spread

spread

Total friction of the shortest accumulated friction path over a map with friction values from a source cell to cell under consideration

Result = spread(points, initialfrictiondist, friction)

points

spatial boolean, nominal, ordinal

initialfrictiondist

spatial, non spatial scalar

friction

spatial, non spatial scalar

Result

spatial scalar

Options

--unittrue or --unitcell

--unittrue

distance is measured in true distance (default)

--unitcell

distance is measured in number of cell lengths

Operation

The expression points identifies those cells from which the shortest accumulated friction path to every cell centre is calculated. The spreading for determination of these friction-distances starts at the centre of cells which have a non zero value on points. The initial friction-distance (at the start of the spreading) is taken from the values at these point cells on initialfrictiondist. During spreading a path is followed over the consecutive neighbouring cells. While following this path the friction-distance increases. The increase of friction-distance per unit distance is specified by the cell values on friction. Using these values, increase when travelling from one cell to its neighbouring cell is calculated as follows: Let friction(sourcecell) and friction(destinationcell) be the friction values at the cell where is moved from and where is moved to, respectively. While moving from the source cell to the destination cell the increase of friction- distance is:

distance x {(friction(sourcecell)+friction(destinationcell)}/2

where distance is the distance between the sourcecell and the destination cell. This distance equals the cell length if the source cell and the destination cell are neighbours in horizontal or vertical directions; it equals sqrt(2) multiplied by the cell length if the cells are neighbours in diagonal directions.

During operation of the command, the spreading is executed from all non zero cells on points, over all possible paths. For determination of the accumulated friction-distance cell values on Result, for each cell the path from a non zero cell on points is chosen with the shortest friction-distance. So during the execution of the spread operation, for each cell, the friction-distance for each possible path from the non zero cells on points to the cell under consideration is calculated and then the path with the shortest friction-distance is chosen. On Result each cell has a value which is the friction-distance covered when moving over this shortest path from a non zero cell on points.

Notes

The values on friction must be larger than zero.

Missing value cells on points, initialfrictiondist and friction are assigned a missing value on Result. Potential shortest paths that cross missing value cells on points, initialfrictiondist or friction are ignored.

If no path is found for a cell (for instance if the cell is surrounded by missing values), a missing value is assigned to that cell on Result.

Group

This operation belongs to the group of Neighbourhood operators; spread operators

See Also

Friction paths, ldddist, slopelength

Examples

1. • pcrcalc

   binding

   Result2 = Result2.map;

   Points2 = Points2.map;

   Initial2 = Initial2.map;

   FrictMat2 = FrictMat2.map;

   initial

   report Result2 = spread(Points2,Initial2,FrictMat2);

   
   

   • python

   Points2 = readmap(“Points2.map”)

   Initial2 = readmap(“Initial2.map”)

   FrictMat2 = readmap(“FrictMat2.map”)

   Result2 = spread(Points2,Initial2,FrictMat2)

   Result2.map	Points2.map	Initial2.map	FrictMat2.map

   
   
2. • pcrcalc

   binding

   Result1 = Result1.map;

   Points = Points.map;

   initial

   report Result1 = spread(Points,0,1);

   
   

   • python

   Points = readmap(“Points.map”)

   Result1 = spread(Points,0,1)

   Result1.map	Points.map