cs 431/636 advanced rendering techniquesdavid/classes/cs431/lectures/cgii_pres3.pdfcs 431/636...

CS 431/636 Advanced Rendering Techniques"

Dr. David Breen"Korman 105D"Wednesday 6PM → 8:50PM"

Presentation 3"4/18/12"

Slide Credits

n Jonathan Cohen - Johns Hopkins

n Yizhou Yu - University of Illinois

n Kevin Suffern -University of Technology,

Sydney, Australia

n G. Drew Kessler, Larry Hodges - Georgia

Institute of Technology

Color Models

Johns Hopkins Department of Computer ScienceCourse 600.456: Rendering Techniques, Professor: Jonathan Cohen

Frequency SpectrumFrequency SpectrumFrequency Spectrum

Spectrum describes frequency distribution of Spectrum describes frequency distribution of a light sourcea light source

Wavelength (nm)Wavelength (nm)

Am

plitu

deA

mpl

itude

400400 450450 500500 550550 600600 650650 700700

redredyelyel..greengreenblueblue


DefinitionsDefinitionsDefinitions

Hue: quality that distinguishes one color Hue: quality that distinguishes one color family from another (i.e. red, yellow, green, family from another (i.e. red, yellow, green, blue, etc.)blue, etc.)

ChromaChroma: degree of color’s departure from : degree of color’s departure from greyscalegreyscale

Value/Lightness: quality distinguishing light Value/Lightness: quality distinguishing light from dark colorsfrom dark colors


More definitionsMore definitionsMore definitions

Achromatic light: literally light without Achromatic light: literally light without chromachroma, or , or greyscale greyscale lightlight•• fairly uniform frequency distributionfairly uniform frequency distribution

Monochromatic light: light which has all Monochromatic light: light which has all intensity near a single frequencyintensity near a single frequency


Color Mixture - SubtractiveColor Mixture Color Mixture -- SubtractiveSubtractive

Applies when mixing pigments and dyesApplies when mixing pigments and dyes•• Each substance absorbs certain frequenciesEach substance absorbs certain frequencies

•• Combining substances absorbs the union of Combining substances absorbs the union of these frequenciesthese frequencies

•• Resulting reflected light is intersection of colors Resulting reflected light is intersection of colors reflected by eachreflected by each


Subtractive Mixture ExampleSubtractive Mixture ExampleSubtractive Mixture Example

from Gerald from Gerald MurchMurch, “Color Displays and Color Science”, in , “Color Displays and Color Science”, in Color and the Color and the ComputerComputer, H. John , H. John DurrettDurrett, ed., page 10., ed., page 10.

41

•  Primary colors: –  cyan, magenta, yellow

•  Secondary colors: –  blue = cyan ∧ magenta

–  red = magenta ∧ yellow

–  green = yellow ∧ cyan •  All colors:

–  black = cyan ∧ magenta ∧ yellow (in theory).

–  Black (K) ink is used in addition to C,M,Y to produce solid black.

–  white = no color of ink (on white paper, of course). http://prometheus.cecs.csulb.edu/~jewett/colors/

CMY(K) is a Subtractive Color Model


Color Mixture - AdditiveColor Mixture Color Mixture -- AdditiveAdditive

Applies to mixing of luminescent colors, such Applies to mixing of luminescent colors, such as color CRT and LCD displays, etc.as color CRT and LCD displays, etc.•• Color refers to actual frequency spectrum of Color refers to actual frequency spectrum of

lightlight

•• Combining lights adds their frequency spectraCombining lights adds their frequency spectra


Additive Color ExampleAdditive Color ExampleAdditive Color Example

38

RGB is an Additive Color Model

•  Primary colors: –  red, green, blue

•  Secondary colors: –  yellow = red + green, –  cyan = green + blue, –  magenta = blue + red.

•  All colors: –  white = red + green +

blue (#FFFFFF) –  black = no light

(#000000).

http://prometheus.cecs.csulb.edu/~jewett/colors/


3 Types of retinal cones3 Types of retinal cones3 Types of retinal cones

From Foley, From Foley, vanDamvanDam, , FeinerFeiner, , and Hughes, and Hughes, Computer Computer Graphics: Principles and Graphics: Principles and Practice, 2nd edition, page Practice, 2nd edition, page 577577


Efficient Color Computations in Computer GraphicsEfficient Color Computations in Efficient Color Computations in Computer GraphicsComputer Graphics

Represent frequency spectrum as discrete set Represent frequency spectrum as discrete set of samplesof samples•• Typically 3 samples: red, green, and blueTypically 3 samples: red, green, and blue

•• Monitors also use samples corresponding to Monitors also use samples corresponding to different phosphorsdifferent phosphors

•• Eye also has 3 samples (types of cones)Eye also has 3 samples (types of cones)

Does Does notnot imply that three samples for initial imply that three samples for initial and intermediate produce accurate and intermediate produce accurate computationscomputations


Color Space GamutColor Space GamutColor Space GamutColor gamut: subspace of visible colorsColor gamut: subspace of visible colorsNo system of mixing colors from fixed No system of mixing colors from fixed

number of primaries can represent all number of primaries can represent all visible colorsvisible colors

from Gerald Murch, “Color Displays and Color Science”, in Color and the Computer, H. John Durrett, ed., page 13.


Color Spaces - RGB cubeColor Spaces Color Spaces -- RGB cubeRGB cube

Shortcomings:Shortcomings:•• perceptually nonperceptually non--linearlinear•• nonnon--intuitive for human specificationintuitive for human specification

From Alan Watt, 3D Computer Graphics, 2nd edition, p. 416

from Foley, vanDam, Feiner, and Hughes, Computer Graphics: Principles and Practice, plate II.4


Color Spaces - HSV hexaconeColor Spaces Color Spaces -- HSV HSV hexaconehexaconeStill not perceptually Still not perceptually

linearlinearAxes correspond to Axes correspond to

more intuitive more intuitive perceptual qualitiesperceptual qualities•• Selection similar to Selection similar to

artist color mixingartist color mixing•• choose hue of base choose hue of base

pigment, add white, pigment, add white, add blackadd black

Derived from Derived from projections of RGB projections of RGB cubecube

From Alan Watt, 3D Computer Graphics, 2nd edition, p. 419


CIE Color SpaceCIE Color SpaceCIE Color Space

Employs 3 artificial primaries: X, Y, ZEmploys 3 artificial primaries: X, Y, Z•• Mathematical abstractions, not physically Mathematical abstractions, not physically

realizablerealizable

•• Allow Allow supersaturationsupersaturation

Larger than visible spectrumLarger than visible spectrum

Standard for representing colors and Standard for representing colors and converting between spacesconverting between spaces


CIE Space and Device GamutsCIE Space and Device CIE Space and Device GamutsGamuts

from Foley, vanDam, Feiner, and Hughes, Computer Graphics: Principles and Practice, plates II.1 and II.2

Chromaticity DiagramChromaticity Diagram


Gamma CorrectionGamma CorrectionGamma Correction

Exponential function converts from deviceExponential function converts from device--independent RGB space to deviceindependent RGB space to device--dependent RGBdependent RGB•• Gamma is exponentGamma is exponent•• Every monitor is differentEvery monitor is different•• Monitor color intensities are nonMonitor color intensities are non--linear with linear with

respect to phosphor excitation levelsrespect to phosphor excitation levels

Light Models

david

david

Spot Light

Dl

Pl

Ps

φ

θ

n Specified by

n Position, Direction

n Cone angle, sharpness

n L = Pl - P

s

n if φ > θn I

L= 0

n else

n IL= cosn((π/2)(φ/θ))

Shading Models

Computer Graphics Rendering Techniques: Reflection Models © KG Suffern 1991-20001 5

Consider the process of looking at (or photographing) a scene through awindow.

At every point on the window the light from the scene has a certainintensity I(x, y).

Intensity is a measure of the brightness of the light.

Generally there will be a mixture of light of different wavelengths ateach point on the window: I = I(x, y, !) where ! is the wavelength.

We don't discuss the wavelength dependency in these notes.


Types of illumination

Direct illumination

Light striking the objects comes directly from the light sources


Indirect illumination

Light striking the objects has been reflected off at least one other objectsince leaving the light source.

The light could also have been refracted through transparent objects.


Reflection Models

There exists a number of reflection models that model the real world tovarying degrees of realism.

In general, the more realistic a model is, the more physics andcomputation is involved.

Most reflection models incorporate direct illumination.

The indirect illumination is very expensive to calculate.

Only the most advanced rendering techniques incorporate indirectillumination.

Examples are ray tracing and radiosity.


Some more terminology

Direct illumination is referred to as local illumination.

Indirect illumination is referred to as global illumination.


Interaction of light and objects.

We must also model the way that light interacts with the surfaces ofobjects.

When light hits the surface of an object, it can be:

• Reflected

• Absorbed

• Transmitted (for transparent objects)

We see opaque objects by the light they reflect.


The way in which light interacts with real objects is very complicated.

The interaction depends on:

• the material properties of the object

• the wavelength of the incident light

• the angle of incidence of the light and the surface

The polarisation of the light is also involved, but rarely modelled incomputer graphics.


Diffuse reflection

The incident light is scattered equally in all directions

incident light

surface

This is characteristic of dull, matt surfaces such as paper, bricks, carpet,etc.


Specular reflection

The reflected light is concentrated around the direction of mirrorreflection, and is spread out.

incident light

surface

mirror reflectiondirection

This can be used to model shiny surfaces.

Calculating the Reflected Ray

n r = (2 ∗ (n · L) ∗ n) - Ln Derivation left for the students

n Clamp all dot products to zero. They

shouldn’t be negative, but they can be

n MAX (0, n · L)


"90

o#90

o

1.0 cos "

cos "2

cos "10

cos "25


N

RL

V

" " $diffuse

diffuse + specular

n = 10

n = 25

Diffuse + specular reflection

Originally from Larry F. Hodges, G. Drew Kessler 7

Light-source AttenuationThus far we have ignored the inverse square law: energy decays with the

inverse square of the distance dL to the light source. Including this termwe get

I = Iaka + Ipkd (L•N)/dL2

However, due to our previous assumptions of a point light source anduniform ambient light, using the dL

2 term gives too rapid of a decreasein illumination intensity to look realistic. The 1/dL

2 term is usuallyreplaced by fatt where

fatt = MIN (1/(c1dL), 1)

I = Iaka + Ipkd (N•L)*fatt

Including Surface Color

I =

for all lights {

IL kd C cos( ) + IL ks C cosn( ) }+ Ia ka C

C - RGB surface color

Could dene Cd, Cs and Ca, but youdon t have to

Cook and Torrance Illumination!

Distribution Functions

Cook and Torrance Illumination!

Results

Larry F. Hodges, G. Drew Kessler 11

Too Intense

With multiple light sources, it is easy to generated values of I > 1

One solution is to set the color value to be MIN(I, 1)

• An object can change color, saturating towards whiteEx. (0.1, 0.4, 0.8) + (0.5, 0.5, 0.5) = (0.6, 0.9, 1.0)

Another solution is to renormalize the intensities to vary from 0 to 1if one I > 1.

• Requires calculating all I’s before rendering anything.

• No over-saturation, but image may be too bright, and contrasts alittle off.

Image-processing on image to be rendered (with original I’s) willproduce better results, but is costly.

Calculating Normals

v -1 -1 -1v 1 -1 -1v -1 1 -1v 1 1 -1v -1 -1 1v 1 -1 1v -1 1 1v 1 1 1f 1 3 4f 1 4 2f 5 6 8f 5 8 7f 1 2 6f 1 6 5f 3 7 8f 3 8 4f 1 5 7f 1 7 3f 2 4 8f 2 8 6

vertices

triangles

n Create vector structure

(for normals) same size as

vertex structure

n For each face

n Calculate unit normal

n Add to normal structure

using vertex indicesn Normalize all the normals

n N(α,β,γ)= αNa+ βN

b+ γN

c

Normal for Triangle

plane n · (p - p0 ) = 0

n = (p1 - p0 ) × (p2 - p0 )

normalize n ← n / |n|

p0

p1

p2

n

p

Note that right-hand rule determines outward face

Shading Pixels Overview

for (i=0; i++; i < hres)

for (j=0; j++; j < vres) {

Calculate Ray

for (k=0; k++; k < NumObject) {

Attempt to intersect Ray with Objectk for all intersections

Save t, ObjectID & xsect pt/param

}

Perform shading calculation on closest point

(intersection with the lowest non-negative t)

Set pixel value at Image[i,j]

}

Supersample & Average Image

n hres

and vres

are even

for (i=0; i++; i < hres

/2)

for (j=0; j++; j < vres

/2) {

offset = 2 ∗ [i,j];

newImage[i,j] = (oldImage[offset] +

oldImage[offset + [0,1]] +

oldImage[offset + [1,0]] +

oldImage[offset + [1,1]])/4;

}

Wrap Up

n Discuss next week’s programming

assignment

n Add point lights with color

n Add color, shading parameters and

normals to models

n Phong shading

n Supersample image

n Discuss status/problems/issues with

this week’s programming assignment

cs 431/636 advanced rendering techniquesdavid/classes/cs431/lectures/cgii_pres3.pdfcs 431/636...

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