Conventions#

This page outlines the coordinate system and mathematical conventions used throughout Genesis.

Coordinate System#

Genesis uses a right-handed coordinate system with the following conventions:

  • +X axis: Points out of the screen (towards the viewer)

  • +Y axis: Points to the left

  • +Z axis: Points upward (vertical)

Quaternion Representation#

Quaternions in Genesis follow the (w, x, y, z) convention, where:

  • w: Scalar component (real part)

  • x, y, z: Vector components (imaginary parts)

This is also known as the “scalar-first” or “Hamilton” convention. When specifying rotations using quaternions, always provide them in this order.

Example#

# Quaternion representing a 90-degree rotation around the Z-axis
rotation = [0.707, 0, 0, 0.707]  # [w, x, y, z]

Gravity#

The gravitational force vector is defined as:

  • Gravity direction: -Z (pointing downward)

  • Default magnitude: 9.81 m/s²

This means objects will naturally fall in the negative Z direction when no other forces are applied.