tm_fwd: Transverse Mercator projection

In geographiclib: Access to 'GeographicLib'

Transverse Mercator projection

Description

Convert geographic coordinates to/from Transverse Mercator projection with user-specified central meridian and scale factor.

Two versions are provided:

• tm_fwd()/tm_rev(): Series approximation, fast, accurate to ~5 nanometers

• tm_exact_fwd()/tm_exact_rev(): Exact formulation, slower but accurate everywhere

Usage

tm_fwd(x, lon0, k0 = 0.9996)

tm_rev(x, y, lon0, k0 = 0.9996)

tm_exact_fwd(x, lon0, k0 = 0.9996)

tm_exact_rev(x, y, lon0, k0 = 0.9996)

Arguments

x	For forward conversion: a two-column matrix or data frame of coordinates (longitude, latitude) in decimal degrees. For reverse conversion: numeric vector of x (easting) coordinates in meters.
lon0	Central meridian in decimal degrees. Can be a vector to specify different central meridians for each point.
k0	Scale factor on the central meridian. Default is 0.9996 (UTM). Common values: 0.9996 (UTM), 1.0 (many national grids), 0.9999 (some state planes).
y	Numeric vector of y (northing) coordinates in meters (reverse only).

Details

The Transverse Mercator projection is a conformal cylindrical projection commonly used for:

• UTM (Universal Transverse Mercator) zones

• Many national and state coordinate systems

• Large-scale topographic mapping

Unlike utmups_fwd() which automatically selects UTM zones, these functions allow you to specify any central meridian and scale factor.

The series approximation (tm_fwd/tm_rev) is accurate to ~5 nanometers within 3900 km of the central meridian. The exact version (tm_exact_fwd/tm_exact_rev) is slower but works accurately everywhere.

The lon0 parameter is vectorized, allowing different central meridians for each point (useful for processing data across multiple zones).

Value

Data frame with columns:

• For forward conversion:

  • x: Easting in meters

  • y: Northing in meters

  • convergence: Grid convergence in degrees

  • scale: Scale factor at the point

  • lon, lat: Input coordinates (echoed)

  • lon0: Central meridian (echoed)

• For reverse conversion:

  • lon: Longitude in decimal degrees

  • lat: Latitude in decimal degrees

  • convergence: Grid convergence in degrees

  • scale: Scale factor at the point

  • x, y: Input coordinates (echoed)

  • lon0: Central meridian (echoed)

See Also

utmups_fwd() for automatic UTM zone selection.

Examples

# Basic Transverse Mercator (like UTM zone 55)
pts <- cbind(lon = c(147, 148, 149), lat = c(-42, -43, -44))
tm_fwd(pts, lon0 = 147, k0 = 0.9996)

# Compare with UTM
utmups_fwd(pts)

# Custom scale factor (k0 = 1.0)
tm_fwd(pts, lon0 = 147, k0 = 1.0)

# Different central meridian for each point
tm_fwd(pts, lon0 = c(147, 148, 149), k0 = 0.9996)

# Round-trip conversion
fwd <- tm_fwd(pts, lon0 = 147, k0 = 0.9996)
tm_rev(fwd$x, fwd$y, lon0 = 147, k0 = 0.9996)

# Exact version for high precision or extreme locations
tm_exact_fwd(pts, lon0 = 147, k0 = 0.9996)

geographiclib documentation built on March 4, 2026, 9:07 a.m.