# distanceFromEachPoint: Calculate distances and directions between many points and many grid cells

## Description

This is a modification of `distanceFromPoints` for the case of many points. This version can often be faster for a single point because it does not return a RasterLayer. This is different than `distanceFromPoints` because it does not take the minimum distance from the set of points to all cells. Rather this returns the every pair-wise point distance. As a result, this can be used for doing inverse distance weightings, seed rain, cumulative effects of distance-based processes etc. If memory limitation is an issue, maxDistance will keep memory use down, but with the consequences that there will be a maximum distance returned. This function has the potential to use a lot of memory if there are a lot of `from` and `to` points.

## Usage

```distanceFromEachPoint(from, to = NULL, landscape, angles = NA_real_, maxDistance = NA_real_, cumulativeFn = NULL, distFn = function(x) 1/(1 + x))
.pointDistance(from, to, angles = NA, maxDistance = NA_real_)```

## Arguments

from
matrix with 2 or 3 columns, x and y, representing x and y coordinates of "from" cell, and optional "id" which will be matched with "id" from `to`
to
matrix with 2 or 3 columns (or optionally more, all of which will be returned), x and y, representing x and y coordinates of "to" cells, and optional "id" which will be matched with "id" from `from`. Default is all cells.
landscape
RasterLayer. optional. This is only used if `to` is NULL, in which case all cells are considered `to`
angles
Logical. If `TRUE`, then the function will return angles in radians, as well as distances.
maxDistance
Numeric in units of number of cells. The algorithm will build the whole surface (from `from` to `to`), but will remove all distances that are above this distance. Using this will keep memory use down.
cumulativeFn
A function that can be used to incrementally accumulate values in each `to` location, as the function iterates through each `from`. See Details.
distFn
A function, of "x", to convert the distance in cells to some other set of units that will be accumulated by the `cumulativeFn`. See Details.

## Value

A sorted matrix on `id` with same number of rows as `to`, but with one extra column, `"dists"` indicating the distance between from and to.

## Details

If the user requires an id (indicating the from cell for each to cell) to be returned with the fuction, the user must add an identifier to the `from` matrix, such as "id". Otherwise, the function will only return the coordinates and distances.

`distanceFromEachPoint` calls `.pointDistance`, which is not intended to be called directly by the user.

This function has the potential to return a very large object, as it is doing pairwise distances (and optionally directions) between from and to. If there are memory limitations because there are many `from` and many `to` points, then `cumulativeFn` and `distFn` can be used. These two functions together will be used iteratively through the `from` points. The `distFn` should be a transformation of distances to be used by the `cumulativeFn` function. For example, if `distFn` is 1/(1+x), the default, and `cumulativeFn` is ``+``, then it will do a sum of inverse distance weights. See examples.

`rings`, `cir`, `distanceFromPoints`, which can all be made to do the same thing, under specific combinations of arguments. But each has different primary use cases. Each is also faster under different conditions. For instance, if `maxDistance` is relatively small compared to the number of cells in the `landscape`, then `cir` will likely be faster. If a minimum distance from all cells in the `landscape` to any cell in `from`, then `distanceFromPoints` will be fastest. This function scales best when all `to` is many or all cells (which is default).

## Examples

Run this code
``````library(raster)
N <- 2
distRas <- raster(extent(0,40,0,40), res = 1)
coords <- cbind(x = round(runif(N, xmin(distRas), xmax(distRas)))+0.5,
y = round(runif(N, xmin(distRas), xmax(distRas)))+0.5)

# inverse distance weights
dists1 <- distanceFromEachPoint(coords, landscape = distRas)
indices <- cellFromXY(distRas,dists1[,c("x","y")])
invDist <- tapply(dists1[,"dists"], indices, function(x) sum(1/(1+x))) # idw function
distRas[] <- as.vector(invDist)
if (interactive()) Plot(distRas, new = TRUE)

# With iterative summing via cumulativeFn to keep memory use low, with same result
dists1 <- distanceFromEachPoint(coords[, c("x", "y"), drop = FALSE],
landscape = distRas, cumulativeFn = `+`)
idwRaster <- raster(distRas)
idwRaster[] <- dists1[,"val"]
if (interactive()) Plot(idwRaster)

all(idwRaster[] == distRas[]) # TRUE

``````

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