[PPT] - CS-184: Computer Graphics Lecture #3: Shading Prof. James OBrien PowerPoint Presentation

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CS-184: Computer Graphics

Lecture #3: Shading

Prof. James O’Brien

University of California, Berkeley

V2016-F-03-1.0

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Today

Local Illumination & Shading
The BRDF
Simple diffuse and specular approximations
Shading interpolation: flat, Gouraud, Phong
Some miscellaneous tricks

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Local Shading

Local: consider in isolation
1 light
1 surface
The viewer
Recall: lighting is linear
Almost always...

Counter example: photochromatic materials

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Local Shading

Examples of non-local phenomena
Shadows
Reflections
Refraction
Indirect lighting

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The BRDF

ρ(θV,θL) ρ(v,l,n)

ρ = =

The Bi-directional Reflectance Distribution Function
Given
Surface material
Incoming light direction
Direction of viewer
Orientation of surface
Return:
fraction of light that reaches the viewer
We’ll worry about physical units later...

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The BRDF

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Ideal specular

Perfect mirror reflection

Ideal diffuse

Equal reflection in all directions

Glossy specular

Majority of light reflected near

mirror direction Retro-reflective

Light reflected back towards light

source

Diagrams illustrate how light from incoming direction is reflected in various outgoing directions.

Ren Ng

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The BRDF

ρ(v,l,n) ˆ v ˆ l ˆ n

Spatial variation capture by “the material”
Frequency dependent
Typically use separate RGB functions
Does not work perfectly
Better:

ρ = ρ(θV,θL,λin,λout) 7

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Obtaining BRDFs

Measure from real materials

Images from Marc Levoy

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Obtaining BRDFs

Measure from real materials
Computer simulation
Simple model + complex geometry
Derive model by analysis
Make something up

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Beyond BRDFs

The BRDF model does not capture everything
e.g. Subsurface scattering (BSSRDF)

Images from Jensen et. al, SIGGRAPH 2001

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Beyond BRDFs

The BRDF model does not capture everything
e.g. Inter-frequency interactions

ρ = ρ(θV,θL,λin,λout)This version would work....

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A Simple Model

Approximate BRDF as sum of
A diffuse component
A specular component
A “ambient” term

+ =

+

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Diffuse Component

Lambert’s Law
Intensity of reflected light proportional to cosine of angle between

surface and incoming light direction

Applies to “diffuse,” “Lambertian,” or “matte” surfaces
Independent of viewing angle
Use as a component of non-Lambertian surfaces

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Diffuse Component

l n

Steve Marschner

Top face of cube  receives a certain   amount of light Top face of   60º rotated cube  intercepts half the light In general, light per unit  area is proportional to  cos θ = l • n

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Diffuse Component

kdI(ˆ l· ˆ n)

Comment about two-side lighting in text is wrong...

max(kdI(ˆ l· ˆ n),0)

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Diffuse Component

Plot light leaving in a given direction:
Plot light leaving from each point on surface

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Specular Component

Specular component is a mirror-like reflection
Phong Illumination Model
A reasonable approximation for some surfaces
Fairly cheap to compute
Depends on view direction

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Specular Component

ksI(ˆ r· ˆ v)p

ksI max(ˆ r· ˆ v,0)p

L R V N

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Specular Component

Computing the reflected direction

ˆ r = −ˆ l+2(ˆ l· ˆ n)ˆ n

n l r

l

θ n cos θ n cos θ

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Specular Component

“Half-angle” approximation for specular

n l h ω e

ˆ h = ˆ l+ ˆ v ||ˆ l+ ˆ v||

*Don’t use half-angle approximation in your assignments!

ksI(ˆ h · ˆ n)p

different specular term

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Specular Component

Plot light leaving in a given direction:
Plot light leaving from each point on surface

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Specular Component

Specular exponent sometimes called “roughness”

n=1 n=2 n=4 n=8 n=256 n=128 n=64 n=32 n=16

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Ambient Term

Really, its a cheap hack
Accounts for “ambient, omnidirectional light”
Without it everything looks like it’s in space

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Summing the Parts

Recall that the are by wavelength
RGB in practice
Sum over all lights

R = kaI +kdI max(ˆ l· ˆ n,0)+ksI max(ˆ r· ˆ v,0)p

k? +

= +

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Anisotropy

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Metal -vs- Plastic

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Metal -vs- Plastic

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Other Color Effects

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Materials: Diffuse

Ren Ng

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Materials: Plastic

Ren Ng

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Materials: Paint

Ren Ng

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Materials: Paint

Ren Ng

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Materials: Mirror

Ren Ng

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Materials: Metallic

Ren Ng

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Other Color Effects

Images from Gooch et. al, 1998 + =

pure blue to yellow pure black to object color darken select final tone

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Measured BRDFs

Images from Cornell University Program of Computer Graphics

BRDFs for automotive paint

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Measured BRDFs

Images from Cornell University Program of Computer Graphics

BRDFs for aerosol spray paint

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Measured BRDFs

Images from Cornell University Program of Computer Graphics

BRDFs for house paint

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Measured BRDFs

Images from Cornell University Program of Computer Graphics

BRDFs for lucite sheet

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Ashikhmin-Shirley BRDF

More realistic specular term (for some materials)
Anisotropic specularities
Fresnel behavior (grazing angle highlights)
Energy preserving diffuse term
Sum of diffuse and specular terms (as before)

Michael Ashikhmin and Peter Shirley. 2000. An anisotropic phong BRDF model. J. Graph. Tools 5, 2 (February 2000), 25-32.  https://www.cs.utah.edu/~shirley/papers/jgtbrdf.pdf

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ρ(ˆ l, ˆ v) = ρd(ˆ l, ˆ v) + ρs(ˆ l, ˆ v)

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Ashikhmin-Shirley BRDF

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F(ˆ h · ˆ e) = Ks + (1 − Ks)(1 − (ˆ h · ˆ e))5 ρs(ˆ l,ˆ e) = p (pu + 1)(pv + 1) 8π (ˆ n · ˆ h)pu cos2 φ+pv sin2 φ (ˆ h · ˆ e) max ⇣ (ˆ n · ˆ e), (ˆ n ·ˆ l) ⌘F(ˆ h · ˆ e) Light direction Viewer (eye) direction Specular powers Normal Half angle Specular coefficient (color) Parametric directions

ˆ l ˆ e pu, pv ˆ n ˆ h Ks ˆ u, ˆ v

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Ashikhmin-Shirley BRDF

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ρs(ˆ l,ˆ e) = p (pu + 1)(pv + 1) 8π (ˆ n · ˆ h)

pu(ˆ h·ˆ u)2+pu(ˆ h·ˆ v)2 1−(ˆ h·ˆ n)2

(ˆ h · ˆ e) max ⇣ (ˆ n · ˆ e), (ˆ n ·ˆ l) ⌘F(ˆ h · ˆ e) F(ˆ h · ˆ e) = Ks + (1 − Ks)(1 − (ˆ h · ˆ e))5 Light direction Viewer (eye) direction Specular powers Normal Half angle Specular coefficient (color) Parametric directions

ˆ l ˆ e pu, pv ˆ n ˆ h Ks ˆ u, ˆ v

Approximate Fresnel function

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Ashikhmin-Shirley BRDF

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Light direction Viewer (eye) direction Specular powers Normal Half angle Specular coefficient (color) Parametric directions

ˆ l ˆ e pu, pv ˆ n ˆ h Ks ˆ u, ˆ v

ρd(ˆ l,ˆ e) = 28Kd 23π (1 − Ks) 1 − ✓ 1 − ˆ n · ˆ e 2 ◆5! 0 @1 − 1 − ˆ n ·ˆ l 2 !51 A

Note: The Phong diffuse term (Lambertian) is independent of

view. But this term accounts for unavailable light due to

specular/Fresnel reflection.

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Ashikhmin-Shirley BRDF

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Ashikhmin-Shirley BRDF

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Ashikhmin-Shirley BRDF

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nv = 10000 nv = 1000 nv = 100 nv = 10 nu = 10 nu = 100 nu = 1000 nu = 10000

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Details Beget Realism

The “computer generated” look is often due to a lack of

fine/subtle details... a lack of richness.

From bustledress.com

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Details Beget Realism

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Direction -vs- Point Lights

For a point light, the light direction changes over the

surface

For “distant” light, the direction is constant
Similar for orthographic/perspective viewer

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Falloff

r intensity  here: I/r2 I 1 intensity  here: Steve Marschner

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Falloff

Physically correct: light intensify falloff
Tends to look bad (why?)
Not used in practice
Sometimes compromise of used

1/r2 1/r 51

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Spot and Other Lights

Other calculations for useful

effects

Spot light
Only light certain objects
Negative lights
etc.

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Ugly....

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Ugly....

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The normal vector at a point on a surface is perpendicular

to all surface tangent vectors

For triangles normal given by right-handed cross product

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Surface Normals

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Flat Shading

Use constant normal for each triangle (polygon)
Polygon objects don’t look smooth
Faceted appearance very noticeable, especially at specular highlights
Recall mach bands...

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Smooth Shading

Compute “average” normal at vertices
Interpolate across polygons
Use threshold for “sharp” edges
Vertex may have different normals for each face

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Smooth Shading

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Smooth Shading

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From blender.stackexchange.com

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Gouraud Shading

Compute shading at each vertex
Interpolate colors from vertices
Pros: fast and easy, looks smooth
Cons: terrible for specular reflections

Flat Gouraud

Note: Gouraud was hardware rendered...

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Gouraud

Phong Shading

Compute shading at each pixel
Interpolate normals from vertices
Pros: looks smooth, better speculars
Cons: expensive

Phong

Note: Gouraud was hardware rendered...