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Graphics
Graphics Lab @ Korea University
Illumination Model
고려대학교 컴퓨터 그래픽스 연구실
CGVR
Graphics Lab @ Korea University
Illumination
How do We Compute Radiance for a Sample Ray? Must derive computer models for ...
Emission at light sources Scattering at surfaces Reception at the camera
Wireframe WithoutIllumination
DirectIllumination
CGVR
Graphics Lab @ Korea University
Overview
Direct Illumination Emission at light sources Scattering at surfaces
Global Illumination Shadows Refractions Inter-object reflections
Direct Illumination
CGVR
Graphics Lab @ Korea University
Overview
Direct Illumination Emission at light sources Scattering at surfaces
Global Illumination Shadows Refractions Inter-object reflections
Direct Illumination
CGVR
Graphics Lab @ Korea University
Modeling Light Source
IL(x,y,z,) Describes the intensity of energy, Leaving a light source Arriving at location(x,y,z) From direction () With wavelength
CGVR
Graphics Lab @ Korea University
Empirical Model
Ideally Measure Irradiant Energy for “All” Situations Too much storage Difficult in practice
CGVR
Graphics Lab @ Korea University
Light Source Model
Simple Mathematical Models: Point light Directional light Spot light
CGVR
Graphics Lab @ Korea University
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)
2q1c
0
kkk
I
ddIL
2q1c
0
kkk
I
ddIL
CGVR
Graphics Lab @ Korea University
Directional Light Source
Models Point Light Source at Infinity (E.g., Sun) Intensity (I0)
Direction (dx,dy,dz)
No attenuationwith distance 0ILI 0ILI
CGVR
Graphics Lab @ Korea University
Spot Light Source
Models Point Light Source with Direction (E.g., Luxo) Intensity (I0),
Position (px, py, pz) Direction (dx, dy, dz) Attenuation
2
q1c
0
kkk
LDI
ddIL
2
q1c
0
kkk
LDI
ddIL
CGVR
Graphics Lab @ Korea University
Overview
Direct Illumination Emission at light sources Scattering at surfaces
Global Illumination Shadows Refractions Inter-object reflections
Direct Illumination
CGVR
Graphics Lab @ Korea University
Modeling Surface Reflection
Rs(,) Describes the amount of incident energy Arriving from direction () Leaving in direction (,) With wavelength
CGVR
Graphics Lab @ Korea University
Empirical Model
Ideally Measure Radiant Energy for “All” Combinations of Incident Angles Too much storage Difficult in practice
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
Based on modelproposed by Phong
Based on modelproposed by Phong
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
Based on modelproposed by Phong
Based on modelproposed by Phong
CGVR
Graphics Lab @ Korea University
Diffuse Reflection
Assume Surface Reflects Equally in All Directions Examples: chalk, clay
CGVR
Graphics Lab @ Korea University
Diffuse Reflection
How Much Light is Reflected? Depends on angle of incident light dLdAcos
CGVR
Graphics Lab @ Korea University
Diffuse Reflection
Lambertian Model Cosine law (dot product)
LDD IKI LN LDD IKI LN
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
Based on modelproposed by Phong
Based on modelproposed by Phong
CGVR
Graphics Lab @ Korea University
Specular Reflection
Reflection is Strongest Near Mirror Angle Examples: mirrors, metals
CGVR
Graphics Lab @ Korea University
Specular Reflection
How Much Light is Seen? Depends on angle of incident light and angle to
viewer
CGVR
Graphics Lab @ Korea University
Specular Reflection
Phong Model {cos()}n
Ln
SS IKI RV Ln
SS IKI RV
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
Based on modelproposed by Phong
Based on modelproposed by Phong
CGVR
Graphics Lab @ Korea University
Emission
Represents Light Emitting Directly From Polygon
Emission ≠ 0Emission ≠ 0
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
Based on modelproposed by Phong
Based on modelproposed by Phong
CGVR
Graphics Lab @ Korea University
Ambient Term
Represents Reflection of All Indirect Illumination
This is a total hack (avoids complexity of global illumination)!
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
CGVR
Graphics Lab @ Korea University
Reflectance Model
Simple Analytic Model: Diffuse reflection + Specular reflection + Emission + “Ambient”
CGVR
Graphics Lab @ Korea University
Reflectance Model
Sum Diffuse, Specular, Emission, and Ambient
CGVR
Graphics Lab @ Korea University
Surface Illumination Calculation
Single Light Source:
Ln
SLDALAE IKILNKIKII RV Ln
SLDALAE IKILNKIKII RV
CGVR
Graphics Lab @ Korea University
Surface Illumination Calculation
Multiple Light Sources:
i i
niSiiDALAE IKILNKIKII )RV(
i in
iSiiDALAE IKILNKIKII )RV(
CGVR
Graphics Lab @ Korea University
Overview
Direct Illumination Emission at light sources Scattering at surfaces
Global Illumination Shadows Refractions Inter-object reflections
Global Illumination
CGVR
Graphics Lab @ Korea University
Global Illumination
CGVR
Graphics Lab @ Korea University
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
L LL
nSDAAE ISKLNKIKII )RV(
L LLn
SDAAE ISKLNKIKII )RV(
ShadowTerm
CGVR
Graphics Lab @ Korea University
Ray Casting
Trace Primary Rays from Camera Direct illumination from unblocked lights only
L LL
nSDAAE ISKLNKIKII )RV(
L LLn
SDAAE ISKLNKIKII )RV(
CGVR
Graphics Lab @ Korea University
Recursive Ray Tracing
Also Trace Secondary Rays from Hit Surfaces Global illumination from mirror reflection and
transparency
TTRSL LLn
SDAAE IKIKISKLNKIKII )RV( TTRSL LLn
SDAAE IKIKISKLNKIKII )RV(
CGVR
Graphics Lab @ Korea University
Mirror Reflection
Trace Secondary Ray in Direction of Mirror Reflection Evaluate radiance along secondary ray and include it into
illumination model
TTRSL LLn
SDAAE IKIKISKLNKIKII )RV( TTRSL LLn
SDAAE IKIKISKLNKIKII )RV(
Radiancefor mirror
reflection ray
CGVR
Graphics Lab @ Korea University
Transparency
Trace Secondary Ray in Direction of Refraction Evaluate radiance along secondary ray and include it into
illumination model
TTRSL LLn
SDAAE IKIKISKLNKIKII )RV( TTRSL LLn
SDAAE IKIKISKLNKIKII )RV(
Radiance forrefraction ray
CGVR
Graphics Lab @ Korea University
Transparency
Transparency coefficient is fraction transmitted KT = 1 if object is translucent, KT = 0 if object is opaque
0 < KT < 1 if object is semi-translucent
TTRSL LLn
SDAAE IKIKISKLNKIKII )RV( TTRSL LLn
SDAAE IKIKISKLNKIKII )RV(
TransparencyCoefficient
CGVR
Graphics Lab @ Korea University
Refractive Transparency
For Thin Surfaces, Can Ignore Change in Direction Assume light travels straight through surface
LT LT
CGVR
Graphics Lab @ Korea University
Refractive Transparency
For Solid Objects, Apply Snell’s Law: r sin risin i
Lη
ηN)coscos
η
η(T
r
iri
r
i Lη
ηN)coscos
η
η(T
r
iri
r
i
CGVR
Graphics Lab @ Korea University
Summary
Direct Illumination Ray casting Usually use simple analytic approximations for light
source emission and surface reflectance
Global illumination Recursive ray tracing Incorporate shadows, mirror reflections,
and pure refractions
CGVR
Graphics Lab @ Korea University
Illumination Terminology
Radiant power [flux] (Φ) Rate at which light energy is transmitted (in Watts).
Radiant Intensity (I) Power radiated onto a unit solid angle in direction( in Watt/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)
Irradianc (E) Incident flux density on a locally planar area (in Watts/m2 )
Radiosity (B) Exitant flux density from a locally planar area ( in Watts/m2 )