Guidance Note Number 7, part 2

Coordinate Conversions and Transformation including Formulas

Revision history:

Version

Date

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Amendments

35

April 2008

PDF | Word (zipped)

Longitude wrap-around note clarified. For Oblique Mercator, corrected symbol in formula for longitude. For Krovak, clarified defining parameters. Amended Vertical Offset description and formula. Added geographic/topocentric conversions, geocentric/topocentric conversions, Vertical Perspective, Orthographic, Lambert Cylindrical Equal Area, ellipsoidal development of Equidistant Cylindrical. Removed section on identification of map projection method.

34

July 2007

 

Note on longitude wrap-around added prior to preample to map projection formulas, section 1.4. For Laborde, corrected formula for q'. For Albers Equal Area, corrected formulae for α and β'.

33

March 2007

 

For Krovak example, corrected axis names.

32

February 2007

 

Descriptive text for Oblique Mercator amended; formula for Laborde projection for Madagascar added. Added polar aspect equations for Lambert Azimuthal Equal Area. Corrected example in polynomial transformation for Spain. For Lambert 1SP, corrected equation for r'.

31

August 2006

 

Corrected sign of value for G in Modified Azimuthal Equidistant example.

30

August 2006

 

Added Hyperbolic Cassini-Soldner. Corrected FE and FN values in example for Modified Azimuthal Equidistant. Added note to Krovak. Amended Abridged Molodensky description, corrected example.

29

April 2006

 

Typographic errors corrected. (For oblique stereographic, corrected formula for w. For Lambert azimuthal equal area, changed example. For Albers equal area, corrected formulae for alpha. For modified azimuthal equidistant, corrected formula for c. For Krovak, corrected formula for theta', clarified formulae for tO and lat. For Cassini, in example corrected radian value of longitude of natural origin). References to EPSG updated.

28

November 2005

 

Corrected error in formula for t and false grid coordinates of 2SP example in Mercator projection

27

September 2005

 

Miscellaneous linear coordinate operations paragraphs re-written to include reversibility and UKOOA P6. Improved formula for r' in Lambert Conic Near-Conformal.

26

August 2005

 

Further correction to Lambert Azimuthal Equal Area formulae. Correction to Moldenski-Badekas example.

25

May 2005

Amended reverse formulas for Lambert Conic Near-Conformal. Corrected Lambert Azimuthal Equal Area formulae. Symbol for l atitude of pseudo standard parallel parameter made consistent. Corrected Affine Orthogonal Geometric transformation reverse example. Added Modified Azimuthal Equidistant projection.

24

October 2004

From this revision, published as part 2 of a two-part set.

Corrected equation for u in Oblique Mercsator. Added Guam projection, Geographic 3D to 2D conversion, vertical offset and gradient method, geoid models, bilinear interpolation methods. Added tables giving projection parameter definitions. Amended Molodensky-Badekas method name and added example. Added section on reversibility to Helmert 7-parameter transformations. Transformation section 2 reordered. Section 3 (concatenated operations) added.

Problem in reverse formulas for Lambert Conic Near-Conformal to be resolved.

23

January 2004

Database codes for Polar Stereographic variants corrected. Degree representation conversions withdrawn.

22

December 2003

Errors in FE and FN values in example for Lambert Azimuthal Equal Area corrected.

21

October 2003

Typographic errors in example for Lambert Conic (Belgium) corrected. Polar Stereographic formulae extended for secant variants. General polynomial extended to degree 13. Added Abridged Molodensky and Lambert Azimuthal Equal Area examples and Reversible polynomial formulae.

20

May 2003

Font for Greek symbols in Albers section amended.

19

December 2002

Polynomial formulas amended. Formula for spherical radius in Equidistant Cylindrical projection amended. Formula for Krovak projection amended. Degree representation conversions added. Editorial amendments made to subscripts and superscripts.

18

August 2002

Revised to include ISO 19111 terminology. Section numbering revised.

Added Preface. Lambert Conformal (West Orientated), Lambert Azimuthal Equal Area, Albers, Equidistant Cylindrical (Plate Carrée), TM zoned, Bonne, Molodensky-Badedas methods added. Errors in Transverse Mercator (South Orientated) formula corrected.

17

June 2001

Lambert Conformal, Mercator and Helmert formulas corrected.

16

December 2000

Lambert Conformal (Belgium) remarks revised; Oblique Mercator methods consolidated and formulas added. Similarity Transformation reversibility remarks amended.

15

June 2000

General Polynomial and Affine methods added

14

December 1999

Stereographic and Tunisia Mining Grid formulas corrected. Krovacmethod added.

13

July 1999

Lambert ConicNear Conformal and American Polyconic methods added

12

February 1999

Abridged Molodensky formulas corrected

11

November 1998

Polynomial for Spain and Tunisia Mining Grid methods added

10

May 1998

Additionally issued as an EPSG guidance note

1

December 1993

First release - POSC Epicentre