1. Computer Graphics Imaging
Ying Zhu
Lecture 04
Transformation, View, and Projection

2. Before we start Short animation films to inspire your idea
Go to GSU E-journal locator
Type in “computer graphics” and search
Select “Computer graphics proceedings, annual conference series”
Click on “Association for Computing Machinery”
If off-campus, use the ID on your Panther card to log in
Click on “SVR: SIGGRAPH Video Review”
Selected short animation films from SIGGRAPH conference

3. Project Teams Send me an email with a link to your team web site
All I need is a web site with a list of team members

4. Today’s lecture Transformations View 3D projection
Translate, rotate, and scale
View
The camera
3D projection
Orthographic projection
Perspective projection

5. Coordinate systems
Each point and vector is defined in reference to a coordinate system
Once we fix the origin of the coordinate system, we can represent all points unambiguously
A 3D coordinate system is defined by its three base vectors (x, y, and z axis)

6. Geometric transformation
In 3D graphics, animation is achieved by transforming geometric objects in the virtual world
Transforming geometric objects means transforming points (vertices) and vectors
Transformation of points and vectors can be conveniently achieved by matrix multiplications
Introduced by Larry Roberts in 1966

7. Transformations in computer graphics
There are three basic transformations in computer graphics
Translation
Rotation
Scaling
Sophisticated 3D animations can be achieved by concatenating a series of basic transformations

8. Translation
Translation P’ P d x y

9. Scaling
Scaling

10. Rotation Rotation about the origin
Counter-clock wise rotation by 90 degree.

11. 2D Transformation Summary
Translation
Scaling
Rotation

12. 3D Affine Transformations
3D affine transformations are an extension of the 2D transformations.
Use 4x4 matrices instead of 3x3 matrices in 2D transformations.
For example
3D scaling

13. 3D Translation 3D translation matrix
OpenGL function: glTranslatef(tx, ty, tz)

14. 3D Scaling
3D scaling matrix
OpenGL Function: glScalef(Sx, Sy, Sz)

15. 3D Rotation About the Origin
3D rotation is more complicated than 2D rotation.
Rotation about X axis
Rotation about Y axis
Rotation about Z axis

16. Transformations in Blender
See Blender User’s Manual
Interaction in 3D

17. 3D Scenes and Camera
In computer graphics, we often use terms that are analog to theatre or photography
A virtual world is a “scene”
Objects in the scene are “actors”
There is a “camera” to specify viewing position and viewing parameters.
Viewing and projection is about how to position the camera and project the 3D scene to a 2D image

18. Viewing There should be at least one camera in the scene
You can switch cameras in the animation sequence
Camera can be animated too
The 3D scene is rendered through the viewpoint of the camera
It’s important to make sure your objects are visible through the camera, not just your eyes
Note the difference between a camera in CG and a real camera

19. Camera in computer graphics
Computer graphics uses the pinhole camera model
This results in perfectly sharp images
Real cameras use lenses with variable aperture sizes
This causes depth-of-field: out-of-focus objects appear blurry

20. Projection For each camera, there is a view volume for projection
Everything inside the view volume will be projected to the 2D plane
Everything outside the view volume will be “clipped” and ignored
Two basic projections
Orthographic projection
Perspective projection

21. Orthographic Projection
Projection lines are orthogonal to projection surface

22. Orthographic Projection
Projection plane parallel to principal face
Usually form front, top, side views
isometric (not multiview
orthographic view)
front
in CAD and architecture,
we often display three
multiviews plus isometric
side
top

23. Orthographic Projection
Preserves both distances and angles
Shapes preserved
Can be used for measurements
Building plans
Manuals
Cannot see what object really looks like because many surfaces hidden from view
Often we add the isometric view

24. Perspective Projection
Projectors converge at center of projection
Perspective projection reflects real world experience

25. Perspective Projection
The view frustum of perspective projection

26. Camera parameters in Blender
The default projection in Blender is perspective projection, you can switch to orthographic view
You can modify the following parameters in Blender
Field of view
Near plane
Far plane

27. Camera parameters in Blender
In 3D view, select camera, press F9
Demonstration

28. Summary Three basic transformations
Translation
Rotation
Scaling
Camera in CG is different from camera in the real world
Two basic projections
Orthographic projection
Perspective projection

29. Readings See Blender User’s Manual
Interaction in 3D ( ion_in_3D)