1. Rendering Pipeline Aaron Bloomfield CS 445: Introduction to Graphics
Fall 2006
(Slide set originally by Greg Humphreys)

2. 3D Polygon Rendering
Many applications use rendering of 3D polygons with direct illumination

3. 3D Polygon Rendering
Many applications use rendering of 3D polygons with direct illumination
Quake II
(Id Software)

4. 3D Polygon Rendering
Many applications use rendering of 3D polygons with direct illumination

5. 3D Rendering Pipeline This is a pipelined sequence of operations
3D Geometric Primitives
Modeling
Transformation
Lighting
This is a pipelined
sequence of operations
to draw a 3D primitive
into a 2D image
(this pipeline applies only for direct illumination)
Viewing
Transformation
Projection
Transformation
Clipping
Scan
Conversion
Image

6. of 3D rendering pipeline
Example: OpenGL
Modeling
Transformation
glBegin(GL_POLYGON);
glVertex3f(0.0, 0.0, 0.0);
glVertex3f(1.0, 0.0, 0.0);
glVertex3f(1.0, 1.0, 1.0);
glVertex3f(0.0, 1.0, 1.0);
glEnd();
Viewing
Transformation
Lighting &
Texturing
Projection
Transformation
OpenGL executes steps
of 3D rendering pipeline
for each polygon
Clipping
Scan
Conversion
Image

7. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Viewing
Transformation
Lighting &
Texturing
Projection
Transformation
Clipping
Scan
Conversion
Image

8. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system
Done with modeling transformation
Viewing
Transformation
Lighting &
Texturing
Projection
Transformation
Clipping
Scan
Conversion
Image

9. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system
Done with modeling transformation
Viewing
Transformation
Illuminate according to lighting and reflectance
Apply texture maps
Lighting &
Texturing
Projection
Transformation
Clipping
Scan
Conversion
Image

10. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system
Done with modeling transformation
Viewing
Transformation
Illuminate according to lighting and reflectance
Apply texture maps
Lighting &
Texturing
Projection
Transformation
Transform into 2D screen coordinate system
Clipping
Scan
Conversion
Image

11. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system
Done with modeling transformation
Viewing
Transformation
Illuminate according to lighting and reflectance
Apply texture maps
Lighting &
Texturing
Projection
Transformation
Transform into 2D screen coordinate system
Clipping
Clip primitives outside camera’s view
Scan
Conversion
Image

12. 3D Geometric Primitives
3D Rendering Pipeline
3D Geometric Primitives
Modeling
Transformation
Transform into 3D world coordinate system
Transform into 3D camera coordinate system
Done with modeling transformation
Viewing
Transformation
Illuminate according to lighting and reflectance
Apply texture maps
Lighting &
Texturing
Projection
Transformation
Transform into 2D screen coordinate system
Clipping
Clip primitives outside camera’s view
Scan
Conversion
Draw pixels (includes texturing, hidden surface, ...)
Image

13. Camera Coordinates Canonical coordinate system
Convention is right-handed (looking down -z axis)
Convenient for projection, clipping, etc.
Camera up vector
maps to Y axis y
Camera right vector
maps to X axis
Camera back vector
maps to Z axis
(pointing out of screen) z x

14. Viewing Transformation
Mapping from world to camera coordinates
Eye position maps to origin
Right vector maps to X axis
Up vector maps to Y axis
Back vector maps to Z axis
back up
right x y z
World
View
plane
Camera

15. Viewing Transformations
p(x,y,z)
3D Object Coordinates
Modeling
Transformation
3D World Coordinates
Viewing
Transformation
Viewing Transformations
3D Camera Coordinates
Projection
Transformation
2D Screen Coordinates
Window-to-Viewport
Transformation
2D Image Coordinates
p’(x’,y’)

16. Projection General definition: In computer graphics:
Transform points in n-space to m-space (m<n)
In computer graphics:
Map 3D camera coordinates to 2D screen coordinates
For perspective transformations, no two “rays” are parallel to each other

17. Taxonomy of Projections
FVFHP Figure 6.10

18. Parallel Projection Center of projection is at infinity
Direction of projection (DOP) same for all points
DOP
View
Plane
Angel Figure 5.4

19. Orthographic Projections
DOP perpendicular to view plane
Front
Top
Side
Angel Figure 5.5

20. Oblique Projections DOP not perpendicular to view plane Cavalier
(DOP  = 45o)
Cabinet
(DOP  = 63.4o)
H&B Figure 12.24

21. Parallel Projection View Volume
H&B Figure 12.30

22. Parallel Projection Matrix
General parallel projection transformation:

23. Taxonomy of Projections
FVFHP Figure 6.10

24. Perspective Projection
Map points onto “view plane” along “projectors” emanating from “center of projection” (COP)
Projectors
Center of
Projection
View
Plane
Angel Figure 5.9

25. Perspective Projection
How many vanishing points?
The difference is how many of the three principle directions are parallel/orthogonal to the projection plane
3-Point
Perspective
2-Point
1-Point
Angel Figure 5.10

26. Perspective Projection View Volume
Plane
H&B Figure 12.30

27. Camera to Screen Remember: Object  Camera  Screen
Just like raytracer
“screen” is the z=d plane for some constant d
Origin of screen coordinates is (0,0,d)
Its x and y axes are parallel to the x and y axes of the eye coordinate system
All these coordinates are in camera space now

28. Overhead View of Our Screen
Yeah, similar triangles!

29. The Perspective Matrix
This “division by z” can be accomplished by a 4x4 matrix too!
What happens to the point (x,y,z,1)?
What point is this in non-homogeneous coordinates?

30. Taxonomy of Projections
FVFHP Figure 6.10

31. Perspective vs. Parallel
Perspective projection
Size varies inversely with distance - looks realistic
Distance and angles are not (in general) preserved
Parallel lines do not (in general) remain parallel
Parallel projection
Good for exact measurements
Parallel lines remain parallel
Angles are not (in general) preserved
Less realistic looking

32. Classical Projections
Angel Figure 5.3

33. Viewing in OpenGL
OpenGL has multiple matrix stacks – trans-formation functions right-multiply the top of the stack
Two most important stacks: GL_MODELVIEW and GL_PROJECTION
Points get multiplied by the modelview matrix first, and then the projection matrix
GL_MODELVIEW: Object->Camera
GL_PROJECTION: Camera->Screen
glViewport(0,0,w,h): Screen->Device

34. Summary Camera transformation Projection transformation
Map 3D world coordinates to 3D camera coordinates
Matrix has camera vectors as columns
Projection transformation
Map 3D camera coordinates to 2D screen coordinates
Two types of projections:
Parallel
Perspective