## Coordinate Frames §

Let be the original basis and be the new basis

Then:

• is , how to transform the coordinate
• is how much of we need to make one
• is how much of we need to make one
• is , how to transform the coordinate
• is how much of we need to make one
• is how much of we need to make one
• is , the translation of the entire frame
• is how much of we need to get from to
• is how much of we need to get from to

The translation from to can be represented as

## Transformation Matrices §

• Translate(x,y,z)
• Rotate(z,theta)
• Scale(x,y,z)

### Transformations §

1. Object Coordinate System: modeling transformation
2. World Coordinate System: viewing transformation
3. Viewing Coordinate System (Camera): projection transformation
4. Clipping Coordinate System: /h
5. Normalized Device Coordinate System (NDCS): viewport transformation
6. Device Coordinate System

In a scene hierarchy, the Camera Coordinate Frame () is generally the root.

Transformations in scene graphs are written right to left, starting with source frame and ending with target frame.

## Viewing Transformation §

• Defined using
• eye point
• target point
• up vector