COTA 751 Form Visualization: Handout 2

Coordinate Systems
Coordinates are an ordered set of values which specify a location relative to some origin. There are a variety of coordinate systems. Some examples follow:

2D vs. 3D
A 2D coordinate system is used to specify all locations in 2D space.
A 3D coordinate system is used to specify all locations in 3D space.

Cartesian (rectangular) coordinate systems
In a 2D Cartesian coordinate system each location is specified by an ordered set of two distances, an x-coordinate and a y-coordinate, represented as (x, y). The two coordinates are "ordered" because their order matters. The x-coordinate of a point location comes first; the y-coordinate comes next. For instance, (2, 3) and (3, 2) specify two different locations.

In a 3D Cartesian coordinate system each location is specified by an ordered set of three coordinates, an x-coordinate, a y-coordinate, and a z-coordinate, (x, y, z).

Other types of 3D coordinate systems: spherical coordinate systems and polar coordinate systems
In a spherical or azimuthal coordinate system each location is specified by a distance and two angles. The spherical coordinate system is often used to navigate through the world by specifying camera positions in terms of the camera's angle around the horizon, its angle above the horizon, and its distance from the object.

In a 3D polar coordinate system each location is specified by two distances and one angle.

Right-handed vs. left-handed
In a right-handed coordinate system the direction in which your hand closes to make a fist is the direction of a positive rotation around any axis represented by the extended right-hand thumb.

In a left-handed coordinate system the direction in which your hand closes to make a fist is the direction of a positive rotation around any axis represented by the extended left-hand thumb.

Object space and world space
Each object is defined in its object space (also called object coordinate system or local coordinate system.) A scene containing a single object or multiple objects is defined in the world space (also called world coordinate system or global coordinate system.)

NOTES:

• Maya uses a right-handed 3D Cartesian coordinate system.
• The y-axis is the vertical axis in Maya and many other 3D computer applications but in some software packages the z-axis is the vertical axis. Be aware of the orientation of the major axes when you are transferring objects from one software to another.
• Suppose that you have an object which is off-centered in its object space. Even if you place the object at the origin of the world space, the object won't be centered at the world space's origin.