Converting between coordinates system WGS 74 and WGS 84

I'm working on rasterisation of the GSHHS database basically converting shoreline polygons and river lines to raster.

http://www.soest.hawaii.edu/pwessel/gshhg/

The rivers and shores databases are two different files.

I noticed misalignment of hundreds of meters between rivers and shores at points where they are clearly should be aligned. One thing I noticed in the README is that the shorelines database uses WGS84 coordinates and river database was generated form other source using WGS 72. The difference should be in shift of prime meridian and difference in primary axis dimensions of the Earth.

I've searched over the internet about conversion between the two sets and couldn't found.

Answers I need:

• How can I convert between them?

Or alternatively

• How do I solve misalignment in GSHHS database?

Here are the formulas and parameters to transform WGS 72 coordinates to WGS 84 coordinates

FORMULAS

• Δφ" = (4.5 cos φ) / (a sin 1") + (Δf sin 2φ) / (sin 1") (Unit = Arc Seconds)
• Δλ" = 0.554 (Unit = Arc Seconds)
• Δh = 4.5 sin φ + a Δf sin2 φ - Δa + Δr (Unit = Meters)

---

• Δφ = Δφ" x 1" (Unit = radians)
• Δλ = Δλ" x 1" (Unit = radians)

PARAMETERS

• Δf = 0.3121057 x 10-7
• a = 6378135 m
• Δa = 2.0 m
• Δr = 1.4 m
• 1" = pi / (3600.0 * 180.0) rad

To obtain WGS 84 coordinates, add the Δφ, Δλ, Δh changes calculated using WGS 72 coordinates to the WGS 72 coordinates (φ, λ, h, respectively). Latitude is positive north and longitude is positive east (0° to 180°).

RESULT

• φ WGS84 = φ + Δφ
• λ WGS84 = λ + Δλ
• h WGS84 = h + Δh

Documentation [p105-106]