EPSG Dataset :: v12.003

Bonne

Coordinate Operation Method Details [VALID]

Name:

Bonne

Code:

9827

Operation is Reversible:

Yes

Formula:

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The formulas to convert geodetic latitude and longitude (lat, lon) to Easting and Northing are:

E = (rho . sin T) + FE
N = (a . mO / sin(latO) – rho . cos T) + FN

where
m = cos(lat) / (1 – e^2sin^2(lat))^0.5
with lat in radians and mO for latO, the latitude of the origin, derived in the same way.

M = a[(1 – e^2/4 – 3e^4/64 – 5e^6/256 –....)lat – (3e^2/8 + 3e^4/32 + 45e^6/1024+....)sin(2 lat) + (15e^4/256 + 45e^6/1024 +.....)sin(4 lat) – (35e^6/3072 + ....)sin(6 lat) + .....]
with lat in radians and MO for latO, the latitude of the origin, derived in the same way.

rho = a . mO / sin(latO) + MO – M
T = a . m (lon – lonO) / rho with lon and lonO in radians

For the reverse calculation:
X = E – FE
Y = N – FN
rho = ± [X^2 + (a . mO / sin(latO) – Y)^2]^0.5 taking the sign of latO
M = a . mO / sin(latO) + MO – rho
mu = M / [a (1 – e^2/4 – 3e^4/64 – 5e^6/256 – …)]
e1 = [1 – (1 – e^2)^0.5] / [1 + (1 – e^2)^0.5]
lat = mu + ((3 e1 / 2) – (27 e1^3 / 32) +.....)sin(2 mu) + ((21 e1^2 / 16) – (55 e1^4 / 32) + ....)sin(4 mu)
+ ((151 e1^3 / 96) +.....)sin(6 mu) + ((1097 e1^4 / 512) – ....)sin(8 mu) + ......

m = cos(lat) / (1 – e^2 sin^2(lat))^0.5

If latO is not negative
lon = lonO + rho {atan2[X / (a . mO , sin(latO) – Y)]} / a . m
but if lonO is negative
lon = lonO + rho {atan2[–X , –(a . mO , sin(latO) – Y)]} / a . m
In either case, if lat = ±90°, m = 0 and the equation for lon is indeterminate, so use lon = lonO. See implementation notes in GN7-2 preface for atan2 convention.

Example:

See information source.

Method
Parameters:

Parameter Name	Parameter Code	Sign reversal	Parameter Description
Latitude of natural origin	8801	No	The latitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the latitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0).
Longitude of natural origin	8802	No	The longitude of the point from which the values of both the geographical coordinates on the ellipsoid and the grid coordinates on the projection are deemed to increment or decrement for computational purposes. Alternatively it may be considered as the longitude of the point which in the absence of application of false coordinates has grid coordinates of (0,0). Sometimes known as "central meridian (CM)".
False easting	8806	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Easting, FE, is the value assigned to the abscissa (east or west) axis of the projection grid at the natural origin.
False northing	8807	No	Since the natural origin may be at or near the centre of the projection and under normal coordinate circumstances would thus give rise to negative coordinates over parts of the mapped area, this origin is usually given false coordinates which are large enough to avoid this inconvenience. The False Northing, FN, is the value assigned to the ordinate (north or south) axis of the projection grid at the natural origin.

Meta Data

Information Source:

"Map Projections - A Working Manual" by John P. Snyder, USGS Professional Paper 1395.

Data Source:

EPSG

Revision Date:

June 29, 2023

Change ID:

[2017.024] [2023.004]

Wildcard	Example
% or *	Any wildcard characters
? or _	One wildcard character
[ - ]	[ - ] Range e.g. N[a-c] will return all geodetic objects that contains a string starting with the letter 'N' or 'n' followed by any of the letters contained within the range specified within the square bracket, e.g. letters a, b and c.
\|	Or e.g. E[a\|e]M will return all geodetic objects that contains a string starting with the letter E(e), ends with the letter M(m) and also contain either the letter a or letter e.