Grid Types

CartesianGrid

CartesianGrid(lc, hc, n)

Structure

A CartesianGrid{N, T} represents a uniform Cartesian grid in N dimensions with floating-point coordinates of type T.

Fields

• lc::SVector{N, T} — lower corner coordinates
• hc::SVector{N, T} — upper corner coordinates
• n::NTuple{N, Int} — number of nodes in each dimension

Creating a Grid

using CartesianGrids

# 2D grid: [-1,1]² with 32 nodes per direction
grid = CartesianGrid((-1.0, -1.0), (1.0, 1.0), (32, 32))

# 3D grid: [-2,2]³ with varying node counts
grid3d = CartesianGrid((-2.0, -2.0, -2.0), (2.0, 2.0, 2.0), (16, 32, 64))

CartesianGrid{3, Float64}([-2.0, -2.0, -2.0], [2.0, 2.0, 2.0], (16, 32, 64))

Accessing Grid Information

using CartesianGrids

# Create a 2D grid
grid = CartesianGrid((-1.0, -1.0), (1.0, 1.0), (32, 32))

# Get grid size (number of nodes per dimension)
size(grid)  # (32, 32)

# Get total number of nodes
length(grid)  # 1024

# Get dimension count
CartesianGrids.dimension(grid)  # 2

# Get 1D grid for a specific dimension
x_grid = CartesianGrids.grid1d(grid, 1)  # LinRange(-1.0, 1.0, 32)

# Get all 1D grids
all_grids = CartesianGrids.grid1d(grid)  # (x_grid, y_grid)

(LinRange{Float64}(-1.0, 1.0, 32), LinRange{Float64}(-1.0, 1.0, 32))

Grid Spacing

using CartesianGrids

# Create a 2D grid
grid = CartesianGrid((-1.0, -1.0), (1.0, 1.0), (32, 32))

# Node spacing (distance between adjacent nodes)
spacing = CartesianGrids.meshsize(grid)  # [2/31, 2/31]

# Node spacing for a specific dimension
x_spacing = CartesianGrids.meshsize(grid, 1)  # 2/31

# Cell spacing (cell width)
cell_spacing = CartesianGrids.cell_spacing(grid)  # [2/32, 2/32]

# Cell spacing for a specific dimension
x_cell_spacing = CartesianGrids.cell_spacing(grid, 1)  # 2/32

0.0625

Indexing and Iteration

using CartesianGrids

# Create a 2D grid
grid = CartesianGrid((-1.0, -1.0), (1.0, 1.0), (32, 32))

# Access a grid point by Cartesian index
coords = grid[CartesianIndex(1, 1)]  # SVector(-1.0, -1.0)
coords = grid[1, 1]  # Same as above

# Get cell center coordinates
center = CartesianGrids.cell_center(grid, CartesianIndex(1, 1))

# Iterate over all grid points
for coords in grid
    println(coords)
end

# Get CartesianIndices for the grid
indices = CartesianGrids.CartesianIndices(grid)  # CartesianIndices((32, 32))

CartesianIndices((32, 32))

AbstractMesh

abstract type AbstractMesh{N,T}

All grid types in CartesianGrids inherit from AbstractMesh{N, T} where:

• N is the dimension
• T is the floating-point type