Understanding Coordinate Systems in 3D Space

• A coordinate system is used to identify the location of a point or other geometric objects.

Cartesian Coordinates

• A point at coordinates (3,3) is given as an example

Coordinate Frame Conventions

• Conventions for left-handed and right-handed coordinate frames exist.

Coordinate Frame

• The coordinate frame is the foundation for defining content in 3D space.
• Without a reference coordinate frame, the definition of a point is meaningless.
• It is always necessary to specify the reference frame to provide context.

Defining 3D Space

• Three values are required to fully define the position of any point in the world in three-dimensional space.

• These three values are represented by the x, y, and z-axes of the coordinate frame.

• Each of the 3 axes is orthogonal, intersecting at a 90-degree angle.

• The intersection point of the 3 axes is the origin, represented as [0, 0, 0] in [x, y, z] coordinates.

• A point "p" is positioned at 3 meters on the x-axis, 2 meters on the y-axis, and 5 meters on the z-axis.

• The point in [x, y, z] coordinates is expressed as [3, 2, 5].

Coordinate Representation

• Types of coordinate representation include Modelling Coordinates, World Coordinates, Viewing Coordinates, and Device Coordinates.

Modelling Coordinates

• When an object is created in a modelling program, the modeller chooses a point as the origin for that object and the orientation of the object to a set of model axes.
• When modelling a desk, the modeller might choose a point in the center of the desk top for the origin, or the point in the center of the desk at floor level, or the bottom of one of the legs of the desk.
• When this object is moved to a point in the world coordinate system, the origin of the object moves to the new world coordinates, and all other points in the model are moved by an equal amount.
• The origin of the object model is usually somewhere on the model, but it does not have to be.
• The origin of a doughnut or a tire might be in the vacant space in the middle.

World Coordinates

• The world coordinate system is also known as the "universe" or sometimes "model" coordinate system.
• It is the base reference system for the overall model, generally in 3D, to which all other model coordinates relate.

Viewing Coordinates

• The viewing coordinate is also known as the "camera" coordinate system.
• This coordinate system is based upon the viewpoint of the observer and changes as they change their view.
• Moving an object "forward" in this coordinate system moves it along the direction that the viewer happens to be looking at the time.

Device Coordinates

• This 2D coordinate system refers to the physical coordinates of the pixels on the computer screen, based on the current screen resolution, e.g., 1024x768.

Homogeneous Coordinates

• These coordinates make it possible to represent affine transformations (such as rotation, scaling, shear, and translation) and projective transformations as 4x4 matrices.