This is an API for the Augmented City (AC) platform. For more information, please visit our website https://www.augmented.city

Local coordinate system is a right-handed cartesian coordinate system of a single reconstruction. It’s based on camera coordinate system. The local camera coordinate system of an image is defined in a way that the X axis points to the right, the Y axis to the bottom, and the Z axis to the front as seen from the image.

The local reconstruction coordinate system has no metric scale. Each reconstruction has a unique coordinate system with its own scale.

AC supports two geographic coordinate systems ECEF and ENU.

ECEF

ECEF, also known as ECR, is a geographic and Cartesian coordinate system and is sometimes known as a "conventional terrestrial" system. It represents positions as X, Y, and Z coordinates. The point is defined as the center of mass of Earth, hence the term geocentric coordinates. Read more on Wikipedia

ENU

Local tangent plane coordinates (LTP) are a geographic coordinate system based on the tangent plane defined by the local vertical direction and the Earth's axis of rotation. It consists of three coordinates: one represents the position along the northern axis, one along the local eastern axis, and one represents the vertical position. The local ENU coordinates are formed from a plane tangent to the Earth's surface fixed to a specific location and hence it is sometimes known as a "Local Tangent" or "local geodetic" plane. By convention the east axis is labeled x, the north y and the up z. Read more on Wikipedia

GeoPose is a geographically-anchored pose with 6 degrees of freedom. Position is presented as WGS-84 Geodetic point, rotation is presented as quaternion in ENU coordinate system. Example:

{
  "position": {
    "lat": 59.93930066333559,
    "lon": 30.216465340943543,
    "h": 6.6434114027277181
  }
  "quaternion": {
    "w": -0.3363841028150708,
    "x": 0.6584681350287606,
    "y": -0.4366714830997145,
    "z": -0.5124289866630708
  }
}

See OSCP GeoPose Protocol

Position

1. Select a reference geodetic point (lat_ref, lon_ref, h_ref), which will be the origin of your local coordinate system. For example, this could be the first position of a camera.

2. Convert geodetic position of GeoPose to position in ECEF coordinate system:

import math

a = 6378137
b = 6356752.3142
f = (a - b) / a
e_sq = f * (2 - f)

# Converts WGS-84 Geodetic point (lat, lon, h) to the
# Earth-Centered Earth-Fixed (ECEF) coordinates (x, y, z).
def geodetic_to_ecef(lat, lon, h):
  lamb = math.radians(lat)
  phi = math.radians(lon)
  s = math.sin(lamb)
  N = a / math.sqrt(1 - e_sq * s * s)

  sin_lambda = math.sin(lamb)
  cos_lambda = math.cos(lamb)
  sin_phi = math.sin(phi)
  cos_phi = math.cos(phi)

  x = (h + N) * cos_lambda * cos_phi
  y = (h + N) * cos_lambda * sin_phi
  z = (h + (1 - e_sq) * N) * sin_lambda

  return x, y, z

3. Convert ECEF position to ENU position:

# Converts the Earth-Centered Earth-Fixed (ECEF) coordinates (x, y, z) to
# East-North-Up coordinates in a Local Tangent Plane that is centered at the
# (WGS-84) Geodetic point (lat_ref, lon_ref, h_ref).
def ecef_to_enu(x, y, z, lat_ref, lon_ref, h_ref):
  lamb = math.radians(lat_ref)
  phi = math.radians(lon_ref)
  s = math.sin(lamb)
  N = a / math.sqrt(1 - e_sq * s * s)

  sin_lambda = math.sin(lamb)
  cos_lambda = math.cos(lamb)
  sin_phi = math.sin(phi)
  cos_phi = math.cos(phi)

  x0 = (h_ref + N) * cos_lambda * cos_phi
  y0 = (h_ref + N) * cos_lambda * sin_phi
  z0 = (h_ref + (1 - e_sq) * N) * sin_lambda

  xd = x - x0
  yd = y - y0
  zd = z - z0

  xEast = -sin_phi * xd + cos_phi * yd
  yNorth = -cos_phi * sin_lambda * xd - sin_lambda * sin_phi * yd + cos_lambda * zd
  zUp = cos_lambda * cos_phi * xd + cos_lambda * sin_phi * yd + sin_lambda * zd

  return xEast, yNorth, zUp

Orientation

Use quaternion as is.

Example

def geodetic_to_enu(lat, lon, h, lat_ref, lon_ref, h_ref):
  x, y, z = geodetic_to_ecef(lat, lon, h)

  return ecef_to_enu(x, y, z, lat_ref, lon_ref, h_ref)

geopose = {"position": {
              "lat": 59.93930063661516,
              "lon": 30.21646537256484,
              "h": 6.6359911204808377
           }
           "quaternion": {
              "w": 0.24078175147153705,
              "x": 0.23898354967230406,
              "y": -0.6720152706953141,
              "z": -0.6582601971079732
            }}

lat_ref = 59.93930066333559
lon_ref = 30.216465340943543
h_ref = 0.434114027277181

lat = geopose['position']['lat']
lon = geopose['position']['lon']
h = geopose['position']['h']

position_ref = geodetic_to_enu(lat_ref, lon_ref, h_ref, lat_ref, lon_ref, h_ref)
print(f"Reference ENU position: {position_ref}")

position = geodetic_to_enu(lat, lon, h, lat_ref, lon_ref, h_ref)
quaternion = [geopose['quaternion']['w'], geopose['quaternion']['x'],
              geopose['quaternion']['y'], geopose['quaternion']['z']]

print(f'Object ENU position: {position}\nObject ENU orientation: {quaternion}')

Output:

Reference ENU position: (0.0, 0.0, 0.0)
Object ENU position: (0.0017677017435744347, -0.0029769590309327576, 6.201877094031028)
Object ENU orientation: [0.24078175147153705, 0.23898354967230406, -0.6720152706953141, -0.6582601971079732]

For detailed information about coordinate systems, see Geographic coordinate system.

1. Convert from Geopose to ENU coordinate system as shown above
2. Convert from ENU, which is a right-handed, X forward, Y to the left, Z up coordinate system, to WebXR, which is also right-handed but X to the right, Y up, Z backwards coordinate system.

Check WebXR OSCP client

Camera

Object

1. Convert from Geopose to ENU coordinate system as shown above
2. Convert from ENU, which is a right-handed, X forward, Y to the left, Z up coordinate system, to Unity, which is a left-handed, X to the right, Y up, Z forward coordinate system.

Check OSCP Unity Client example

Camera

Object

Augmented City implementation of OSCP API

See more on https://www.openarcloud.org/oscp and https://github.com/OpenArCloud