Rodin::Distance::Eikonal class

Distance function computation using the Eikonal equation.

Template parameters
FES	Finite element space type
Data	Data storage type for the solution

This class solves the Eikonal equation to compute distance functions on meshes using the Fast Marching Method. It can optionally compute signed distance functions by specifying interior regions.

Mathematical Background

The Eikonal equation describes the propagation of wavefronts with unit speed, which is equivalent to computing distances. The Fast Marching Method solves this equation efficiently on unstructured meshes.

Usage Example

P1 fes(mesh);
GridFunction u(fes);
Eikonal eikonal(u);
eikonal.setInterface(interfaceAttr)
       .setInterior(interiorAttr)
       .solve()
       .sign();

Base classes

template<class Derived> class Base<Eikonal<FES, Data>>: Base class for distance function computation models using CRTP.

Public types

using SolutionType = Variational::GridFunction<FES, Data>: Solution type: grid function containing the distance values.

Constructors, destructors, conversion operators

Eikonal(SolutionType& u): Constructs an Eikonal distance solver.

Public functions

auto solve() -> Eikonal&: Solves the Eikonal equation to compute the distance function.
auto sign() -> Eikonal&: Computes the sign of the distance function.

Function documentation

template<class FES, class Data>
Rodin::Distance::Eikonal<FES, Data>::Eikonal(SolutionType& u)

Constructs an Eikonal distance solver.

Parameters
u in/out	Grid function to store the computed distance values

template<class FES, class Data>
Eikonal& Rodin::Distance::Eikonal<FES, Data>::solve()

Solves the Eikonal equation to compute the distance function.

Returns	Reference to this object for method chaining

This method seeds the Fast Marching Method at the interface region and propagates the distance values throughout the domain.

template<class FES, class Data>
Eikonal& Rodin::Distance::Eikonal<FES, Data>::sign()

Computes the sign of the distance function.

Returns	Reference to this object for method chaining

This method assigns negative values to the distance function in the interior region, converting an unsigned distance to a signed distance function. Must be called after solve().