Viewing Transformations
1. Introduction
In computer graphics, objects are defined in a world coordinate system. Viewing transformations determine which part of the scene is visible and how it appears on the display.
- Defines camera position and orientation
- Controls what is visible on screen
2. Viewing Pipeline
The viewing pipeline is a sequence of steps that convert a 3D scene into a 2D image on the display device.
- World coordinates
- Viewing coordinates
- Projection
- Viewport mapping
3. World Coordinate System
The world coordinate system defines the positions of all objects in the scene before viewing transformations are applied.
- Global reference system
- Independent of viewer position
4. Viewing Coordinate System
The viewing coordinate system is defined with respect to the observer or camera. Objects are transformed from world coordinates to viewing coordinates.
- Camera-centered system
- Determines perspective
5. View Window
The view window specifies the rectangular region in the viewing coordinate system that is selected for display.
- Selects visible portion of the scene
- Defined in world or view coordinates
6. Viewport
A viewport is the rectangular area on the display device where the contents of the view window are mapped.
- Defined in screen coordinates
- Controls image size and position
7. Window-to-Viewport Transformation
This transformation maps points from the view window to corresponding positions in the viewport.
xv = xvmin + (xw − xwmin) × (xvmax − xvmin) / (xwmax − xwmin) yv = yvmin + (yw − ywmin) × (yvmax − yvmin) / (ywmax − ywmin)
8. Importance of Viewing Transformations
- Controls camera position and orientation
- Determines visible scene area
- Essential for realistic rendering
9. Applications
- 3D graphics rendering
- Game engines
- Simulation and CAD systems
Practice Questions
- What is viewing transformation?
- Explain the viewing pipeline.
- Differentiate view window and viewport.
- Why is window-to-viewport transformation needed?
- Where are viewing transformations used?