DEC package

Package managers:

David Coeurjolly, Pierre Gueth

Since

0.8

LICENSE: LGPL

Package Overview

Discrete exterior calculus (DEC) provides an easy and efficient way to describe linear operator over various structure. Basic operators, such as Hodge duality operator or exterior derivative, can be combined to create classical vector analysis operator such as gradient, curl and divergence.

Note

To use this package, you have to build DGtal with the Eigen option (and with Cairo option to have the examples compiled). By using cmake you have to use these options: -DWITH_EIGEN=true -DWITH_CAIRO=true.

Modules

• Discrete Exterior Calculus approach
  • Discrete exterior calculus (Pierre Gueth)
  • Embedding n-dimensional DEC structures into m-dimensional space (Pierre Gueth)
  • Poisson problem (Pierre Gueth)
  • Helmoltz decomposition (Pierre Gueth)
  • Propagation (Pierre Gueth)
  • Heat Kernel Laplace–Beltrami Operator (Thomas Caissard)
  • Piecewise-smooth approximation using a discrete calculus model of Ambrosio-Tortorelli functional (Jacques-Olivier Lachaud, Marion Foare, David Coeurjolly, Pierre Gueth)
• Discrete differential calculus on polygonal surfaces (David Coeurjolly, Jacques-Olivier Lachaud, Baptiste Genest)
• Geodesics In Heat using discrete polygonal calculus (David Coeurjolly, Jacques-Olivier Lachaud)
• Vector Heat Method using discrete polygonal calculus (Baptiste Genest, David Coeurjolly)

Package Concepts Overview

• DEC Main Concepts

Related examples

• exampleDECSurface.cpp
• examplePropagation.cpp
• exampleDiscreteExteriorCalculusUsage.cpp
• exampleDiscreteExteriorCalculusSolve.cpp
• exampleDiscreteExteriorCalculusChladni.cpp
• exampleHarmonicParametrization.cpp
• exampleVectorHeatMethod.cpp
• dgtalCalculus-poisson.cpp
• dgtalCalculus.cpp
• dgtalCalculus-single.cpp
• dgtalCalculus-geodesic.cpp
• dgtalCalculus-halfsphere.cpp
• dgtalCalculus-bunny.cpp
• exampleVectorHeatMethod.cpp
• exampleHarmonicParametrization.cpp
• exampleBunnyHead.cpp