This is an old revision of the document!

The CowEyes Coordinate System

The cow coordinate system is a right handed coordinate system, where looking on the screen the x-axis points to the right, the y-axis points down and the z axis point into the screen.

The rotation of an object is defined as a counterclockwise rotation. However since the coordinate system is viewed from the back the rotation appears as what is normally known as clockwise.

Rotation Conventions and Coordinate system

Coordinate System with Rotation

Shown is the Coordinate system with rotation directions.

Image Placement

Shown is the how an image is placed into the coordinate system.
Left for 2D images, right for 3D images.
The rotation center is marked in the middle of the image.

Definition of Coordinate Axes:

  • X-Axis (Axis of abscissas) from left to right
  • Y-Axis (Axis of ordinates) from top to bottom
  • Z-Axis (Axis of applicants) from front to back

Euler Convention:

ZXZs

That is:

  1. Alpha (α) rotation around static global Z-Axis
  2. Beta (β) rotation around static global X-Axis
  3. Gamma (γ) rotation around static global Z-Axis

Rotation:

  • Rotations use the right hand thumb rule.
  • If right thumb points along an axis, then curved fingers point in the positive direction of rotation.
  • The rotation center is the center of the image.