# donut

## Nearest
Neighbour Search with Variables on a Torus

### What does donut do?

There are several R packages, such as RANN and nabor that find the
\(k\) nearest neighbours in a dataset
of specified query points, based on some metric, such as L2 or L1. The
donut package considers the situation where one or more of the variables
in the dataset is periodic on a finite interval. For example, direction
is periodic on the interval \((0,
360)\) degrees. In the small dataset \(\{10, 90, 350\}\) degrees 350 is closer to
10 than is 90: 10 and 350 are separated by 20 degrees, 10 and 90 by 80
degrees.

The function `nnt()`

finds the \(k\) nearest neighbours of each of a set of
points of interest, wrapping periodic variables on a torus so that this
periodicity is reflected. The user chooses the function to use to find
the nearest neighbours. The nearest neighbour functions from the
aforementioned packages are used as examples.

### An example

We use a simple example from the `RANN:nn2()`

documentation. We suppose that both variables should be wrapped, on the
ranges \((0, 2\pi)\) and \((0, 3)\) respectively. We choose the query
points of interest to illustrate the wrapping of the variables. In the
plot, query points are indicated with colour-coded crosses and the 8
nearest neighbours of each point are shaded in the same colour. By
default `nnt()`

uses the function `RANN::nn2()`

(based on the L2 metric) to find the nearest neighbours.

```
library(donut)
set.seed(20092019)
x1 <- runif(100, 0, 2 * pi)
x2 <- runif(100, 0, 3)
DATA <- data.frame(x1, x2)
ranges <- rbind(c(0, 2 * pi), c(0, 3))
query <- rbind(c(6, 1.3), c(2 * pi, 3), c(3, 1.5), c(4, 0))
library(RANN)
#> Warning: package 'RANN' was built under R version 4.2.3
res2 <- nnt(DATA, query, k = 8, torus = 1:2, ranges = ranges)
plot(res2)
```

### Installation

To get the current released version from CRAN:

`install.packages("donut")`

### Vignette

See `vignette("donut-vignette", package = "donut")`

for an
overview of the package.