Domain

ContinuousUnboundedDomain{N,T}

Struct for a basic unbounded continuous domain.

ContinuousBoundedDomain{N,T,B}

Struct for a basic bounded continuous domain.

ContinuousBoundedEllipsoidDomain{N,T,S<:Grid{N,T}}

Struct for a basic bounded continuous domain formed by a finite number of ellipsoids.

abstract type Grid{N, T} end

Defines an abstract type for grid-based structures in N dimensions with floating-point values T.

get_pos_by_coord(grid::Grid{N, T}, x::SVector{N, T}) -> NTuple{N, Int}

Returns the discrete position (grid indices) corresponding to a coordinate x.

• The cell (0,0) is centered between -h/2 and +h/2.
• h is the length of a grid cell in each dimension.

GridFree{N,T} <: Grid{N,T}

Uniform grid on unbounded space, centered at orig and with steps set by the vector h.

GridEllipsoidalRectangular{N,T} <: Grid{N,T}

Uniform grid on rectangular space rect, centered at orig and with steps set by the vector h. Cells are (possibly overlapping) ellipsoids defined at each grid point c as (x-c)'P(x-c) ≤ 1.

DeformedGrid{N, T} <: Grid{N, T}

Represents a deformed version of a GridFree grid, where points are mapped via an invertible transformation f and its inverse fi.

Fields

• grid::GridFree{N, T} : The underlying grid.
• f::Function : The forward transformation (physical -> deformed).
• fi::Function : The inverse transformation (deformed -> physical).
• A::Union{Nothing, SMatrix{N, N, T, N*N}} : Optional linear transformation matrix for volume calculations.

get_volume(Dgrid::DeformedGrid) -> T

Computes the volume of a grid cell.

• If A is provided (linear transformation), uses det(A).
• Otherwise, defaults to the volume of the base grid.

abstract type DomainType{N, T} end

General abstract type for spatial domains in N dimensions with elements of type T.

abstract type GridDomainType{N, T} <: DomainType{N, T}

An abstract interface for grid-based domains, enforcing required methods for interaction.

merge_to_hyperrectangles_pos(domain::GridDomainType)

Aggregates the grid elements in GridDomainType into the largest possible hyperrectangles. Returns a list of HyperRectangles that efficiently represent the domain.

merge_hyperrectangles_real(domain_list::GridDomainType)

Uses the existing merge_to_hyperrectangles(domain_list) function to merge elements in grid positions, then converts the result into real-world HyperRectangles using get_rec(grid, pos).

DomainList{N,T,S<:Grid{N,T}}

Struct for a basic domain based on a Grid.

PeriodicDomainList{N, T, S} <: GridDomainType{N, T}

A periodic extension of DomainList, where specified dimensions wrap around at given periods.

Fields

• domain::DomainList{N, T, S} : The underlying domain structure.
• periodic_dims::Vector{Bool} : Boolean vector indicating which dimensions are periodic.
• periods::SVector{N, T} : The length of the period in each dimension.
• start::SVector{N, T} : The start of the periodic cycle in each dimension.

Features

• Uses DomainList for element management.
• Implements periodic boundary conditions for wrapping elements.

has_same_periodicity(domain1::PeriodicDomainList, domain2::PeriodicDomainList) -> Bool

Returns true if both domains have the same periodic settings.

wrap_pos(domain::PeriodicDomainList, pos::NTuple{N, Int}) -> NTuple{N, Int}

Wraps a grid position pos into its equivalent within periodic boundaries.

Handles periodicity correctly based on how the grid is defined.

wrap_coord(domain::PeriodicDomainList, coord::SVector{N, Float64}) -> SVector{N, Float64}

Transforms a coordinate into its wrapped equivalent within the periodic boundaries.

GeneralDomainList{N,E<:AbstractSet{NTuple{N,Int}},T,S<:Grid{N,T},F} <: DomainType{N,T}

Struct for a rectangular domain with rectangular obstacles.

RectangularObstacles{VT} <: AbstractSet{VT}

Struct for a rectangular domain with rectangular obstacles.

CustomList{N, T} <: DomainType{N, T}

A flexible, generic domain representation that stores elements as a list of SVector{N, T}. Useful for managing discrete sets of points in an N-dimensional space.