CS 551 / 645: Introductory Computer Graphics Color Continued Clipping in 3D David Luebke 5/4/2018

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 http://www.cs.virginia.edu/glunch This week: Antialiasing on LCD screens Graphical interface stuff in Windows2000 David Luebke 5/4/2018

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 5/4/2018

Recap: Physiology of Vision The retina Rods Cones David Luebke 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

CIE Chromaticity Diagram (1931) David Luebke 5/4/2018

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 5/4/2018

Device Color Gamuts The RGB color cube sits within CIE color space something like this: David Luebke 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

Next Topic: 3-D Clipping David Luebke 5/4/2018

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 5/4/2018

Perspective Projection Recall the matrix: Or, in 3-D coordinates: David Luebke 5/4/2018

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 5/4/2018

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 5/4/2018

Recap: Perspective Projection The typical view volume is a frustum or truncated pyramid In viewing coordinates: x or y z David Luebke 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018

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 5/4/2018