Schematic Diagram Showing Transformation of Coordinates ... · PDF file... (UTM φ,...
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Schematic Diagram Showing Transformation of Coordinates between WGS84 Geographic Coordinates and HK 1980 Grid Coordinates This diagram should be read in conjunction with 1."Explanatory Notes on Geodetic Datums in Hong Kong" and 2."Geodetic Datum Transformation and Map Projection Parameter Set for Computation between ITRF96 Geodetic Coordinates (or Cartesian Coordinates) and HK1980 Grid Coordinates" ` where a = semi-major axis of the reference ellipsoid f = flattening of the reference ellipsoid e 2 = first eccentricity of reference ellipsoid = 2 f - f 2 Eq.3, Eq.4, & Eq.5 (*5) Eq.1, Eq.2, & Eq.3 (*5) υ = radius of curvature in prime vertical = a Notes: *1 Using WGS84 Datum (UTM <-> φ, λ ) projection parameters *2 Using 7P_ITRF96_HK80_V1.0 (ITRF96 to HK80) transformation parameters *3 Using 7P_ITRF96_HK80_V1.0 (HK80 to ITRF96) transformation parameters *4 Using HK80 Datum (UTM <-> φ, λ ) projection parameters *5 Eq.1 to Eq.5 refer "Explanatory Notes on Geodetic Datums in Hong Kong" Using HK80 Datum (HK1980 Grid <-> φ, λ ) projection parameters *6 Approximate level must be provided in upward calculation, the computed ellipsoid height is only an approximate value ( 1 - e 2 sin 2 φ ) ρ = radius of curvature in the meridian = a ( 1 - e 2 ) ( 1 - e 2 sin 2 φ ) 3 ψ = isometric latitude = υ ρ WGS84 Datum Geographic Coordinates Latitude φ Longitude λ Ellipsoid Height H WGS84 Datum Cartesian Coordinates X,Y,Z HK80 Datum Geographic Coordinates Latitude φ Longitude λ Ellipsoid Height H HK80 Datum Cartesian Coordinates X,Y,Z HK80 Datum HK 1980 Grid Coordinates N, E (*6) ( υ + H ) cos φ cos λ ( υ + H ) cos φ sin λ ( ( 1 - e 2 ) υ + H ) sin φ X Y Z = = = (*1) ΔX (1+S) θ z -θ y ΔY + -θ z (1+S) θ x ΔZ θ y -θ x (1+S) X Y Z X Y = Z HK80 WGS84 (*2) Y X tan φ = H = ( X sec λ sec φ ) - υ X 2 + Y 2 tan λ = Z + e 2 υ sin φ (*4) ΔX (1+S) θ z -θ y ΔY + -θ z (1+S) θ x ΔZ θ y -θ x (1+S) X Y Z X Y = Z WGS84 HK80 (*3) Y X tan φ = H = ( X sec λ sec φ ) - υ X 2 + Y 2 tan λ = Z + e 2 υ sin φ (*1) ( υ + H ) cos φ cos λ ( υ + H ) cos φ sin λ ( ( 1 - e 2 ) υ + H ) sin φ X Y Z = = = (*4)
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Transcript of Schematic Diagram Showing Transformation of Coordinates ... · PDF file... (UTM φ,...
Schematic Diagram Showing Transformation of Coordinates between WGS84 Geographic Coordinates and HK 1980 Grid Coordinates
This diagram should be read in conjunction with 1."Explanatory Notes on Geodetic Datums in Hong Kong" and 2."Geodetic Datum Transformation and Map Projection Parameter Set forComputation between ITRF96 Geodetic Coordinates (or Cartesian Coordinates) and HK1980 Grid Coordinates"
`
where a = semi-major axis of the reference ellipsoid
f = flattening of the reference ellipsoid
e2 = first eccentricity of reference ellipsoid
= 2 f - f 2
Eq.3, Eq.4, & Eq.5 (*5) Eq.1, Eq.2, & Eq.3 (*5) υ = radius of curvature in prime vertical
= a
Notes:*1 Using WGS84 Datum (UTM <-> φ, λ ) projection parameters*2 Using 7P_ITRF96_HK80_V1.0 (ITRF96 to HK80) transformation parameters*3 Using 7P_ITRF96_HK80_V1.0 (HK80 to ITRF96) transformation parameters*4 Using HK80 Datum (UTM <-> φ, λ ) projection parameters*5 Eq.1 to Eq.5 refer "Explanatory Notes on Geodetic Datums in Hong Kong" Using HK80 Datum (HK1980 Grid <-> φ, λ ) projection parameters*6 Approximate level must be provided in upward calculation, the computed ellipsoid height is only an approximate value
( 1 - e2 sin 2φ )
ρ = radius of curvature in the meridian
= a ( 1 - e2 )
( 1 - e2 sin 2φ )3
ψ = isometric latitude
= υ ρ
WGS84 DatumGeographic Coordinates
Latitude φLongitude λEllipsoid Height H
WGS84 DatumCartesian Coordinates
X,Y,Z
HK80 DatumGeographic Coordinates
Latitude φLongitude λEllipsoid Height H
HK80 DatumCartesian Coordinates
X,Y,Z
HK80 DatumHK 1980 GridCoordinates
N, E (*6)
( υ + H ) cos φ cos λ ( υ + H ) cos φ sin λ ( ( 1 - e2 ) υ + H ) sin φ
XYZ
===
(*1)
ΔX (1+S) θz -θy
ΔY + -θz (1+S) θx
ΔZ θy -θx (1+S)
XYZ
XY =Z
HK80 WGS84
(*2)
YX
tan φ =
H = ( X sec λ sec φ ) - υ
X 2 + Y 2
tan λ =
Z + e2 υ sin φ
(*4)
ΔX (1+S) θz -θy
ΔY + -θz (1+S) θx
ΔZ θy -θx (1+S)
XYZ
XY =Z WGS84 HK80
(*3)
YX
tan φ =
H = ( X sec λ sec φ ) - υ
X 2 + Y 2
tan λ =
Z + e2 υ sin φ
(*1)
( υ + H ) cos φ cos λ ( υ + H ) cos φ sin λ ( ( 1 - e2 ) υ + H ) sin φ
XYZ
===
(*4)
