Graphics Illumination Model 고려대학교 컴퓨터 그래픽스 연구실 cgvr.korea.ac.kr Graphics Lab @ Korea University Illumination  CGVR How do We Compute Radiance for a Sample Ray?  Must derive computer models.

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Transcript Graphics Illumination Model 고려대학교 컴퓨터 그래픽스 연구실 cgvr.korea.ac.kr Graphics Lab @ Korea University Illumination  CGVR How do We Compute Radiance for a Sample Ray?  Must derive computer models. 

Graphics
Illumination Model
고려대학교 컴퓨터 그래픽스 연구실
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Illumination

CGVR
How do We Compute Radiance for a Sample
Ray?
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Must derive computer models for ...
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Emission at light sources
Scattering at surfaces
Reception at the camera
Wireframe
cgvr.korea.ac.kr
Without
Illumination
Direct
Illumination
Graphics Lab @ Korea University
Overview

Direct Illumination



CGVR
Emission at light sources
Scattering at surfaces
Global Illumination



Shadows
Refractions
Inter-object reflections
Direct Illumination
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Overview

Direct Illumination



CGVR
Emission at light sources
Scattering at surfaces
Global Illumination


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Shadows
Refractions
Inter-object reflections
Direct Illumination
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Modeling Light Source
CGVR
 IL(x,y,z,q,f,l)
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Describes the intensity of energy,
Leaving a light source
Arriving at location(x,y,z)
From direction (q,f)
With wavelength l
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Empirical Model

CGVR
Ideally Measure Irradiant Energy for “All”
Situations
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Too much storage
Difficult in practice
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Light Source Model
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CGVR
Simple Mathematical Models:
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Point light
Directional light
Spot light
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Point Light Source
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CGVR
Models Omni-Directional Point Source (E.g.,
Bulb)
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Intensity (I0)
Position (px, py, pz)
Factors (kc, kl, kq) for attenuation with distance (d)
I0
IL 
k c  k1d  k q d 2
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Directional Light Source
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CGVR
Models Point Light Source at Infinity (E.g., Sun)
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Intensity (I0)
Direction (dx,dy,dz)
No attenuation
with distance
cgvr.korea.ac.kr
I L  I0
Graphics Lab @ Korea University
Spot Light Source
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CGVR
Models Point Light Source with Direction (E.g.,
Luxo)
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Intensity (I0),
Position (px, py, pz)
Direction (dx, dy, dz)
Attenuation
I0 D  L
IL 
k c  k1d  k q d 2
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Overview

Direct Illumination



CGVR
Emission at light sources
Scattering at surfaces
Global Illumination


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Shadows
Refractions
Inter-object reflections
Direct Illumination
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Modeling Surface Reflection
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CGVR
Rs(q,f,g,y,l)
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Describes the amount of incident energy
Arriving from direction (q,f)
Leaving in direction (g,y)
With wavelength l
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Empirical Model
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CGVR
Ideally Measure Radiant Energy for “All”
Combinations of Incident Angles
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Too much storage
Difficult in practice
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model
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CGVR
Simple Analytic Model:
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Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:
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Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection

CGVR
Assume Surface Reflects Equally in All
Directions
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Examples: chalk, clay
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection
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CGVR
How Much Light is Reflected?
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Depends on angle of incident light
dL  dA cos Q
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Diffuse Reflection
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CGVR
Lambertian Model
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Cosine law (dot product)
I D  K D N LI L
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:
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Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection
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CGVR
Reflection is Strongest Near Mirror Angle
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Examples: mirrors, metals
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection
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CGVR
How Much Light is Seen?
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Depends on angle of incident light and angle to
viewer
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Specular Reflection
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CGVR
Phong Model
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{cos(a)}n
I S  KS V R  I L
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Emission

CGVR
Represents Light Emitting Directly From
Polygon
Emission ≠ 0
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
Based on model
proposed by Phong
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Ambient Term

CGVR
Represents Reflection of All Indirect Illumination
This is a total hack (avoids complexity of global illumination)!
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model

CGVR
Simple Analytic Model:




Diffuse reflection +
Specular reflection +
Emission +
“Ambient”
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Reflectance Model
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CGVR
Sum Diffuse, Specular, Emission, and Ambient
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Surface Illumination
Calculation
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CGVR
Single Light Source:
I  I E  K A I AL  KD N  LI L  KS V R  I L
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Surface Illumination
Calculation

CGVR
Multiple Light Sources:
I  I E  K A I AL  i ( K D  N  Li I i  K S V  R i  I i )
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Overview

Direct Illumination

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
CGVR
Emission at light sources
Scattering at surfaces
Global Illumination



Shadows
Refractions
Inter-object reflections
Global Illumination
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Global Illumination
cgvr.korea.ac.kr
CGVR
Graphics Lab @ Korea University
Shadows

CGVR
Shadow Terms Tell Which Light Sources are
Blocked
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Cast ray towards each light source Li
Si = 0 if ray is blocked, Si = 1 otherwise
Shadow
Term
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Ray Casting
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CGVR
Trace Primary Rays from Camera
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Direct illumination from unblocked lights only
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Recursive Ray Tracing

CGVR
Also Trace Secondary Rays from Hit Surfaces
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Global illumination from mirror reflection and
transparency
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L  K S I R  KT I T
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Mirror Reflection

CGVR
Trace Secondary Ray in Direction of Mirror Reflection

Evaluate radiance along secondary ray and include it into
illumination model
Radiance
for mirror
reflection ray
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L  K S I R  KT I T
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Transparency

CGVR
Trace Secondary Ray in Direction of Refraction

Evaluate radiance along secondary ray and include it into
illumination model
Radiance for
refraction ray
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L  K S I R  KT I T
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Transparency
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CGVR
Transparency coefficient is fraction transmitted
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KT = 1 if object is translucent, KT = 0 if object is opaque
0 < KT < 1 if object is semi-translucent
Transparency
Coefficient
I  I E  K A I A  L ( K D N  L   K S V  R  ) S L I L  K S I R  KT I T
n
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Refractive Transparency

CGVR
For Thin Surfaces, Can Ignore Change in
Direction
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Assume light travels straight through surface
T  L
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Refractive Transparency

CGVR
For Solid Objects, Apply Snell’s Law:

hr sin Qr  hi sin Qi
ηi
ηi
T  ( cosQi  cosQr ) N  L
ηr
ηr
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Summary
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Direct Illumination
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
CGVR
Ray casting
Usually use simple analytic approximations for light
source emission and surface reflectance
Global illumination
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Recursive ray tracing
Incorporate shadows, mirror reflections,
and pure refractions
cgvr.korea.ac.kr
Graphics Lab @ Korea University
Illumination Terminology
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Radiant power [flux] (Φ)
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Rate at which light energy is transmitted (in Watts).
Radiant Intensity (I)
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Power radiated onto a unit solid angle in direction( in Watt/sr)
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Radiant intensity per unit projected surface area( in Watts/m2sr)
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e.g.: light carried by a single ray (no inverse square law)
Irradianc (E)
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e.g.: energy distribution of a light source (inverse square law)
Radiance (L)
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CGVR
Incident flux density on a locally planar area (in Watts/m2 )
Radiosity (B)
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Exitant flux density from a locally planar area ( in Watts/m2 )
cgvr.korea.ac.kr
Graphics Lab @ Korea University