CartesianGrids.jl

Installation

using Pkg
Pkg.add("CartesianGrids")

Overview

CartesianGrids.jl is a Julia package for uniform Cartesian grid generation and management. It provides efficient tools for creating and manipulating structured grids in arbitrary dimensions.

The package includes:

• Grid creation with customizable dimensions and node counts
• Efficient node and cell spacing calculations
• Grid indexing and iteration utilities
• Type-stable implementations using StaticArrays

Quick Example

using CartesianGrids, StaticArrays

# Create a 2D Cartesian grid: [-1,1]² with 32 nodes in each direction
grid = CartesianGrid((-1.0, -1.0), (1.0, 1.0), (32, 32))

# Get node spacing (distance between adjacent nodes)
meshsize = CartesianGrids.meshsize(grid)
# Returns: [2/31, 2/31] (since 32 nodes over distance 2)

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

# Extract 1D grid along a dimension
x_grid = CartesianGrids.grid1d(grid, 1)
# Returns: LinRange(-1.0, 1.0, 32)

# Get coordinates of a specific grid point
coords = grid[CartesianIndex(1, 1)]
# Returns: [-1.0, -1.0]

# Get cell center coordinates
center = CartesianGrids.cell_center(grid, CartesianIndex(1, 1))
# Returns: [-31/32, -31/32] (center of first cell)

2-element StaticArraysCore.SVector{2, Float64} with indices SOneTo(2):
 -0.96875
 -0.96875

Drawing

	y
	↑
	|
	|   o───o───o  ← hc = (x_H, y_H)
	|   │   │   │
	|   o───o───o
	|   │   │   │
	|   o───o───o
    |   
	+────────────→ x

with n = (nx, ny) = (3, 3) nodes per dimension, lc the lower corner, and hc the upper corner. o denotes grid nodes, and the lines indicate cell edges. The grid is uniform, so node spacing is constant in each direction. Top left node : (i=1, j=3), center node : (i=2, j=2).

Main Sections

• Grid Types
• API Reference

Performance

The package is designed for efficiency with:

• Allocation-free operations where possible
• Type-stable implementations using StaticArrays
• Fast indexing and iteration over grid points