Lighting vs. Shading Shading Commonly misused terms. Computing - - PDF document

1 Material Properties

Illumination Models / BRDFs

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.

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)

2

BRDF

• Bi-directional Reflectance Function

) , , , (

r r i i r

f BRDF θ φ θ φ =

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.

) , , , , ( λ θ φ θ φ

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 of that same wavelength

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

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

3

Illumination Models

• Illumination Models and Viewing Direction

– Generally, BRDFs are independent of viewing direction – Most Illumination models take viewing direction into consideration

Illumination Models

• Geometry

N H S V R

reflection viewer normal Half-way source

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

θ 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!

4

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

• f 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.

Lambertian Model

• Lambert Model

θ 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

• bject 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)

5

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

Phong-Blinn Model

• BRDF Viewer

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

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

6

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)

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 θ θ θ θ θ θ θ θ

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 of 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

7

Cook-Torrance Model

• Roughness

Cook-Torrance Model

• Putting it all together

π 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

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 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!

8

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)

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

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

9

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]