04b Lighting Full

7/27/2019 04b Lighting Full

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ThomasFunkhouser2000

()

Thomas Funkhouser

Princeton University

C0S 426, Fall 2000


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Ray Casting

Image RayCast(Camera camera, Scene scene, int width, int height){

Image image = new Image(width, height);

for (int i = 0; i < width; i++) {

for (int j = 0; j < height; j++) {

Ray ray = ConstructRayThroughPixel(camera, i, j);Intersection hit = FindIntersection(ray, scene);

image[i][j] = GetColor(scene, ray, hit);

}

}

return image;}

Wireframe


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Ray Casting







}

}

return image;}

Without Illumination


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Ray Casting







}

}

return image;}

With Illumination


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Illumination

How do we compute radiance for a sample ray?

Angel Figure 6.2



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Goal

Must derive computer models for ... Emission at light sources

Scattering at surfaces

Reception at the camera

Desirable features Concise

Efficient to compute

Accurate


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Overview

Direct Illumination Emission at light sources


Global illumination Shadows

Refractions

Inter-object reflections

Direct Illumination

Shadows


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Modeling Light Sources

IL(x,y,z,q,f,l) ... describes the intensity of energy,

leaving a light source,

arriving at location(x,y,z), ...

from direction (q,f), ... with wavelength l (x,y,z)

Light


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Empirical Models

Ideally measure irradiant energy for all situations Too much storage

Difficult in practice

l


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OpenGL Light Source Models

Simple mathematical models: Point light

Directional light

Spot light


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Point Light Source

Models omni-directional point source (e.g., bulb) intensity (I0),

position (px, py, pz),

factors (kc, kl, kq) for attenuation with distance (d)

2

qlc

0

kkk

I

ddI

L

d

Light

(px, py, pz)


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Directional Light Source

Models point light source at infinity (e.g., sun) intensity (I0),

direction (dx,dy,dz)

0IIL

(dx, dy, dz)

No attenuationwith distance


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Spot Light Source

Models point light source with direction (e.g., Luxo) intensity (I0),

position (px, py, pz),

direction D=(dx, dy, dz)

attenuation

2

qlc

0

kkk

)(I

dd

LDI

L

d

Light

(px, py, pz)

D

L g


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Overview




Refractions


Direct Illumination


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Modeling Surface Reflectance

Rs(q,f,g,y,l) ... describes the amount of incident energy,

arriving from direction (q,f), ...

leaving in direction (g,y),

with wavelength l

Surface


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Empirical Models

Ideally measure radiant energy forall combinations of incidentangles Too much storage

Difficult in practice

Example BRDF (Bidirectional reflectance

distribution function)

Surface

(q,f)

(y,l)

l


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OpenGL Reflectance Model

Simple analytic model: diffuse reflection +

specular reflection +

emission +

ambient

Surface

Based on model

proposed by Phong inhis PhD dissertation

1973


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Diffuse Reflection

Diffuse: Spread Out / To pass byspreading every way / To extendin all directions

Assume surface reflects equally

in all directions Examples: chalk, clay

Surface


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Diffuse Reflection

How much light is reflected? Depends on angle of incident light

Surface

dL

cosdAdL

dA

q


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Diffuse Reflection

Lambertian model cosine law (dot product)

Surface

N

Lq

cos

cos

( )D D L

N L N L

N L

I K N L I


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emission +

ambient

Surface


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Specular Reflection

Reflection is strongest near mirror angle Examples: mirrors, metals

N

LR qq


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Specular Reflection

How much light is seen? Depends on angle of incident light and angle to viewer

N

LR

V

Viewer

a

qq


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Specular Reflection

Phong Model cos(a)n

L

n

SSIRVKI )(

N

LR

V

Viewer

a

qq

Phong exponent: apparentsmoothness of the surface


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Specular Reflection

Phong Examples

Direction of light source and shininess exponent is varied


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emission +

ambient

Surface


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Emission

Emission 0 Represents light eminating directly from polygon


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emission +

ambient

Surface


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Ambient Term

This is a total hack (avoids complexity of global illumination)!

Represents reflection of all indirect illumination


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emission +

ambient

Surface


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emission +

ambient

Surface


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Surface Illumination Calculation

Single light source:

L

n

SLDALAEIRVKILNKIKII )()(

N

LR

V

Viewera

qq


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Surface Illumination Calculation

Multiple light sources:

))()(( i in

iSiiDALAEIRVKILNKIKII

N

L2

V

Viewer L1


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Overview




Transmissions


Global Illumination


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Global Illumination

Greg Larson


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Shadows

Shadow terms tell which light sources are blocked Cast ray towards each light source Li Si = 0 if ray is blocked, Si = 1 otherwise

Angel Figure 6.44

L LLn

SDAAEISRVKLNKIKII ))()((

ShadowTerm


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Ray Casting

Trace primary rays from camera Direct illumination from unblocked lights only

L LLn

SDAAEISRVKLNKIKII ))()((


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TTRSL LL

n

SDAAEIKIKISRVKLNKIKII ))()((

Recursive Ray Tracing

Also trace secondary rays from hit surfaces Global illumination from mirror reflection and

transparency


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Mirror reflections

Trace secondary ray in direction of mirror reflection Evaluate radiance along secondary ray and

include it into illumination model

TTRSL LL

n


Radiancefor mirror

reflection ray

IR


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Transparency

Trace secondary ray in direction of refraction Evaluate radiance along secondary ray and

include it into illumination model

TTRSL LL

n


Radiance forrefraction ray

IT


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TTRSL LL

n


Transparency

Transparency coefficient is fraction transmitted KT = 1 if object is translucent, KT = 0 if object is opaque

0 < KT < 1if object is semi-translucent

TransparencyCoefficient

KT


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Refractive Transparency

For thin surfaces, can ignore change in direction Assume light travels straight through surface

N

Li

T

r

hr

hi

i

TLT


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Refractive Transparency

N

L

i

Tr

hr

hi

LNT

r

i

ri

r

i

h

h

h

h )coscos(

For solid objects, apply Snells law:

iirr sinsin hh


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Ray tree represents illumination computation

Ray traced through scene Ray tree

TTRSL LL

n



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Ray tree represents illumination computation

Ray traced through scene Ray tree

TTRSL LL

n



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Image RayTrace(Camera camera, Scene scene, int width, int height)

{


for (int i = 0; i < width; i++) {for (int j = 0; j < height; j++) {

Ray ray = ConstructRayThroughPixel(camera, i, j);

Intersection hit = FindIntersection(ray, scene);


}}

return image;

}

GetColorcalls RayTrace recursively


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Summary

Ray casting (direct Illumination) Usually use simple analytic approximations for

light source emission and surface reflectance

Recursive ray tracing (global illumination) Incorporate shadows, mirror reflections,

and pure refractions

More on global illumination later!

All of this is an approximationso that it is practical to compute


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Illumination Terminology

Radiant power [flux] (F) Rate at which light energy is transmitted (in Watts).

Radiant Intensity (I) Power radiated onto a unit solid angle in direction (in Watts/sr)

e.g.: energy distribution of a light source (inverse square law)

Radiance (L) Radiant intensity per unit projected surface area (in Watts/m2sr)

e.g.: light carried by a single ray (no inverse square law)

Irradiance (E) Incident flux density on a locally planar area (in Watts/m2 )

e.g.: light hitting a surface along a

Radiosity (B) Exitant flux density from a locally planar area (in Watts/ m2 )

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