Introduction

Curver was designed to test out the Bell–Webb algorithm [BellWebb16] to determine the Nielsen–Thurston type of a mapping class. Its development has enabled several optimisations of the original algorithm to be found. We hope that this will continue to the point at which this algorithm is actually practical to use.

Flipper

The underlying framework of curver is based on flipper. This means that curver can do many of the things that flipper can, however, curver has several advantages including:

  • Curves and Arcs are now proper classes.
  • Homology is handled separately.
  • The ability to perform Dehn twists about all (multi)curves.
  • The ability to perform half-twists about all arcs.
  • Fast twists and half-twists.
  • Polynomial-time curve simplification.
  • Component extraction.
  • The ability to crush along (multi-)curves.
  • The ability to determine the topological type of a multicurve.
  • The ability to procedurally generate the mapping class group of any surface.

At some point someone(’s graduate student) should port these features back to flipper.

If you are looking for a basic framework for manipulating curves, arcs and mapping classes then you should probably base your code on curver.

Curver License

MIT License

Copyright (c) 2017 Mark Bell

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.