1. David Luebke2/23/2016 CS 551 / 645: Introductory Computer Graphics Color Continued Clipping in 3D

2. David Luebke2/23/2016 Administrivia l Hand back assignment 1 (finally…) l Hand out assignment 3 l Graphics Lunch (Glunch)…Fridays at noon, typically in Olsson 236D (this week in 228E) –Announcements on uva.cs.graphics or at http://www.cs.virginia.edu/glunch http://www.cs.virginia.edu/glunch –This week: n Antialiasing on LCD screens n Graphical interface stuff in Windows2000

3. David Luebke2/23/2016 Recap: Basics of Color l Physics: –Illumination n Electromagnetic spectra –Reflection n Material properties (i.e., conductance) n Surface geometry and microgeometry (i.e., polished versus matte versus brushed) l Perception –Physiology and neurophysiology –Perceptual psychology

4. David Luebke2/23/2016 Recap: Physiology of Vision l The retina –Rods –Cones

5. David Luebke2/23/2016 Recap: Cones l 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)

6. David Luebke2/23/2016 Recap: Metamers l A given perceptual sensation of color derives from the stimulus of all three cone types l Identical perceptions of color can thus be caused by very different spectra

7. David Luebke2/23/2016 Recap: Perceptual Gotchas l 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:

8. David Luebke2/23/2016 Color Spaces l Three types of cones suggests color is a 3D quantity. How to define 3D color space? l 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: l How closely does this correspond to a color CRT? l Problem: sometimes need to “subtract” R to match

9. David Luebke2/23/2016 CIE Color Space l The CIE (Commission Internationale d’Eclairage) came up with three hypothetical lights X, Y, and Z with these spectra: l Idea: any wavelength can be matched perceptually by positive combinations of X,Y,Z l Note that: X ~ R + B Y ~ G + everything Z ~ B

10. David Luebke2/23/2016 CIE Color Space l The gamut of all colors perceivable is thus a three-dimensional shape in X,Y,Z: l 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

11. David Luebke2/23/2016 CIE Chromaticity Diagram (1931)

12. David Luebke2/23/2016 Device Color Gamuts l Since X, Y, and Z are hypothetical light sources, no real device can produce the entire gamut of perceivable color l Example: CRT monitor

13. David Luebke2/23/2016 Device Color Gamuts l The RGB color cube sits within CIE color space something like this:

14. David Luebke2/23/2016 Device Color Gamuts l We can use the CIE chromaticity diagram to compare the gamuts of various devices: l Note, for example, that a color printer cannot reproduce all shades available on a color monitor

15. David Luebke2/23/2016 Converting Color Spaces l Simple matrix operation: The transformation C 2 = M -1 2 M 1 C 1 yields RGB on monitor 2 that is equivalent to a given RGB on monitor 1

16. David Luebke2/23/2016 Converting Color Spaces l Converting between color models can also be expressed as such a matrix transform: l 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!

17. David Luebke2/23/2016 Gamma Correction l We generally assume colors are linear l But most display devices are inherently nonlinear –I.e., brightness(voltage) != 2*brightness(voltage/2) l 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

18. David Luebke2/23/2016 Next Topic: 3-D Clipping

19. David Luebke2/23/2016 3-D Clipping l 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 l 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…)

20. David Luebke2/23/2016 Perspective Projection l Recall the matrix: l Or, in 3-D coordinates:

21. David Luebke2/23/2016 Clipping Under Perspective l 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). l Solution A: clip before multiplying the point by the projection matrix –I.e., clip in camera coordinates l Solution B: clip before the homogeneous divide –I.e., clip in homogeneous coordinates

22. David Luebke2/23/2016 Clipping Under Perspective l We will talk first about solution A: Clip against view volume Apply projection matrix and homogeneous divide Transform into viewport for 2-D display 3-D world coordinate primitives Clipped world coordinates 2-D device coordinates Canonical screen coordinates

23. David Luebke2/23/2016 Recap: Perspective Projection l The typical view volume is a frustum or truncated pyramid –In viewing coordinates: x or y z

24. David Luebke2/23/2016 Perspective Projection l The viewing frustum consists of six planes l 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?

25. David Luebke2/23/2016 Perspective Projection l The viewing frustum consists of six planes l 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? l The problem: clipping a line segment to an arbitrary plane is relatively expensive –Dot products and such

26. David Luebke2/23/2016 Perspective Projection l In fact, for simplicity we prefer to use the canonical view frustum: 1 x or y z Front or hither plane Back or yon plane Why is this going to be simpler?

27. David Luebke2/23/2016 Perspective Projection l In fact, for simplicity we prefer to use the canonical view frustum: 1 x or y z Front or hither plane Back or yon plane Why is the yon plane at z = -1, not z = 1?

28. David Luebke2/23/2016 Clipping Under Perspective l So we have to refine our pipeline model: –Note that this model forces us to separate projection from modeling & viewing transforms Apply normalizing transformation projection matrix; homogeneous divide Transform into viewport for 2-D display 3-D world coordinate primitives 2-D device coordinates Clip against canonical view volume

29. David Luebke2/23/2016 Clipping Homogeneous Coords l 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

30. David Luebke2/23/2016 Clipping Homogeneous Coords l Other advantages: –Can transform the canonical view volume for perspective projections to the canonical view volume for parallel projections n Clip in the latter (only works in homogeneous coords) n Allows an optimized (hardware) implementation –Some primitives will have w  1 n For example, polygons that result from tesselating splines n Without clipping in homogeneous coords, must perform divide twice on such primitives

31. David Luebke2/23/2016 Clipping: The Real World l In the Real World, a common shortcut is: Projection matrix; homogeneous divide Clip in 2-D screen coordinates Clip against hither and yon planes Transform into screen coordinates