Logistics Checkpoint 1 all graded Material Properties Grades / - - PDF document

SLIDE 1

1 Material Properties

Illumination Models / BRDFs

Logistics

 Checkpoint 1 all graded

 Grades / comments on mycourses

 Project Proposals all graded

 Comments in mycourses  List of projects on course Web site

 Reminder

 Readings: undergrad - 1 / week  Grads: - 1/ class

 Checkpoint 2

 Due Monday

 Questions?

Plan for today

 BRDFs -- Reflectivity

Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

Shading

 Computing the light that leaves a point  Shading point - point under investigation  Illumination model - function or algorithm

used to describe the reflective characteristics of a given surface.

 Shading model – algorithm for using an

illumination model to determine the color of a point on a surface.

 For efficiency’s sake, most illumination models

are approximations.

Lighting vs. Shading

 Commonly misused terms.  What’s the difference?  Lighting / Illumination designates the

interaction between materials and light sources.

 Shading is the process of determining the

color of a pixel.

 Usually determined by lighting.  Could use other methods: random color, NPR, etc.

SLIDE 2

2

Reflections

 Ambient – light uniformly incident from the

environment

 Diffuse – light scattered equally in all

directions

 Ambient and Diffuse – color of material plays

a part

 Specular – highlights connected with

mirrorness

 Specular – mostly color of light

Bi-directional Reflectance Functions (BRDF)

BRDF

 Bi-directional Reflectance Function

) , , , (

r r i i r

f BRDF

• =

At a given point, gives relative reflected illumination in any direction with respect to incoming illumination coming from any direction; Note: The θ’s are elevation, ϕ’s are measured about the surface normal. The i’s refer to the incident ray; the r’s to the reflected ray.

BRDF Geometry BRDF

 Can return any positive value.  Generally wavelength specific.

) , , , , (

• r

r i i r

f BRDF =

BRDF

 Simplifying Assumptions wrt the BRDF

 Light enters and leaves from the same point.

 Not necessarily true  Subsurface scattering  Skin, marble

 Light of a given wavelength will only reflect back light

• f that same wavelength

 Not necessarily true  Light Interference  Oily patches, peacock feathers

SLIDE 3

3

Illumination Models

 Illumination model - function or

algorithm used to describe the reflective characteristics of a given surface.

 Revise to…

 function or algorithm used in

approximating the BRDF.

Illumination Modeling

 Four approaches

 Simplistic

 Based on physics, abiet with many assumptions

 Heuristic

 The kludge!  Usually simple, yet not physically based

 Simulation

 Employ physical model  More complex than heuristic, but more accurate

 Empirical

 Use measured samples

Illumination Models

 Illumination Models and Viewing

Direction

 Generally, BRDFs are independent of

viewing direction

 Most Illumination models take viewing

direction into consideration

Reflection and color

 Color “response” is based on color that

reaches the eye or sensor

 http://www.cs.brown.edu/exploratories/freeS

• ftware/repository/edu/brown/cs/exploratorie

s/applets/spectrum/reflection_guide.html

 http://www.cs.brown.edu/exploratories/freeS

• ftware/repository/edu/brown/cs/exploratorie

s/applets/spectrum/two_materials_java_brow ser.html

Reflections

 Ambient – light uniformly incident from the

environment

 Diffuse – light scattered equally in all directions  Ambient and Diffuse – color of material plays a part  Specular – highlights connected with mirrorness  Specular – mostly color of light

Illumination Models

 Geometry

N H S V R

reflection viewer normal Half-way source

SLIDE 4

4

Illumination Models

 Geometry

 N - normal vector  S - direction of incoming light  R - direction of perfect mirror reflection  H - halfway between light direction and

viewing direction.

 V - viewing direction.

Illumination Models

 Recall from Linear Algebra

θ u v

• cos

v u v u =

• Just one reason to normalize!

Illumination Modeling

 Four approaches

 Simplistic

 Lamertian

 Heuristic

 Phong

 Simulation

 Cook-Torrance

 Empirical

 Use measured samples

Illumination Models

 BRDF Viewer

 bv by Szymon Rusinkiewicz (Princeton)  http://graphics.stanford.edu/~smr/brdf/bv  SGI, Linux, and Java versions although not

readily available for Java. I have it, if you want it, and you’ll need to load Java3D as well!

Simplistic

 Lambertian Model

 Perfectly diffuse surface  reflection is constant in all directions (kd)  Independent of viewer direction  Based on Lambert’s cos law.  Sometimes mistakenly attributed to Gouraud.

 Gouraud didn’t introduce a new lighting model, just a

shading method.

Lambert’s Cosine Law

 The reflected luminous intensity in

any direction from a perfectly diffusing surface varies as the cosine of the angle between the direction of incident light and the normal vector of the surface.

 Intuitively

 cross-sectional area of

the “beam” intersecting an element

• f surface area is smaller for greater

angles with the normal.

SLIDE 5

5

Lambertian Model

 Lambert Model

• cos

) (

d Sk

L V L = ) ( ) ( S N k L V L

d S

• =

Lambertian Model

 BRDF Viewer

http://graphics.stanford.edu/~smr/brdf/ bv

Those Were the Days

 (Or: how not to motivate a 21st century

computer graphics paper.)

 “In trying to improve the quality of the

synthetic images, we do not expect to be able to display the object exactly as it would appear in reality, with texture, overcast shadows, etc. We hope only to display an image that approximates the real object closely enough to provide a certain degree of realism.” – Bui Tuong Phong, 1975

Phong Model

 Phong Model

 introduces specular (mirror-like) reflections  Viewer direction becomes more important  three components

 ambient - background light (ka)  diffuse - Lambertian reflection (kd)  specular – mirror-like reflection(ks)

Phong Model

specular diffuse ambient

V) R ( N) S ( ) (

∑ ∑

• +
• +

=

i k i i s i i i d a a

e

L k L k L k V L

Note: Ln are radiance terms, include both light and material info

Phong-Blinn Model

 Uses halfway angle rather than reflected

specular diffuse ambient

N) H ( N) S ( ) (

∑ ∑

• +
• +

=

i k i i s i i i d a a

e

L k L k L k V L

SLIDE 6

6

Phong-Blinn Model

 BRDF Viewer

http://graphics.stanford.edu/~smr/brdf/ bv Break?

Physically based

 based on physics of a surface

 Actually developed by Torrance & Sparrow, physicists.  Jim Blinn was the first to apply to CG  Cook & Torrance’s was the first complete implementation

 components

 microfacet model - describes geometry of surface  And how much the microfacets shadow each other.  Fresnel term - describes reflectance  Roughness - describes microfacet distribution.

Cook-Torrance Model

 Microfacets

 surface is composed of V shaped grooves

(microfacets)

 Light interactions with microfacets

 Reflect - causes specular reflections  Scatter - causes diffuse reflections

Cook-Torrance Model

 Microfacets

Cook-Torrance Model

 Microfacets – GeometryTerm

 Some microfacets may shadow others

     

• =

H) (V S) H)(N N ( 2 , H) (V V) H)(N N ( 2 , 1 min G

Note: S from before is the L in these diagrams

Cook-Torrance Model

 Fresnel Equation for polarized light

 Describes reflectance as a function of:

 Wavelength of incident light (λ)  Index of refraction (η(λ))  Extinction coefficient (ease at which wave can

penetrate a surface) (κ(λ))

 Angle of incidence (θ)

SLIDE 7

7

Cook-Torrance Model

 Fresnel equations for polarized light

θ θ θ θ

2 2 2 2 2 2

cos cos 2 cos cos 2 + + + + − + = a b a a b a Fs

• 2

2 2 2 2 2 2 2

tan sin tan sin 2 tan sin tan sin 2 + + + +

• +

= a b a a b a F F

s p

a, b are functions

• f η, κ, and θ

η, κ are functions

• f λ

p s

F F F 2 1 2 1 + =

F is total reflectance

Perpendicular component Parallel component

Cook-Torrance Model

 Fresnel

 If all quantities known, use Fresnel

equations

 If not, approximate using reflectance off

normal

 See [Glassner] or [Cook/Torrance81] for details

Cook-Torrance Model

 Roughness

 Characterizes the distribution of the slopes

• f the microfacets

 Roughness parameter, m

 m between 0 -1  small m - smooth surface, specular reflectance  large m - rough surface, diffuse reflectance

 Statistical models

Cook-Torrance Model

 Roughness

2

) / ( m

ce D

α −

=

α

α

4 2 ) / ) ((tan

cos

2

m e D

m −

=

Gaussian Model c is arbitrary constant Beekman Model

Cook-Torrance Model

 Roughness

Cook-Torrance Model

 Putting it all together

• 1

=

d

f

V) S)(N N ( 1

• ×

× = G D F fs π

diffuse specular d s r

df sf f + =

total reflectance

Where D is the roughness function, F is the Fresnel function, and G is the geometrical attenuation factor from previous pages

SLIDE 8

8

Cook-Torrance Model

 Complete Cook-Torrance Model

∑

• +

=

i i r i a a r

d f L R L L ϖ ) Si)( N (



Parameters for fr:

 m – roughness value  Type of material (determines terms for Fresnel eqn)  Wavelength of incident light (determines terms for Fresnel eqn)  Diffuse / specular contribution constants  La Ra is the ambient radiance reflected by Ra  Li is the light’s radiance

Cook-Torrance Models

 examples

Cook-Torrance Model

Henry Johan

Cook-Torrance Models

 BRDF Viewer

http://graphics.stanford.edu/~smr/brdf/ bv

Cook-Torrance Model

 Summary

 Complicated model based on physics  Components

 Microfacets  Fresnel equation  Roughness

 Want accuracy? Go to the source!

Illumination Models

 There are many other illumination models -

both empirical approximations and rigorous physically based solutions.

 Looking ahead

 All these models are predefined with fixed

parameters

 For extensibility in defining BDRFs, use a

procedural system (I.e. shaders)

SLIDE 9

9

Empirical

 Can use empirical data  BRDFs measured using a goniometer  See [Ward92]

Measuring BRDFs

Light Receptor

Measuring BRDFs

 Storage using spherical sampling

Measuring BRDFs

 BRDF Databases

 Cornell

 http://www.graphics.cornell.edu/online/measurements

 Columbia-Utrecht

 http://www.cs.columbia.edu/CAVE/curet

Measured BRDFs

From Matrix Reloaded

Measured BRDFs

From Matrix Reloaded

SLIDE 10

10

Measuring BRDFs

 Problems with measured BRDFs

 Large  Difficult to control measuring device  Can be noisy, due to measurement device  Non-extensible

 Specific to a given material

Summary

 BRDFs - defines reflection off surface in

each direction as result from light arriving at each direction.

 Illumination models - approximations to

BRDF

 Can use measured BRDFs

Summary

 BRDF  Approaches

 Simplistic

 Lambertian

 Hueristic

 Phong

 Physically-based

 Cook-Torrance

 Empirical

Further Reading

 Glassner, Principles of Digital Image

Synthesis, Chapter 15.

 See paper list (on Web) for papers on

individual models

 [Cook81]  [Ward92] [Kajiya85] [Poulin90][He91]  [Strauss90]

Next time

 Advanced illumination models  Subsurface scattering  Raytracer: Checkpoint 3