Convert 1m to decimal degrees (WGS84) depending on polygon location

I have a table with small polygons that are scattered around a "continental" area (Brazil). How can I convert 1m to decimal degrees of a wgs84 reference system (longitude / latitude) depending on the position of each polygon?

Broader context: I am trying to use ST_SimplifyVW(geom, tolerance) to remove spikes from polygons (as describe here). The tolerance parameter of ST_SimplifyVW is given in terms of the SRID unit, which are decimal degrees. I would prefer to have the tolerance parameter provided in square meters because: a) is a little more intuitive; b) I would like the tolerance used to be the same regardless of the latitude of the polygons.

So ideally I would have something like:

ST_SimplifyVW(geom, f_m_to_degrees(1,geom) )

where fictitious function "f_m_to_degrees"would convert the supplied distance to degrees to the most precise projection around the location of geom.

• You could just create a simple linestring on a projected coordinate system and then use [ST_Transform|postgis.org/docs/ST_Transform.html] to get the equivalent in degrees. Its a little round-about though, and not what you asked for. – BradHards Dec 26 '15 at 3:55
• There isn't any valid conversion from meters to degrees, even at a point, without also having a direction, as discussed in a multitude of questions. I would recommend you project your data, at which point you can use meters for simplification. – Vince Dec 26 '15 at 13:44

Presumably, ST_SimplifyVW() works on planar coordinates. To convert distance_degrees to distance_meters is simple:

distance_meters = earth_radius_meters * to_radians( distance_degrees )

However, treating coordinates in distance_degrees introduces distortions:

• zero distortion in N-S direction
• distortion proportional to Cosine( latitude ) in E-W direction

An alternative, as suggested in comments, is to project your coordinates to a suitable local coordinate system (having relatively little distortion) then work directly in meters.

• Tks. I suppose I could do ST_Transform to local projection in meters > ST_SimplifyVW( , 1) in meters > ST_Transform back to wgs84. Is that lossless and topology preserving? In case of Brazil, longitude ranges from -73.0 to -28.3. So the appropriate "local" projection will vary. I'm using ST_Transform(geom,utmzone(ST_Centroid(geom)) for that. – LucasMation Dec 27 '15 at 22:35
• Doing the work in UTM will be far better than a hack to get an approximate degrees/meters ratio, do the transform for sure. – Paul Ramsey Jan 7 '16 at 18:39
• And if using UTM, see gis.stackexchange.com/questions/93332/… for how to eliminate distortion completely. – Martin F Jan 8 '16 at 1:35