Shading, lighting, & BRDF...

Shading, lighting, & BRDF Theory Cliff Lindsay, PHD

Overview of today’s lecture

• BRDF Characteristics

• Lights in terms of BRDFs

• Classes of BRDFs

• Ambient light & Shadows in terms of BRDFs

Tomas Akenine-Mőller © 2002

Decomposing Reflection

• Phong = Amb + Diff + Spec

• Don’t Confuse Phong Shading


Refresher on lighting Diffuse component : idiff

• i=iamb+idiff+ispec

• Diffuse is Lambert’s law:


cos lndiffi

Photons are scattered equally in all

directions

diffdiffdiff smlni )(

Lighting

Specular component : ispec

• Diffuse is dull (left)

• Specular: simulates a highlight


Specular component: Phong • Phong specular highlight model


Reflect l around n: l)n2(nlr

n

l r

-l

nln )(

ln shishi mm

speci )(cos)( vr

specspec

m

specshi smvri ))(,0max(

Read about Blinns highlight formula: (n.h)m

Ambient component: iamb

• Ad-hoc – tries to account for light coming from other surfaces

• Just add a constant color:


ambambamb smi

Lighting i=iamb+idiff+ispec

• This is just a hack!

• Has little to do with how reality works! Tomas Akenine-Mőller © 2002

+ +

=

What’s lighting and what’s shading?

• Lighting: the interaction between light and matter

• Shading: do lighting (at vertices) and determine pixel’s colors from these

• Three types of shading:

– Flat, Goraud, and Phong


Now Some Info About Lights


Additions to the lighting equation • Depends on distance: 1/(a+bt+ct )

• Can have more lights: just sum their respective contributions

• Different light types:


2

Lights


Directional Omni with falloff Spotlight

2r

IE

r

pspll

psplr

LL

Omni

Falloff


2

1

rsrssf

qlc

dist

0

,

,1

startend

enddist

rr

rrf

OpenGL way

Typical for Games

Spotlights


0

)(*)(

exps

LL

lsIlI

S- angle

P-penumbra

U - cutoff

BRDF Theory

Ratio between incoming and outgoing light


v l

)cos()(

)(),(

i

o

lE

vLvlf

Outgoing

Incoming

Think of f(l,v) as a function

BRDFs – Better Modeling • Better Modeling:

– Diffuse – define better diffuse

– Specular – different types of specular

– Ambient – beyond just simple Phong ambient


What We’ve Done Already

• For Phong Reflectance – We calculate Lo = f(l,v)*E(l)*cos(i) – Phong = i*mat+i*NL*mat+i*(NR)m*mat


)cos()(

)(),(

i

o

lE

vLvlf

f(l,v) f(l,v) E(l) E(l) E(l)

BRDF Theory • Generally Parameterized by:

– i - incoming – o – outgoing – n – Normal – V – View Vector – L – Light Vector


Easy to param based on

two quantities

BRDF Characteristics

• Helmholtz Reciprocity


),(),( lvfvlf

Conservation of Energy

• What comes in, must go ?

- Out

- Absorbed

- Scattered

Light Material Interaction


Surface Interaction Sub-Surface Interaction

When Light Hits Material:

• Interacts with surface

• Goes through surface an interacts below surface

• Independent of color (most of time for us)

Fresnel Reflectance


Governs interface between two surfaces

• ri is the ideal reflection (look familiar?)

• t is the ideal refraction

•Snell’s Law (n1sin(i) = n2 sin(t) )

•i = 90, glancing angle produces white color

Fresnel Example


Which Would You Drink?


Subsurface Scattering

• Very Important for flesh • Most organic materials exhibit • Lots of other materials too


Without With

Micro-Geometry


Micro-geometry

A. Self Shadowing

B. Masking

C. Interreflection (self)


A B C

Example: Micro-Geometry

Retro-Reflection


Micro-facet

• Special Case Micro-geometry – Facets Assumed to be ideal mirrors – Uses Half-vector h (half-way vector) – NDF: Normal Distribution Function p(h) – Introduces Geometry Factor G(l,v)


Micro-facet • Incorporates:

– NDF – distribution of facets on surface – Geometry – surface geometry – Fresnel


)cos()cos(4

)(),()(),(

oip

h

k

RfvlGhpvlf

Example BRDFs

• Modified Phong


,

0

)cos(

)cos(*

),(

i

m

rmatmat

vlf

,)cos(*

),(

m

rmatmatvlf

Old Phong

Physically Accurate

Phong

Simple Visibility

• Many BRDFs (especially game ones) have no visibility term at all

• This means the visibility term = 1

• Implies geometry factor = nl * nv.


Torrance Sparrow Geometry • invented by Blinn in 1975 as a reformulation of the Torrance-

Sparrow • based on an micro-geometry model • not affected by roughness


More Geometry Factors

• Kelemen-Szirmay-Kalos Geometry Factor

• Has cheap and effective approximation


Rougher = Blurrier


Smith Geometry Factor

kkkkGsmith

o

o

i

i

)1(cos

cos

)1(cos

cos


Incorporates roughness into Geometry Term

k=(2m2/)

Roughness

Many Different Things To Consider


Samples from real-world materials


Demo


More Geometry Factor

Instead of general inclusion within the BRDF We can account for geometry for each geometry specifically


Phong Ambient Ambient Occlusion AO + GI Light

Ambient Occlusion

• At surface points P shoot out rays

– If we hit something shelf-shadow

– If not, calculate lighting (NL) or something

• Incorporate into reflectance function


AO

• Light = local hemisphere

– Centered at current surface point

– Radius = user parameter

• Can be rendered with ray tracing

• Gives perceptual clues of depth, curvature and spatial proximity

• Lots of techniques (For Games: Screen Space,

Horizon-Based, Image-Space)


Example


Other Illumination Models Cliff Lindsay

Overview of today’s lecture

• Refresher on simple lighting models

– Plus some new stuff

• More Advanced Illumination Models


Additions to the lighting equation • Depends on distance: 1/(a+bt+ct )

• Can have more lights: just sum their respective contributions

• Different light types:


2

What’s lighting and what’s shading?

• Lighting: the interaction between light and matter

• Shading: do lighting (at vertices) and determine pixel’s colors from these

• Three types of shading:

– Flat, Goraud, and Phong


Global Models

You have seen:

• Local illumination model: Phong – Ambient

– Diffuse

– Specular

– Point light sources

– No: shadows, inter-object light reflection.

• “More global” illumination model: Ray Tracing – Shadows

– Area light sources (via distributed ray tracing)

– inter-object light reflection

Tradeoffs:

• Improvements in fidelity come at the expense of computational complexity.


Realistic rendering

• For each visible point p in the scene

– How much light is reflected towards the camera


Direct + Indirect


p

Local vs. Global


Indirect Light

• Direct-only

• 1-bounce indirect

• 2-bounce indirect


Ray Tracing


Different Ways to Achieve GI

• Ray Tracing

• Path Tracing

• Photon Mapping

• Radiosity

• Metropolis Light Transport


Put it all together


Date post:	20-Mar-2018
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