#11: Lighting CSE167: Computer Graphics Instructor: Ronen Barzel UCSD, Winter 2006.

#11: Lighting

CSE167: Computer GraphicsInstructor: Ronen Barzel

UCSD, Winter 2006

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Outline for today

Overview of lighting Notes on color Local Illumination Light Sources Shading Advanced Lighting

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Where we are so far…

We know how to rasterize: Given a 3D triangle (or a bunch of triangles) Given a 3D camera… …we know which pixels represent the triangles

But what color should those pixels be?

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Lighting

(non-teapot images by Henrik Wann Jensen)

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Lighting To create a photorealistic image:

Simulate the interaction of light with the objects in the scene

Simulate the interaction of light with the eye or camera I.e., simulation of physics and optics

• Advanced rendering course (CSE168)• Many aspects “solved” in principle but still an area of active research

• Very slow to compute fully• Use global illumination techniques: examine the whole scene at once

• Known as physically-based rendering

For interactive computer graphics: Use a simplified model for speed Empirical/perceptual -- approximate interesting observed

phenomena Use local illumination techniques:

• only direct effect of lights on surfaces

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Basic Components of Lighting

Light sources AKA emitters Color and intensity Geometric attributes: Position, Direction, Shape Spatial attenuation Advanced properties: Spectrum, Polarization, …

Surfaces Geometric attributes: Position, Orientation Material properties: reflectance

• color• shininess, glossiness, …• texture• Advanced: translucency, microstructure, sub-surface scattering, …

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

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Lighting vs. Shading

Lighting: compute the result of light illuminating surfaces

Shading: assign colors to pixels

For photorealistic rendering: in principle, shading==lighting: perform lighting at every pixel

In practice: may take shortcuts may include non-lighting effects

• fog• illustration• cartoon shading

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Vertex Lighting

Each vertex goes through lighting process Lighting computation determines final color at the vertex Based on initial “unlit” vertex color Based on lights in the scene Based on material properties of the surface Based on surface normal

Interpolate colors using Gouraud shading

(Same lighting computation for per-pixel lighting)

rn

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Outline for today


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What is light? What is color?

Light is electromagnetic energy a continuous range of wavelengths varying intensity at each wavelength

Color is a property of the visual system Not an inherent property of light Human eyes have Red, Green, Blue receptors (cones)

• Each receptor responds to a range of wavelengths• Gives rise to “primary colors”:

• all colors expressed as combination of red, green, blue cone stimulation

• Lots of perceptual, psychophysical effects:• adaptation, inhibition, illusion

Physically correct computation requires computing interactions at all wavelengths

Perceptually correct computation Requires taking into account psychophysics

Pretty good approximation: Separate light into red, green, blue components Process each component independently

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Color illusion

The squares marked A and B are the same shade of gray

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

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Color Illusion -- proof



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Color Spaces







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Material Colors

Inherent “material color” which is the color that the object reflects Material reflects different wavelengths of light different amounts

In RGB, have a reflectivity amount for each of red, green, blue

An object can’t reflect more light than it receives Maximum: reflect 100% of light in all wavelengths--bright white

Reasonable: reflect 95% of light, material color =(0.95, 0.95, 0.95)

Material colors range from 0.0 to 1.0 in RGB

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Light Color

No limit to total light intensity reflecting from surface Can make individual light source brighter Can add more lights

Represent a light source using intensity in RGB Range from 0.0 up There is no upper limit to the intensity of light In other words, a bright white light might have color (10,10,10)

Units? physically-based rendering: photon power flux density in practice: arbitrary units (“my light goes up to 11”)

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Color & Intensity

Distinction between material color and light color: Material colors represent the proportion of light reflected

Light colors represent the actual intensity of a beam of light

We never perceive the inherent material color All we see is the light reflected off of a material

Shine a red light…• on a white or red surface: the object appears red• on a grey surface: the object appears dark red• on a blue surface: the object appears black

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Exposure and Display

What do we mean by “white”? Human eyes (and digital cameras) adjust exposure settings

automatically In a moderatly lit room, intensity 0.5 might appear as white In bright sunlight, intensity 100 might appear as (same) white

The monitor has an upper limit to the brightness it can display RGB units: 0=no light at the pixel, 1=full intensity at the pixel exact color light that emerges depends on monitor properties

• brightness, contrast, white point, color balance, … Final result of lighting calculation shouldn’t be more than 1.0 Advanced techniques: exposure control, AKA “tone mapping”

In practice: Assume intensity (1,1,1) is white clamp all final color values to 0.0-1.0 range before storing in

pixel

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Outline for today


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Local Illumination

AKA Local Lighting Models Light on a point on the surface (vertex) Assume we have an incident ray of light

Light coming from a known direction With a given RGB color (intensity)

We will build up empirical material properties Fancy name: Bidirectional Reflectance Distribution Function “BRDF”

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Reflectivity

White sheet of paper might reflect 95% of incident light

A mirror might reflect 95% of incedent light

Yet, these two things look completely different: They reflect light in different directions The paper is a diffuse reflector The mirror is a specular reflector

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“Standard” Lighting Model

Consists of three terms linearly combined: Diffuse component for the amount

of incoming light reflected equally in all directions

Specular component for the amount of light reflected in a mirror-like fashion

Ambient term to approximate light arriving via other surfaces

This is very simple approximation particularly good for plastic particularly good for metal That’s why CG images tend to

look like plastic and metal

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Diffuse Reflection

An ideal diffuse reflector receives light from some direction and bounces it uniformly in all directions very rough at microscopic level

Diffuse materials have a dull or matte appearance example: chalk

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n

Diffuse Reflection

Assume a beam of parallel rays shining on the surface

Consider area of the surface covered by the beam varies based on the angle between the beam and the normal

The larger this area, the less incident light per area

The incident light per unit area is proportional to the cosine of the angle between the normal and the light rays

Object darkens as normal turns away from light This is known as Lambert’s cosine law Diffuse surfaces AKA Lambertian surfaces

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Lambert’s Cosine Law

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Given:rn=surface unit normalrL =unit vector pointing towards the light

θi =angle of incidence, between rL and

rn

kd =material diffuse reflectance coefficient (0.0 to 1.0)cl =color (intensity) of the light source

Diffuse color:

cd =kdcl cos(θi ) =kdcl (rL ⋅

rn)

Notes: Depends on light and normal directions Doesn’t depend on eye position

• diffuse reflection is same in every direction Don’t want to illuminate from rear

• use

Diffuse Reflection

kdcl max(rL⋅

rn,0)

cl

kd

rL

rn

θi

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Diffuse Lighting Examples

A Lambertian sphere at several different lighting angles:

Diffuse lighting provides visual cues indicates 3D depth indicates surface curvature

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Multiple Lights

Can have many light sources in a scene Light (generally) behaves additively Add up the contribution of each light

c =kd cl i

(rL i ⋅ ∑ r

n)

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In the real world, light gets bounced all around the environment Resulting light illuminates surface from every direction. Global illumination techniques attempt to compute this.

Complex. Simple approximation (hack): Ambient light

Assume net effect is a constant color shining from every direction

Add to the net color, attenuated by reflectance coefficient

Effect of ambient light: Keeps unlit areas from going completely black Makes things look flatter

• with ambient and no diffuse: object has solid color, is completely 2D

ka or ca usually small (.1 or less)

Ambient Light

c =kaca + kdcli

rL i ⋅

rn( )∑

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Specular Reflection

Shiny surfaces exhibit specular reflection Polished metal Glossy car finish Plastics

A light shining on a specular surface causes a bright spot: known as a specular highlight essentially, a rough reflection of the light source

Highlight location depends viewer position relative to surface & lights

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Specular Reflection

An ideal specular reflector = mirror perfectly smooth surface bounces an incoming light ray in a single direction

angle of incidence equals the angle of reflection

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p

€

θr =θ i€

θr

€

θi

Law of Reflection

Angle of reflectance = angle of incidence

rR +

rL =2cosθ rn=2

rL ⋅

rn( )

rn

rR =2

rL ⋅

rn( )

rn−

rL

rL

rR

rn

rL

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Specular (Glossy) Reflection

Many materials not quite perfect mirrors Glossy materials look shiny and will show specular highlights

In CG, this is sometimes referred to as glossy reflection

Many formulations for this First: most basic and famous: Phong lighting model (1973)

Then: most popular: Blinn lighting model (1977)

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The surface roughness will vary from material to material Smooth surfaces have sharp highlights Rougher surfaces have larger, more blurry highlights

Assume surface composed of microfacets with random orientation Smooth surfaces: microfacet normals very close to surface

normal Rough surfaces: microfacet normals are spread around more

• on average, microfacet normals close to surface normal

Polished:

Smooth:

Rough:

Very rough:

Shiny materials

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Empirical observation

In general, we expect most reflected light to travel in direction of exact reflection

But because of microscopic surface variations, some light may be reflected in a direction slightly off the ideal reflected ray

So: Most reflected light in direction of ideal reflection Brightest when eye vector (view vector) is aligned with reflection

Intensity decreases as eye vector angle from reflection increases

Use dot product of eye vector with reflection vector

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parameters: specular reflectance coefficient, ks

Phong Exponent p controls the apparent size of the specularity• Higher p, smaller highlight

Phong Lighting Model

ks

rL

rn

θi

cs =kscl

rR ⋅

re( )

p

θr

cl rR

re

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Phong Lighting Model Examples

p=1 p=2 p=4

p=8 p=16 p=32

p=64 p=128 p=256

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Blinn Lighting Model

• Define the unit-length "halfway" vector rh,

halfway between rL and

re :

rh =

rL +

re

rL +

re

• rh represents the normal of a microfacet we would

need to have oriented so as to reflect the light to the eye

ks

rL

rncl

re

rh

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Blinn Lighting Model

• Microfacets roughly line up with surface

• The farther rh is from

rn, the less we expect microfact to align

• So use cos ine of angle between them :

c = ksclrh ⋅

rn( )

s

• Very s imilar in effect to Phong model

• Optimization due to Schick (1994):

replace t s with t

s − st + t

• Fas ter than exponent. Result is different but acceptable

ks

rL

rncl

re

rh

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Complete Blinn Lighting Model

Add to ambient and diffuse Add specular contribution for each light

It appears in a few slightly different forms and in a wide variety of notations…

c =kaca + cli

kd

rL i ⋅

rn( ) + ks

rhi ⋅

rn( )

s

( )∑

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Note on color

Do this in parallel for R,G,B Coefficients ka, kd, ks can be different for each of R,G,B This defines the material ambient color, diffuse color, and specular color.

Other (expensive) terms in expression are shared for each of R,G,B

Generally, use ambient color = diffuse color For metals, specular color = diffuse color

highlight is color of the material For plastics, specular color = white

highlight is the color of the light

c =kaca + cli

kd

rL i ⋅

rn( ) + ks

rhi ⋅

rn( )

s

( )∑

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Note on normals and spaces

Lighting depends on angles between normals, vectors Must be in space that preserves angles

World Space or Camera Space Not normalized view space: perspective doesn’t preserve

angles Conveniently, we can put world-space normals as per-

vertex data Doesn’t get transformed by projection.

But remember, when taking normals from object to world space: if world transform has nonuniform scale, normals must use

inverse-transpose if world transform has uniform scale, normals must be

renormalized if world transform has no scales, normals transform like

vectors

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General Lighting Models

General form: Bidirectional Reflectance Distribution Function BRDF,

B()

There are many lighting models Phong Blinn Cook-Torrance

• includes “roughness”, other parameters Gooch

• non-photorealistic, for illustrations Ward

• includes anisotropy etc…

c = cli

B(rL ,

re)∑

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Cook-Torrance

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Gooch







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Anisotropy

Material reflects differently in different directions

E.g., brushed metal; Ward’s model

isotropic anisotropic

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Outline for today


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Light Sources

In general, light sources can have complex properties Geometric area over which light is produced Anisotropy in direction Variation in color

Some very simple light sources models are standard

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Light Sources

Two aspects of light sources are important for a local shading model: Where is the light coming from (the L vector)? How much light is coming (the I values)?

Various light source types give different answers to the above questions: Directional: Light from a specific direction Point light source: Light from a specific point Spotlight: Light from a specific point with intensity that depends on the direction

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Directional Light

When light is coming from a distant source light rays are parallel light ray direction is the same everywhere in the scene

as if the source were infinitely far away good approximation to sunlight

Specified by a unit length direction vector, and a colorcsrc

rL

rn

rd

rL=−

rd

cl =csrc

cl

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cl

v

pcsrc

Point Lights

For closer light sources, such as light bulbs

Model as a point that radiates light in all directions equally Light vector varies across the surface Intensity from a point light source drops off proportionally to the inverse square of the distance from the light

rL

rn

rL=

p−vp−v

cl =csrc

p−v 2 rn

rLcl

v

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Attenuation

Sometimes, it is desirable to modify the inverse square falloff behavior of point lights A common (although not physically accurate) model for the distance attenuation is:

cl =csrc

kc + kl p−v + kq p−v 2

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Like point source, but intensity depends on direction: Position: the location of the source Spot direction: the center axis of the light Requires falloff parameters:

• how broad the beam is (cone angle)• how light tapers off at edges of he beam (cosine exponent)

Spotlights

csrc

rL

rn

rd

cl

rL=

p−vp−v

cl =0 if −

rL ⋅

rd < cos(θmax)

csrc −rL ⋅

rd( )

fotherwise

⎧⎨⎪

⎩⎪

v

p

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Spotlights

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Outline for today


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Shading

Various techniques: Flat Gouraud Phong Cartoon Procedural

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Flat shading

Compute shading at a representative point and apply to whole polygon OpenGL uses one of the vertices

Advantages: Fast - one shading computation per polygon, fill entire polygon with same color

Disadvantages: Inaccurate Faceted

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Gouraud Shading

Light each vertex with its own location and normal Result is a color at each vertex

Interpolate the colors across each triangle

Default mode for most hardware Advantages:

Fast: incremental calculations when rasterizing Much smoother - use one normal per shared vertex to get continuity between faces

Disadvantages: Don’t get smooth specular highlights C1-discontinuities in colorcause Mach bands: perceptualillusions of edges

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Mach bands



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Phong Shading Want to recompute lighting at every pixel

Need normal vector at each pixel Interpolate vertex normals

Interpolate the normals while scan-converting Typically, bilinearly interpolate x,y,z; then renormalize Also interpolate or transform to get position in

world/camera space Known as Phong Shading or Phong Interpolation

Not to be confused with Phong Lighting Model (though both are often used at the same time)

Advantages: More accurate Better images

Disadvantages: Slow Still not completely accurate

Modern GPUs can perform Phong shading via pixel shaders

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Gouraud vs. Phong shading

Gouraud misses specular hilights

solution: tessellate more finely: use smaller triangles that would help with the polygonal artifacts on the silhouettes too

Gouraud Phong

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Linear interpolation in screen space doesn’t align with linear interpolation in world space

Solutions: Do hyperbolic interpolation (see Buss) Break up into smaller triangles

Z – into the scene

Imageplane

Note: Perspective Distortion

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Cartoon Shading

General approach: Compute diffuse or Phong lighting Remap continuous intensityto two (or a few) levels

Some trickery to draw dark edges



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Procedural Shading

Software or hardware renderer calls an arbitrary routine at every pixel (or sub-pixel) Extreme of “do whatever you want” Can typically implement Phong or any other lighting model Used for patterns or other special effects Used for toon shading

Routine typically written in a special-purpose language RenderMan Shading Language (Pixar) Cg (Nvidia) HLSL (DirectX)

Routine: can get surface normal, position, material properties,

light locations, … computes a color value sometimes can even change the surface position

(displacement)

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Procedural shading




are needed to see this picture.QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.










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Procedural Shading

surface turbulence (float Kd=.8, Ka=.2){ float a,scale,sum; point M; M = transform( "marble", P ); scale = 1; sum = 0; a = sqrt(area(M)); while( a < scale ) { sum += scale * float noise(M/scale); scale *= 0.5; } Oi = sum; Ci = Cs * Oi * (Ka + Kd * I.N * I.N /(I.I * N.N));}



xform to object space

fractal

diffuse lighting (variant)

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Programmable GPUs

Two kinds of routines: vertex shaders: routine run for each vertex pixel shaders: routine run for each pixel

Limits on size of program amount of memory available types of memory and texture access (will talk about texture later)

etc. Technology still improving, capabilities keep expanding

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Outline for today


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Lighting Review

Local Illumination Lighting Models Ambient

• Normals don’t matter Lambert

• Angle between surface normal and light Phong

• Surface normal, light, and viewpoint

What they capture: Direct illumination from light sources Diffuse and Specular reflections (Very) Approximate effects of global lighting

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What they don’t do

Shadows Accurate reflection models Translucency, refraction Caustics (light focusing) Global Illumination Area light sources/emitters Atmospheric effects (fog, clouds) Motion blur Depth of field Lens imperfections Exposure & dynamic range …

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Advanced Lighting







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Done

Next class: more with lighting… Upcoming: Guest Speakers!

Check course web page for info

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#11: Lighting CSE167: Computer Graphics Instructor: Ronen Barzel UCSD, Winter 2006.

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