Paper Summaries Any takers? Material Properties Assignments - - PDF document

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Paper Summaries Any takers? Material Properties Assignments - - PDF document

Paper Summaries Any takers? Material Properties Assignments Projects Proposals Should all have received feedback via e-mail. Checkpoint 2 Grading Due Wednesday ACCEPTED Any questions? CONDITIONALLY


slide-1
SLIDE 1

1 Material Properties

Paper Summaries

  • Any takers?

Assignments

  • Checkpoint 2

– Due Wednesday – Any questions?

Projects

  • Proposals

– Should all have received feedback via e-mail. – Grading

  • ACCEPTED
  • CONDITIONALLY ACCEPTED
  • PLEASE RESUBMIT WITH MORE INFO

Projects

  • Project feedback

– Those who have not sent proposal, please see me!

  • Approx 18 projects
  • Listing of projects now on Web
  • Presentation schedule

– Presentations (15 min max) – Last 3 classes (week 10 + finals week) – Sign up

  • Email me with 1st , 2nd , 3rd choices
  • First come first served.

Plan for today

  • Material Properties

– Bi-directional reflectance distribution functions (BRDFs) – Illumination Models – Using Empirical Data

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SLIDE 2

2

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.

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 Example

Sun behind observer Sun opposite observer

Note: Hidden shadows

BRDF Example

Sun behind observer Sun opposite observer

Note: Specular highlights

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SLIDE 3

3

BRDF Example

Sun behind observer Sun opposite observer

Note: Specular highlights Note: Hidden shadows

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.

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SLIDE 4

4

Illumination Modeling

  • Three approaches

– 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

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 Models

  • Lambertian

– Physically based…but limited

  • Phong

– heuristic

  • Cook-Torrance

– Physically based

  • Ward

– heuristic based on physics – Ansitropic reflection

  • Many others!
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SLIDE 5

5

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!

Lambertian Model

  • Lambert Model

– Perfectly diffuse surface – reflection is constant in all directions (kd) – Independent of viewer direction

Lambertian Model

  • Lambert Model

θ cos ) (

d Sk

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

d S

  • =

Lambertian Model

  • Lambert Model

– why cos θ? – Surface has differential area dA – Intensity varies with projected area on surface – Projected area = cos θ

Lambertian Model

  • BRDF Viewer

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

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)
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SLIDE 6

6

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

Cook-Torrance Model

– 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
  • 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
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SLIDE 7

7

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

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SLIDE 8

8

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!

  • Break.
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SLIDE 9

9

Anisotropic Models

  • Anisotropy

– Isotropic - surfaces reflect equally from any direction of view – Anisotropic - reflection varies not only with angle of incidence, but also with the angle of the incident light w.r.t some viewing angle.

  • Surfaces considered to possess an intrinsic grain
  • Examples: satin, velvet, hair, brushed aluminum

Anisotropic Models

  • Anisotropic reflection -- example

Anisotropic Models

  • Ward Model [Ward92]

– Designed for both accuracy and ease of use – Includes model for anisotropic reflection

Anisotropic Models

  • Ward Model - Isotropic

specular 2 / ) (tan diffuse

) 4 cos cos 1 (

2 2

πα δ θ ρ π ρ ρ

α γ −

  • +

= e

s d

Anisotropic Model

  • Ward Model

– ρd - Diffuse reflectance coefficient (can vary with wavelength) – ρs - Specular reflectance coefficient (can vary with wavelength) – α - Standard deviation of surface slope

Anisotropic Models

  • Ward Model -- anisotropic

specular )) / sin / (cos (tan diffuse

) 4 cos cos 1 (

2 2 2 2 2

y x s d

y x

e α πα δ θ ρ π ρ ρ

α φ α φ γ + −

  • +

=

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SLIDE 10

10

Anisotropic Models

  • Ward Model w/ ansiotropy

– αx - Standard deviation of surface slope in x- direction – αy - Standard deviation of surface slope in y- direction

Anisotropic Models

  • Ward Model - example

Photo Isotropic Anisotropic

Anisotropic Models

  • Other anisotropic models (all based on

physics)

– [Kajia85] – [Poulin90] – [He91]

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)

Measuring BRDFs

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

Measuring BRDFs

Light Receptor

slide-11
SLIDE 11

11

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

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

– Hueristic

  • Phong

– Physically-based

  • Lamert
  • Cook-Torrance

– Heuristic based on physics

  • Ward

– 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]