[GRASS-dev] Question on r.grow 'metrics' parameters

[Glynn Clements]

Patton, Eric wrote:

> I was wondering if anyone could describe, or point me to a link of, the
> various r.grow metrics parameter definitions: euclidian, maximum, and
> manhattan.

Euclidean (aka "Pythagoras' theorem"):

	d(dx,dy) = sqrt(dx^2 + dy^2)

	http://en.wikipedia.org/wiki/Euclidean_metric

Isolines of distance from a point are circles

Manhattan:

	d(dx,dy) = abs(dx) + abs(dy)

	http://en.wikipedia.org/wiki/Manhattan_metric

Isolines of distance from a point are rhombi (diamonds).

[See Hamish' reply for the reason behind the "Manhattan" name.]

Maximum:

	d(dx,dy) = max(abs(dx),abs(dy))

Isolines of distance from a point are squares.

> Also, are the comments regarding how r.grow decides how to grow between
> two equally eligible cells here
> (http://www.nabble.com/-GRASSLIST%3A7611--r.grow-to8629593.html#a8629593)
>  still valid?

Yes.

-- 
Glynn Clements <glynn at gclements.plus.com>