How PocketGudie turns your phone into a personal tourguide?

Input

latitude λ, longitude φ (degrees), radius r (meters)

• GPS location
• Points of interest

screen coordinates x, y (pixels)

• touch

Output

screen coordinates x, y (pixels)

proximity (boolean)

Conversion

Mercator projection

Basic insight

At sea level, we have

• 111111.11 meters (10⁷ / 90) per degree of latitude
• 111111.11 · cos(λ) meters per degree of longitude

On OpenStreetMap (a Mercator map), we have

• 186413.5 pixels (2^{18 + 8} / 360) per degree of longitude
• 186413.5 / cos(λ) pixels per degree of latitude
• 1.6777216 / cos(λ) pixels per meter (2^{18 + 8} / 40 000 000)