# Distance between geometries

### Description

Calculates the distance between the given geometries

### Usage

1 2 3 |

### Arguments

`spgeom1, spgeom2` |
sp objects as defined in package sp. If spgeom2 is NULL then spgeom1 is compared to itself. |

`byid` |
Logical vector determining if the function should be applied across ids (TRUE) or the entire object (FALSE) for spgeom1 and spgeom2 |

`hausdorff` |
Logical determining if the discrete Hausdorff distance should be calculated |

`densifyFrac` |
Numerical value between 0 and 1 that determines the fraction by which to densify each segment of the geometry. |

`dist` |
Numerical value that determines cutoff distance |

### Details

Discrete Hausdorff distance is essentially a measure of the similarity or dissimilarity of the two geometries, see references below for more detailed explanations / descriptions.

If `hausdorff`

is TRUE and `densifyFrac`

is specified then the geometries' segments are densified by splitting each segment into equal length subsegments whose fraction of the total length is equal to `densifyFrac`

.

### Value

gDistance by default returns the cartesian minimum distance between the two geometries in the units of the current projection. If `hausdorff`

is TRUE then the Hausdorff distance is returned for the two geometries.

gWithinDistance returns TRUE if returned distance is less than or equal to the specified `dist`

.

### Author(s)

Roger Bivand & Colin Rundel

### References

Hausdorff Differences: http://en.wikipedia.org/wiki/Hausdorff_distance http://lin-ear-th-inking.blogspot.com/2009/01/computing-geometric-similarity.html

### See Also

`gWithinDistance`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | ```
pt1 = readWKT("POINT(0.5 0.5)")
pt2 = readWKT("POINT(2 2)")
p1 = readWKT("POLYGON((0 0,1 0,1 1,0 1,0 0))")
p2 = readWKT("POLYGON((2 0,3 1,4 0,2 0))")
gDistance(pt1,pt2)
gDistance(p1,pt1)
gDistance(p1,pt2)
gDistance(p1,p2)
p3 = readWKT("POLYGON((0 0,2 0,2 2,0 2,0 0))")
p4 = readWKT("POLYGON((0 0,2 0,2 1.9,1.9 2,0 2,0 0))")
p5 = readWKT("POLYGON((0 0,2 0,2 1.5,1.5 2,0 2,0 0))")
p6 = readWKT("POLYGON((0 0,2 0,2 1,1 2,0 2,0 0))")
p7 = readWKT("POLYGON((0 0,2 0,0 2,0 0))")
gDistance(p3,hausdorff=TRUE)
gDistance(p3,p4,hausdorff=TRUE)
gDistance(p3,p5,hausdorff=TRUE)
gDistance(p3,p6,hausdorff=TRUE)
gDistance(p3,p7,hausdorff=TRUE)
``` |