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.
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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
- Intervals
What is an interval?
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
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?
The Ctc class
- 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
CtcDist
CtcPolar
CtcSegment
CtcPolygon
CtcEllipse
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?
The Sep class
- Basic separators
SepCtcPair
- Set separators
SepUnion
SepInter
SepQInter
SepCartProd
SepProj
SepNot
SepAction
- Analytic separators
SepInverse
SepTransform
- Geometrical separators
SepPolarCart or SepCartPolar
SepPolygon
SepEllipse
- 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
Geometrical tools
Polygons and convex polygons
Polyhedron
- Topology
Extract connected subsets from pavings
Topological degree: verify zeros of an inclusion function
- Tools
Serialization tools
- Codac extensions
CAPD (rigorous numerics in dynamical systems)
Interface with the IBEX library
Sympy (symbolic computation)
- See also
Frequently Asked Questions
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
Changelog
C++ API