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Coordinate System

LUX uses the XYZ coordinate system:

Z ↑ (Up - Vertical)
|
|
+---→ X (East - Horizontal)
 \
  \
   → Y (North - Horizontal)

X-axis - Horizontal, points East

Y-axis - Horizontal, points North

Z-axis - Vertical, points Up

Note: North and East are mostly used for indicating that axes lie in the horizontal plane.

Single-Angle Direction System​

Overview​

The obstruction calculation API uses a simplified single horizontal rotation angle system. The view direction stays in the horizontal plane.

Rotation Convention​

  • Z-axis: Points upward (vertical) ⬆️
  • X-Y plane: Horizontal plane
  • Rotation: Counter-clockwise when viewed from above (looking down the Z-axis)

Direction Angle​

Parameter: direction_angle (float, radians)

Range: 0 to 2π (0 to 360°)

Direction Mapping:

Angle (rad)Angle (°)DirectionCompass
00+XEast
π/290+YNorth
π180-XWest
3π/2270-YSouth

Python Example​

import numpy as np

# Facing east (+X direction)
request = {
    "x": 0.0,
    "y": 0.0,
    "z": 3.0,
    "direction_angle": 0.0,
    "mesh": [...]
}

# Facing north (+Y direction)
request["direction_angle"] = np.pi / 2

# Facing west (-X direction)
request["direction_angle"] = np.pi

# Facing south (-Y direction)
request["direction_angle"] = 3 * np.pi / 2