Shading I June 22, 1999 Motivational Film Graphic Violence - - PowerPoint PPT Presentation

Shading I

June 22, 1999

June 22, 1999

Motivational Film

✔Graphic Violence

– Gritz, Bergen, Darken (1991) – first use of BMRT

✔Mr Will Goes Sailing

June 22, 1999

Logistics

✔Projects

– Returned proposals – Proposal comments

• Accept / Please Resubmit
• Recall: Projects will be judged on what is in the

proposal

– Reminder: Report is bulk of project – Resubmitted proposals due next class

June 22, 1999

Logistics

✔Projects

– Using Java3d/VRML/directX/….

• These are tools (much like “C”)
• Need specifics of what you want to do with it.
• Best way to learn is to implement

something…be clear on what that something is.

• I need to know what to expect from your project

and presentation.

June 22, 1999

Logistics

✔Paper summaries on Shading I

– Any takers?

✔Slides on Web

– Now in B&W and Color

June 22, 1999

Photography and Light

pho•tog•ra•phy, n., the process or art of producing images of objects by the action of light on a sensitized surface, esp, a film in a camera.

Yeah, we get it…photography, light…whatever..

June 22, 1999

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

June 22, 1999

Today’s Class

✔Shading

– Bidirectional reflectance distribution functions (BRDFs) – Shading Models – Using Empirical Data

June 22, 1999

Shading

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

used in determining the shading.

✔For efficiency’s sake, most shading

models are approximations.

June 22, 1999

BDRF

✔Bidirectional Reflectance Function

) , , , (

r r i i r

f BDRF θ φ θ φ =

✔At a given point, gives relative reflected

illumination in any direction with respect to incoming illumination coming from any direction

June 22, 1999

BDRF

✔BDRF Geometry

June 22, 1999

BDRF

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

) , , , , ( λ θ φ θ φ

r r i i r

f BDRF =

June 22, 1999

Shading Models

✔Shading model - function or algorithm

used in determining the shading.

✔Revise to…

– function or algorithm used in approximating the BDRF.

June 22, 1999

Shading Models

✔Shading Models and Viewing Direction

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

June 22, 1999

Shading Models

✔Geometry

June 22, 1999

Shading 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.

June 22, 1999

Shading Models

✔Recall from Linear Algebra

θ u v

θ cos v u v u =

June 22, 1999

Shading Models

✔Lambertian ✔Phong ✔Cook-Torrance ✔Strauss ✔Ward

June 22, 1999

Shading Models

✔Lambert Model

– Perfectly diffuse surface – reflection is constant in all directions (kd)

June 22, 1999

Shading Models

✔Lambert Model

θ cos ) (

d Sk

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

d S

• =

June 22, 1999

Shading Model

✔ Lambert Model

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

June 22, 1999

Shading Models

✔Phong Model

– introduces specular (mirror like) reflections – three components

• ambient - background light (ka)
• diffuse - lamberian reflection (kd)
• specular - mirror like reflection(ks)

June 22, 1999

Shading Models

✔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

June 22, 1999

Shading Models

✔Phong - Blinn

– Uses halfway angle rather than reflected

• specular

diffuse ambient

V) H ( N) S ( ) (

∑ ∑

• +
• +

=

i k i i s i i i d a a

e

L k L k L k V L

June 22, 1999

Shading Models

✔Any questions

– diffuse vs specular reflections

✔Move on to Cook - Torrance model.

June 22, 1999

Shading Models

✔Cook-Torrance Model

– based on physics of a surface – components

• microfacet model - describes geometry of

surface

• Fresnel term - describes reflectance
• Roughness - describes microfacet distribution.

June 22, 1999

Shading Models

✔Cook-Torrance / Microfacets

– surface is composed of V shaped grooves (microfacets) – Light interactions with microfacets

• Reflect - causes specular reflections
• Scatter - causes diffuse reflections

June 22, 1999

Shading Models

✔Cook-Torrance / Microfacets

June 22, 1999

Shading Models

✔ Cook-Torrance / Microfacets - GeometryTerm

     

• =

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

June 22, 1999

Shading Model

✔Cook-Torrance / Fresnel Equation

– Describes reflectance – 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)

June 22, 1999

Shading Models

✔Fresnel Equations

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

p s

F F F 2 1 2 1 + =

For unpolarized light

June 22, 1999

Shading Models

✔Cook-Torrance / Fresnel

– If all quantities known, use Fresnel equations – If not, approximate using reflectance off normal

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

June 22, 1999

Shading Model

✔Cook-Torrance / 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

June 22, 1999

Shading Model

✔Cook-Torrance / Roughness

2

) / ( m

ce D

γ −

=

γ

γ 4 2 ) / ) ((tan

cos

2

m e D

m −

=

Gaussian Model Beekman Model

June 22, 1999

Shading Models

✔Cook-Torrance / Roughness

June 22, 1999

Shading Models

✔Cook-Torrance/putting it all together

• diffuse

specular d s r

df sf f + =

π 1 =

d

f

V) S)(N N ( 1

• ×

× = G D F fs π

June 22, 1999

Shading Models

✔Complete Cook-Torrance Model

∑

• +

=

i i r i a a r

d f L R L L ϖ ) S)( N (

June 22, 1999

Shading Models

✔Cook-Torrance -- examples

June 22, 1999

Shading Models

✔Cook-Torrance summary

– Complicated model based on physics – Components

• Microfacets
• Fresnel equation
• Roughness

June 22, 1999

Shading Models

✔Strauss Model [Strauss90]

– Designed for ease of use and efficiency – Intuitive parameter set – Takes some liberty with physics.

June 22, 1999

Shading Models

✔Strauss Model - parameter set

– Color – Smoothness - 0 = perfectly diffuse, 1 = perfectly specular – Metalness - 0 = dielectric, 1 = metal – Transparency – Index of Refraction.

June 22, 1999

Shading Models

✔Anisotropy

– Isotropic - surfaces reflect equally from any direction of view – Ansiotropic - reflection varies not only with angle of incidence, but also with the angle

• f the incident light w.r.t some viewing

angle

June 22, 1999

Shading Models

✔Ansiotropic reflection -- example

June 22, 1999

Shading Models

✔Ward Model [Ward92]

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

June 22, 1999

Shading Models

✔Ward Model

• specular

2 / ) (tan diffuse

) 2 cos cos 1 (

2 2

πα δ θ ρ π ρ ρ

α γ −

• +

= e

s d

June 22, 1999

Shading Model

✔Ward Model

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

June 22, 1999

Shading Models

✔Ward Model -- w/ansiotropy

• specular

)) / sin / (cos (tan diffuse

) 2 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 + −

• +

=

June 22, 1999

Shading Models

✔Ward Model w/ ansiotropy

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

June 22, 1999

Shading Models

✔Ward Model - example

June 22, 1999

Shading Models

✔Other ansiotropic models (all based on

physics)

– [Kajia85] – [Poulin90] – [He91]

June 22, 1999

Measuring BDRFs

✔Can use empirical data ✔BDRFs measured using a goniometer ✔See [Ward92]

June 22, 1999

Measuring BDRFs

June 22, 1999

Measuring BDRFs

✔Storage using spherical sampling

June 22, 1999

Measuring BDRFs

✔BDRF Database

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

June 22, 1999

Summary

✔BDRFs - defines reflection off surface in

each direction as result from light arriving at each direction.

✔Shading models - approximations to

BDRF

✔Can use measured BDRFs

June 22, 1999

Summary -- Shading Models

✔Lambert Model ✔Phong Model ✔Cook-Torrance (heavy on the physics) ✔Strauss ✔Ward Model (ansiotropic)

June 22, 1999

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]

June 22, 1999

Next Class

✔Functional Shading

– Texture Mapping – Procedural Textures – Shading Languages

June 22, 1999

Remember

✔Resubmitted proposals due next class.

June 22, 1999

Remember

✔Class Web Site:

– http://www.cs.rit.edu/~jmg/virtualPhoto

✔Any questions?