An implementation of the pathfinding algorithm described by

Dimdal / Jönsson, 1997. An optimal pathfinder for vehicles in real-world digital terrain maps. Masters Thesis, The Royal Institute of Science, School of Engineering Physics, Stockholm, Sweden

Demo: https://csbrandt.github.io/dimdal-pathfinder/test/

Installation

$ npm install dimdal-pathfinder

Methods

constructor(options)

options: object

• memInit: string, path to memory initialization file
• heightScaleFactor: number, applied to raw (8 bit) heightmap values
• maxHeightDiff: number, the maximum difference in height between two cells before it is considered as unpassable
• terrainLUT: object,
  • cost: array, terrain class movement costs ordered by class index, infinite costs are represented by the string "Infinity"
• roadLUT: object,
  • cost: array, road class movement costs ordered by class index

findPath(startCoord, endCoord)

startCoord: array, coordinate of the starting cell in X,Y order

endCoord: array, coordinate of the ending cell in X,Y order

Returns

Promise, resolved with an array of coordinates that make up the path

Background

A*

The cost function of the A* (denoted as f(x)) is defined as

f(x) = g(x) + h(x)

where:

• g(x) past path-cost function, which is the known distance from the starting node to the current node x
• h(x) future path-cost function, which is an admissible "heuristic estimate" of the distance from x to the goal[wikipedia]

Dimdal Pathfinder

An addition to g(x) (denoted as w(u,v)) is defined as[2]

w(u,v) = e(u,v) + r(u,v) + s(u,v) + t(u,v) + v(u,v)

where:

• e(u,v) edge check function
• r(u,v) road check function
• s(u,v) slope function
• t(u,v) terrain function
• v(u,v) visibility function

such that:

g(x) = g(u) + w(u,v)

where:

• g(u) movement cost from the starting point to u

The A* heuristic h(x) is defined as

h(x) = ((Diagonal Edge Length * min(dx , dy)) +
       (Axial Edge Length * |dx – dy|)) *
       Minimum Terrain Cost

where:

• dx = |SourceX – DestinationX|
• dy = |SourceY – DestinationY|

Implementation Details

Priority queue

A Fibonacci heap is used as a priority queue within the A* algorithm. Dense search graphs (containing millions of nodes) are generated from processing real-world raster data.

Memory space

Dimdal[1] describes an efficient graph representation that uses 3 bytes per node.

This particular implementation is designed to be used with grayscale heightmaps. Only 1 byte is required to represent the terrain height and total memory footprint per node is reduced to 2 bytes.

Memory initialization

A static memory initialization file is used to store all nodes in the search graph. A memory initialization file must be generated for each region in which searches will be conducted.

To generate a memory initialization file first create a configuration file and run,

$ node tools/generate-mem-init.js test/config.json

Running Tests

Install the development dependencies:

$ npm install

Then run the tests:

$ firefox test/index.html

Browser Bundle

$ npm run build

References

1. Dimdal / Jönsson (1997). An optimal pathfinder for vehicles in real-world digital terrain maps.
2. Sidran (2005). An Analysis of Dimdal’s "An optimal pathfinder for vehicles in real-world digital terrain maps."