Convert Lat/Long to X,Y position within a Bounding Box

Question

I have a bounding box of:

Left -122.27671
Bottom 37.80445
Right -122.26673
Top 37.81449

It could also be converted into NE Lat/Long and SW Lat/Long

Within that bounding box, I'd like to find the X,Y position of a specific Lat/Long. This would be using the Mercator projection.

I've seen answers that find the X,Y of a position on a world map using Mercator, but not within a specific lat/lon.

Any help appreciated!

UPDATE Put this together from another question I saw. Can anyone validate if this seems legit?

map_width = 1240
map_height = 1279

map_lon_left = -122.296916
map_lon_right = -122.243380
map_lon_delta = map_lon_right - map_lon_left

map_lat_bottom = 37.782368
map_lat_bottom_degree = map_lat_bottom * Math::PI / 180

def convert_geo_to_pixel(lat, long)
  x = (long - map_lon_left) * (map_width / map_lon_delta)

  lat = lat * Math::PI / 180
  world_map_width = ((map_width / map_lon_delta) * 360) / (2 * Math::PI)
  map_offset_y = (world_map_width / 2 * Math.log((1 + Math.sin(map_lat_bottom_degree)) / (1 - Math.sin(map_lat_bottom_degree))))
  y = map_height - ((world_map_width / 2 * Math.log((1 + Math.sin(lat)) / (1 - Math.sin(lat)))) - map_offset_y)

  return [x, y]
end

Answer 1

Found a better solution that I've test and validated. Posting this for anyone else who might find it useful. It's written in Ruby but easy to convert to any other language

@north = to_radians(37.81449)
@south = to_radians(37.80445)
@east = to_radians(-122.26673)
@west = to_radians(-122.27671)
# Coordinates above are a subsection of Oakland, CA

@map_width = map_width
@map_height = map_height

def location_to_pixel(lat:, lon:)
  lat = to_radians(lat)
  lon = to_radians(lon)
  ymin = mercator_y(@south)
  ymax = mercator_y(@north)
  x_factor = @map_width/(@east - @west)
  y_factor = @map_height/(ymax - ymin)

  y = mercator_y(lat);
  x = (lon - @west) * x_factor
  y = (ymax - y) * y_factor
  [x, y]
end

def to_radians(deg)
  deg * Math::PI/180
end

def mercator_y(lat)
    Math.log(
      Math.tan(lat/2 + Math::PI/4)
    )
end