R: Distance Metric

metric.object {spatstat.geom} | R Documentation

## Distance Metric

### Description

An object of class `"metric"` defines a measure of distance between points, and supports many operations that involve distances.

### Details

A ‘metric’ d is a measure of distance between points that satisfies

1. d(x,x) = 0 for any point x,

2. d(x,y) > 0 for any two distinct points x and y

3. symmetry: d(x,y) = d(y,x) for any two points x and y

4. triangle inequality: d(x,y) <= d(x,z) + d(z,y) for any three points x,y,z.

The Euclidean distance between points is an example of a metric.

An object of class `"metric"` is a structure that defines a metric and supports many computations that involve the metric. The internal structure of this object, and the mechanism for performing these computations, are under development.

Objects of class `"metric"` are produced by the function `convexmetric` and possibly by other functions.

There are methods for `print` and `summary` for the class `"metric"`. The `summary` method lists the operations that are supported by the metric.

To perform distance calculations (for example, nearest-neighbour distances) using a desired metric instead of the Euclidean metric, first check whether the standard function for this purpose (for example `nndist.ppp`) has an argument named `metric`. If so, use the standard function and add the argument `metric`; if not, use the low-level function `invoke.metric`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`convexmetric`, `invoke.metric`

### Examples

      m <- convexmetric(square(c(-1,1)))
      summary(m)
      y <- nndist(cells, metric=m)

[Package spatstat.geom version 2.3-2 Index]