Codac manual

Welcome to the Codac website. This manual is currently under construction. We are actively working on it and appreciate your patience as we build a comprehensive guide.

Contributors

This list is in alphabetical order by surname.

Auguste Bourgois Cyril Bouvier Quentin Brateau Gilles Chabert Julien Damers Benoît Desrochers

Peter Franek Maël Godard Nuwan Herath M. Luc Jaulin Fabrice Le Bars

Morgan Louédec Damien Massé Bertrand Neveu Verlein Radwan Andreas Rauh

Simon Rohou Joris Tillet Gilles Trombettoni Christophe Viel Raphael Voges

We appreciate all contributions, whether they are code, documentation, bug reports, or suggestions. If you believe you should be listed here and are not, please contact us to update the list.

Provisional Plan

Below is a provisional plan for the structure of this manual. Some pages are already available. Please note that some sections may change or be added as we continue to develop the content.

Overview of Codac

• Intervals and constraints

• The Codac framework

• Target audience

User manual

• Installation guide

  • Python installation

  • C++ installation

  • MATLAB installation

• Intervals

  • What is an interval?

  • The Interval class

  • Boolean intervals

• Linear algebra

  • Vector, Matrix

  • IntervalVector, IntervalMatrix

  • Matrix operations and basic linear solving

  • Reliable inversions of matrices

  • C++: efficient matrix operations using Eigen

• Inclusion functions

  • Analytic inclusion functions

    • Analytic inclusion functions

    • Analytic operators

    • Extension to custom expressions

    • Temporal functions

  • Set-membership functions

    • The class SetMembershipFunction

    • Extension to custom expressions

• Tubes

  • What is a tube?

  • Temporal domains

  • The Tube classes

  • The Trajectory classes

  • Increasing performances using views

• Contractors

  • What are contractors?

  • How to build a contractor

  • Basic contractors

    • CtcIdentity

    • CtcEmpty

    • CtcLazy

    • CtcFixpoint

  • Linear contractors

    • CtcGaussElim

    • CtcGaussSeidel

    • CtcLinearPrecond

  • Set contractors

    • CtcUnion

    • CtcInter

    • CtcQInter

    • CtcCartProd

    • CtcProj

    • CtcNot

    • CtcAction

  • Analytic contractors

    • Directed operators

    • CtcInverse

    • CtcInverseNotIn

  • Geometric contractors

    • The CtcDist contractor

    • CtcPolar

    • CtcSegment

    • CtcPolygon

    • CtcPointCloud

    • CtcEllipse

    • CtcCross / CtcNoCross

  • Shape contractors

    • CtcCtcBoundary

    • CtcWrapper

    • CtcImage

    • CtcDiscreteSet

  • Temporal contractors

    • Using static contractors on tubes

    • CtcDeriv

    • CtcEval

    • CtcDelay

    • CtcLinobs

    • CtcLohner

    • CtcPicard

    • CtcChain

    • CtcDiffInclusion

• Separators

  • What are separators?

  • How to build a separator

  • Basic separators

    • SepCtcPair

  • Set separators

    • SepUnion

    • SepInter

    • SepQInter

    • SepCartProd

    • SepProj

    • SepNot

    • SepAction

  • Analytic separators

    • SepInverse

    • SepTransform

  • Geometrical separators

    • SepPolarCart or SepCartPolar

    • SepPolygon

    • SepEllipse

    • SepCross

  • Shape separators

    • SepCtcBoundary

    • SepWrapper

    • SepImage

  • Contractors obtained from separators

    • CtcInnerOuter

  • Towards thick separators

• Pavers

  • The SIVIA algorithm

  • Pavers for contractors and separators

  • Paving structures

    • RegularPaving

    • NonRegularPaving

• Contractor Networks

  • What is a CN?

  • The ContractorNetwork class

• Geometry

  • Geometric utilities

  • Segment

  • Polygon and ConvexPolygon

  • Polyhedron

• Ellipsoids

  • Ellipsoid in n-dimensional space (matrix definition)

  • The Ellipsoid class

• Topology

  • Extract connected subsets from pavings

  • Topological degree: verify zeros of an inclusion function

• Visualization

  • The 2D Figure classes

  • 2D drawing functions

  • Styles, colors and color maps

  • The VIBes viewer

  • The IPE editor

  • The 3D Figure class

• Tools

  • Serialization tools

  • Affine transformation estimation

• Codac extensions

  • CAPD (rigorous numerics in dynamical systems)

  • Interface with the IBEX library

  • Sympy (symbolic computation)

• See also

  • Frequently Asked Questions

  • Performance considerations

  • Low-level interval library

• References

  • Related papers

  • Contributors

  • How to cite Codac

How-to guides

• Robotics

  • Non-linear state estimation

  • State estimation by solving data association

  • Range-only SLAM

  • Explored area

  • Loop detections and verifications

• Geometry

  • 2d shape registration

• Dynamical systems

  • Lie symmetries for guaranteed integration

  • Solving a discrete Lyapunov equation

  • Stability analysis of a non-linear system

Development

• Information for developers

• Changelog

• C++ API