Converting 360 Spherical to Equirectangular

See ExampleScripts- convert_to_pixels

The script is designed to convert 3D eye-tracking data from Cartesian coordinates (x, y, z) to 2D coordinates on an equirectangular projection, commonly used in 360° videos or panoramic images. Specifically, it's converting these coordinates to pixel coordinates on an equirectangular frame. Here's a breakdown of what each part of the script does:

• Cartesian to Spherical Coordinates:

  • The cartesian_to_spherical function takes 3D Cartesian coordinates (x, y, z) and converts them to spherical coordinates. In spherical coordinates, theta is the angle in the xy-plane (azimuth), and phi is the angle from the positive z-axis (inclination).

  • The normalization step ensures that the (x, y, z) vector is treated as a direction vector, not a position in space.

• Spherical to Equirectangular Projection:

  • The spherical_to_equirectangular function then converts these spherical coordinates into pixel coordinates on an equirectangular projection.

  • theta is mapped linearly across the horizontal axis of the equirectangular frame, and phi is mapped linearly across the vertical axis.

  • The final output is pixel_x and pixel_y, which represent the location on the equirectangular projection where the gaze point would appear.

• Application in the Script:

  • The script reads eye-tracking data from an input file, where each row contains the x, y, z coordinates of the gaze point, among other data.

  • It converts these coordinates to equirectangular projection pixel coordinates for each data point.

  • The output is a CSV file with the original data plus the converted pixel coordinates (pixel_x, pixel_y).

This conversion is useful when you need to map 3D gaze data onto a 2D representation of a 360° environment, such as overlaying gaze points onto a 360° video frame. The pixel coordinates tell you where on the 2D frame the person was looking, based on their 3D gaze direction.