Display Coordinate Systems

1
Display Coordinate Systems

• Coordinate Systems, Windows, Clipping and
  Viewports

2
Coordinate Systems

• To display an image of an object on a graphics
  device, need to
• Specify location of all points on the object in
  3D space
• Map these points to locations on 2D device
  monitor
• Various coordinate systems used to accomplish this

3
Display Coordinate Systems

• Five interrelated coordinate systems
• Model (or local) coordinate system
• World (or global) coordinate system
• Viewing coordinate system
• Projection coordinate system
• Device coordinate system

4
Coordinate System Relationships
5
World and Model Coordinate Systems

• Together used to create a mathematical
  description of an object
• Fixed world cs defines environment of interest
• Model cs attached to object

6
Viewing Coordinate System

• Simplifies conversion to 2D screen coordinates
• Must define
• Viewpoint observers position
• Viewsite point on object
• Line from viewpoint to viewsite defines view
  direction

• Viewing CS Definition
• Origin at viewsite
• Z opposite to viewing direction
• Y - project up vector (in world coordinates)
• X vector product

7
Projection Systems

• Object projected onto a view plane

Perspective projection
Parallel projection
8
Window on View Plane

• Window created on view plane
• Contents of window mapped onto view plane,
  according to projection system
• 3D contents clipped to window contents outside
  window to be discarded

9
View Volume

• 3D world projected onto view plane further
  constrained by front back clipping planes
• View volume for
• Parallel projection
• box
• Perspective projection
• truncated pyramid

10
Projection Coordinate System (normalized)

• View volume contents mapped onto 2D display
  window
• Mapping is normalized (i.e., axes extend
  from 0 to 1)
• Z coordinate not used can later be used for
  hidden line removal algorithms

11
Some Definitions

• Clipping process of determining which lines or
  portions of lines in the picture lie outside of a
  window
• Windowing process of extracting a portion of a
  data base by clipping the data base to the
  boundaries of the window
• Viewport an area of the display device on which
  the clipped window data are presented

12
Device Coordinate System

• Image in window mapped onto viewport area in
  device coordinates
• Device coordinates are integers each coordinate
  pair addresses a pixel

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Coordinate Transformations
14
Display Coordinate Systems

• Coordinate Systems, Windows, Clipping and
  Viewports