1. CS 551 / 645: Introductory Computer Graphics
Color Continued
Clipping in 3D
David Luebke /4/2018

2. Administrivia Hand back assignment 1 (finally…) Hand out assignment 3
Graphics Lunch (Glunch)…Fridays at noon, typically in Olsson 236D (this week in 228E)
Announcements on uva.cs.graphics or at
This week:
Antialiasing on LCD screens
Graphical interface stuff in Windows2000
David Luebke /4/2018

3. Recap: Basics of Color Physics: Perception Illumination Reflection
Electromagnetic spectra
Reflection
Material properties (i.e., conductance)
Surface geometry and microgeometry (i.e., polished versus matte versus brushed)
Perception
Physiology and neurophysiology
Perceptual psychology
David Luebke /4/2018

4. Recap: Physiology of Vision
The retina
Rods
Cones
David Luebke /4/2018

5. Recap: Cones Three types of cones:
L or R, most sensitive to red light (610 nm)
M or G, most sensitive to blue light (560 nm)
S or B, most sensitive to blue light (430 nm)
Color blindness results from missing cone type(s)
David Luebke /4/2018

6. Recap: Metamers
A given perceptual sensation of color derives from the stimulus of all three cone types
Identical perceptions of color can thus be caused by very different spectra
David Luebke /4/2018

7. Recap: Perceptual Gotchas
Color perception is also difficult because:
It varies from person to person (thus std observers)
It is affected by adaptation (transparency demo)
It is affected by surrounding color:
David Luebke /4/2018

8. Color Spaces
Three types of cones suggests color is a 3D quantity. How to define 3D color space?
Idea: shine given wavelength () on a screen, and mix three other wavelengths (R,G,B) on same screen. Have user adjust intensity of RGB until colors are identical:
How closely does this correspond to a color CRT?
Problem: sometimes need to “subtract” R to match 
David Luebke /4/2018

9. CIE Color Space
The CIE (Commission Internationale d’Eclairage) came up with three hypothetical lights X, Y, and Z with these spectra:
Idea: any wavelength  can be matched perceptually by positive combinations of X,Y,Z
Note that:
X ~ R + B
Y ~ G + everything
Z ~ B
David Luebke /4/2018

10. CIE Color Space
The gamut of all colors perceivable is thus a three-dimensional shape in X,Y,Z:
For simplicity, we often project to the 2D plane X+Y+Z=1
X = X / (X+Y+Z)
Y = Y / (X+Y+Z)
Z = 1 - X - Y
David Luebke /4/2018

11. CIE Chromaticity Diagram (1931)
David Luebke /4/2018

12. Device Color Gamuts
Since X, Y, and Z are hypothetical light sources, no real device can produce the entire gamut of perceivable color
Example: CRT monitor
David Luebke /4/2018

13. Device Color Gamuts
The RGB color cube sits within CIE color space something like this:
David Luebke /4/2018

14. Device Color Gamuts
We can use the CIE chromaticity diagram to compare the gamuts of various devices:
Note, for example, that a color printer cannot reproduce all shades available on a color monitor
David Luebke /4/2018

15. Converting Color Spaces
Simple matrix operation:
The transformation C2 = M-12 M1 C1 yields RGB on monitor 2 that is equivalent to a given RGB on monitor 1
David Luebke /4/2018

16. Converting Color Spaces
Converting between color models can also be expressed as such a matrix transform:
YIQ is the color model used for color TV in America. Y is luminance, I & Q are color
Note: Y is the same as CIE’s Y
Result: backwards compatibility with B/W TV!
David Luebke /4/2018

17. Gamma Correction We generally assume colors are linear
But most display devices are inherently nonlinear
I.e., brightness(voltage) != 2*brightness(voltage/2)
Common solution: gamma correction
Post-transformation on RGB values to map them to linear range on display device:
Can have separate  for R, G, B
David Luebke /4/2018

18. Next Topic: 3-D Clipping
David Luebke /4/2018

19. 3-D Clipping
Before actually drawing on the screen, we have to clip (Why?)
Safety: avoid writing pixels that aren’t there
Efficiency: save computation cost of rasterizing primitives outside the field of view
Can we transform to screen coordinates first, then clip in 2-D?
Correctness: shouldn’t draw objects behind viewer (what will an object with negative z coordinates do in our perspective matrix?) (draw it…)
David Luebke /4/2018

20. Perspective Projection
Recall the matrix:
Or, in 3-D coordinates:
David Luebke /4/2018

21. Clipping Under Perspective
Problem: after multiplying by a perspective matrix and performing the homogeneous divide, a point at (-8, -2, -10) looks the same as a point at (8, 2, 10).
Solution A: clip before multiplying the point by the projection matrix
I.e., clip in camera coordinates
Solution B: clip before the homogeneous divide
I.e., clip in homogeneous coordinates
David Luebke /4/2018

22. Clipping Under Perspective
We will talk first about solution A:
Clipped world coordinates
Canonical screen coordinates
Clip against view volume
Apply projection matrix and homogeneous divide
Transform into viewport for 2-D display
3-D world coordinate primitives
2-D device coordinates
David Luebke /4/2018

23. Recap: Perspective Projection
The typical view volume is a frustum or truncated pyramid
In viewing coordinates:
x or y z
David Luebke /4/2018

24. Perspective Projection
The viewing frustum consists of six planes
The Sutherland-Cohen algorithm (clipping polygons to a region one plane at a time) generalizes to 3-D
Clip polygons against six planes of view frustum
So what’s the problem?
David Luebke /4/2018

25. Perspective Projection
The viewing frustum consists of six planes
The Sutherland-Cohen algorithm (clipping polygons to a region one plane at a time) generalizes to 3-D
Clip polygons against six planes of view frustum
So what’s the problem?
The problem: clipping a line segment to an arbitrary plane is relatively expensive
Dot products and such
David Luebke /4/2018

26. Perspective Projection
In fact, for simplicity we prefer to use the canonical view frustum:
x or y 1
Back or yon plane
Front or hither plane z -1
Why is this going to be simpler? -1
David Luebke /4/2018

27. Perspective Projection
In fact, for simplicity we prefer to use the canonical view frustum:
x or y 1
Back or yon plane
Front or hither plane z -1
Why is the yon plane at z = -1, not z = 1? -1
David Luebke /4/2018

28. Clipping Under Perspective
So we have to refine our pipeline model:
Note that this model forces us to separate projection from modeling & viewing transforms
Apply normalizing transformation
Clip against canonical view volume
projection matrix; homogeneous divide
Transform into viewport for 2-D display
3-D world coordinate primitives
2-D device coordinates
David Luebke /4/2018

29. Clipping Homogeneous Coords
Another option is to clip the homogeneous coordinates directly.
This allows us to clip after perspective projection:
What are the advantages?
Clip against
view
volume
Apply projection matrix
Transform into viewport for 2-D display
3-D world coordinate primitives
2-D device coordinates
Homogeneous divide
David Luebke /4/2018

30. Clipping Homogeneous Coords
Other advantages:
Can transform the canonical view volume for perspective projections to the canonical view volume for parallel projections
Clip in the latter (only works in homogeneous coords)
Allows an optimized (hardware) implementation
Some primitives will have w  1
For example, polygons that result from tesselating splines
Without clipping in homogeneous coords, must perform divide twice on such primitives
David Luebke /4/2018

31. Clipping: The Real World
In the Real World, a common shortcut is:
Clip against hither and yon planes
Projection matrix; homogeneous divide
Transform into screen coordinates
Clip in 2-D screen coordinates
David Luebke /4/2018