# The CowEyes Coordinate System

## General definitions

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

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

## Coordinate System with Rotation

## 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:

- Alpha (α) rotation around static global Z-Axis
- Beta (β) rotation around static global X-Axis
- 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.