written in literate programming NoWeb.

Features

  • GUI interface (with localisation)
  • Interactive IPython/Jupyter notebooks
  • Creates animations
  • Works in spaces with any dimensions and signatures
  • Interactive 3D visualisation
  • Google Colab / CodeOcean capsule

Project Samples

Play Video Graphical User Interface Apollonius problem in 3D Nine-points theorem in Euclidean set-up Nine-points theorem in non-Euclidean set-up Nine-points theorem in non-Euclidean set-up---hyperbolic version Jupyter notebook

Project Activity

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