david luebke2/23/2016 cs 551 / 645: introductory computer graphics color continued clipping in 3d

David Luebke 05/05/23

CS 551 / 645: Introductory Computer Graphics

Color ContinuedClipping in 3D


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

http://www.cs.virginia.edu/glunch









Recap: Basics of Color

Physics: – Illumination

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


Recap: Physiology of Vision

The retina– Rods– Cones


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)


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


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:


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


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 + BY ~ G + everythingZ ~ B


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=1X = X / (X+Y+Z)Y = Y / (X+Y+Z)Z = 1 - X - Y


CIE Chromaticity Diagram (1931)


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


Device Color Gamuts

The RGB color cube sits within CIE color space something like this:


Device Color Gamuts

We can use the CIE chromaticity diagram to compare the gamuts of various devices:

Note, for example, that a color printercannot reproduceall shades availableon a color monitor


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

BGR

ZZZYYYXXX

BGR

BGR

BGR

BGR

'''


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!

BGR

QIY

31.052.021.032.028.060.0

11.059.030.0


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

1

xy


Next Topic: 3-D Clipping


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…)


Perspective Projection

Recall the matrix:

Or, in 3-D coordinates:

10100010000100001

zyx

ddzzyx

d

dzy

dzx ,,


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



We will talk first about solution A:

Clip againstview volume

Apply projectionmatrix and

homogeneousdivide

Transform intoviewport for2-D display

3-D world coordinateprimitives

Clippedworld

coordinates

2-D devicecoordinates

Canonicalscreen

coordinates


Recap: Perspective Projection

The typical view volume is a frustum or truncated pyramid– In viewing coordinates:x or y

z



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 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



In fact, for simplicity we prefer to use the canonical view frustum:

1

-1

x or y

z-1

Front or hither plane

Back or yon plane

Why is this going to besimpler?



In fact, for simplicity we prefer to use the canonical view frustum:

1

-1

x or y

z-1

Front or hither plane

Back or yon plane

Why is the yon planeat z = -1, not z = 1?



So we have to refine our pipeline model:

– Note that this model forces us to separate projection from modeling & viewing transforms

Applynormalizing

transformation

projectionmatrix;

homogeneousdivide




Clip against

canonical view

volume


Clipping Homogeneous Coords

Another option is to clip the homogeneous coordinates directly.– This allows us to clip after perspective projection:– What are the advantages?

Clipagainstview

volume

Apply projection

matrix




Homogeneousdivide


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


Clipping: The Real World

In the Real World, a common shortcut is:

Projectionmatrix;

homogeneousdivide

Clip in 2-D screen

coordinates

Clip against

hither andyon planes

Transform intoscreen

coordinates

david luebke2/23/2016 cs 551 / 645: introductory computer graphics color continued clipping in 3d

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