仅使用 OSM 地图中心的坐标和缩放系数计算区域边界

Question

I'm using MapSCII (by rastapasta) for a project with python and nodejs. I need to render some objects by their location within the MapSCII output. MapSCII uses OSM tile layers to generate the ASCII map. I only know the coordinates of the center of the map, the zoom level as well as the number of rows/columns of the ASCII map.

Do you have any hints on how to calculate the boundaries (upper left and lower right corner), so that I can map a local coordinate system onto the ACSII data?

Take these variables for example:

def calculate_boundaries(lat, lng, zoom, width, height) -> tuple:
    ...

lat = 51.5252178
lng = -0.0925642
zoom = 17
width = 80
height = 24
upper_left, lower_right = calculate_boundaries(lat, lng, zoom, width, height)

I stumbled across this wiki entry , but it does not seem to be helpful, as I do not work with the tile numbers but with latitude/longitude.

// Edit Is this even feasible? Or would it be easier to note down, how much lat/lng change when moving in the 2D MapSCII array on each zoom level?

Answer 1

Let's consider width and height in pixels.

Calculation of Meters per Pixel (m/px) The distance (S) represented by 01 (one) pixel is given by:

S=C*cos(y)/2^(z+8) Where:

C is the circumference of the Earth at the Equator; z is the zoom level; y is the latitude where you want to get the scale.

Source: https://wiki.openstreetmap.org/wiki/Pt:Zoom_levels

There were a mistake while converting degree to radian. So I imported pi and convertion.

from math import cos, pi

def calculate_boundaries(lat, lng, zoom, width, height): # -> tuple:
    upper_left, lower_right = {}, {}
    C = 40075 # km - Equator distance around the world
    y = pi * lat / 180 # convert latitude degree to radian
    S = C * cos(y) / 2 ** (zoom + 8) # km distance of 1 px - https://wiki.openstreetmap.org/wiki/Pt:Zoom_levels
    S_deg = S * cos(y) / 100 # convert km (distance of 1 px) to degrees (coordinates)

    upper_left['lat'] = lat + height / 2 * S_deg
    upper_left['lng'] = lng - width / 2 * S_deg

    lower_right['lat'] = lat - height / 2 * S_deg
    lower_right['lng'] = lng + width / 2 * S_deg

    return upper_left, lower_right

# main
lat = 51.5252178
lng = -0.0925642
zoom = 17 # zoom
width = 80 # considered as pixels
height = 24
upper_left, lower_right = calculate_boundaries(lat, lng, zoom, width, height)

print(upper_left, lower_right)