How to Convert Latitude/Longitude to Pixels on a Mercator Projection?

Convert Latitude/Longitude Point to Pixels (x,y) on Mercator Projection

The Mercator projection, commonly used for navigation charts, has straight lines representing parallels and meridians. To convert a latitude/longitude point to a pixel (x,y) coordinate on a Mercator projection image, the following formula can be applied:

Derivation:

The Mercator projection is a limiting case of the Lambert Conic Conformal projection, where the equator is the only standard parallel. This results in straight lines for all parallels and meridians.

Formula:

E = FE + R (λ – λₒ)
N = FN + R ln[tan(π/4 + φ/2)]   

where:

• E and N are the Easting and Northing coordinates
• FE and FN are false easting and false northing (not used in spherical Mercator)
• λ is the longitude
• λ_o is the longitude of origin
• φ is the latitude

Simplified Formula:

For spherical Mercator, the false easting and false northing are not used, simplifying the formula to:

x = (longitude+180)*(mapWidth/360)
y = (mapHeight/2)-(mapWidth*ln(tan((PI/4)+(latitude*PI/180)))/(2*PI))

Example:

Given the following parameters:

• Latitude: 41.145556
• Longitude: -73.995
• Map width: 200 pixels
• Map height: 100 pixels

Applying the formula, we get:

x = 60.0083
y = 32.5903

These pixel coordinates represent the (x,y) location of the point on the Mercator projection image.

The above is the detailed content of How to Convert Latitude/Longitude to Pixels on a Mercator Projection?. For more information, please follow other related articles on the PHP Chinese website!