Technische Universität München Fakultät für Informatik Computer Graphics SS 2014 Lighting Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung

Technische Universität München

Fakultät für Informatik

Computer GraphicsSS 2014

Lighting

Rüdiger WestermannLehrstuhl für Computer Graphik und Visualisierung


Computer Graphics

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Lighting

• Lighting models• Material properties• Surface orientation (normals)• Light sources


Computer Graphics

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Lighting models

• Local– Consider only the direct illumination by point light sources,

independent of any other object, i.e. no shadows

• Global– Interaction with matter– Consider indirect effects, including multiple reflections,

transmission, shadows

eye

eye


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Lighting models

• Physics-based lighting– Use correct units of measurement from physics– Obey material physics, includes reflection models– Numerical simulation of light transport taking into account

visibility (do two points see each other)

– Result: reflected light at the visible points in the scene as illuminated (directly and indirectly) by the light sources


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Lighting models

• Scene description must contain– Geometry: surface and volumes– Light sources: position, orientation, power– Surface properties: reflection properties


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Radiative transfer

• Simulation of the interaction between light and matter– Radiative transfer

Interface between materials Volumetric medium


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Radiative transfer

• Simulation of light-matter interaction– In volumes: volume rendering using in-volume scattering– At surfaces: absorption, reflection and refraction

• Traditional computer graphics:– Surface graphics with vacuum in between, no interaction– Scattering only at surfaces


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Radiative transfer

• Simulation of light-matter interaction


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Radiative transfer

• Simulation of light-matter interaction


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Radiative transfer

• Simulation of volumetric effects


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Radiative transfer

• Radiative transfer describes the changes of radiant intensity due to absorption, emission and scattering

• Expressed by equation of transfer– Photons have energy: E=hn

• h: Planck constant• v: frequency of light wave

– Given all material properties, the radiant intensity can be computed from the transfer equation


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Radiative transfer

• How to simulate radiative transfer?• Wave-particle dualism tells us that light exhibits

properties of both waves and of particles– Wave optics: diffraction, interference, polarization– Ray (geometric) optics: direction, position

• Assumption: structures are large with respect to wavelength of light

• Light as a set of light rays• Standard in CG


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Radiative transfer

• Light is treated as a physical, i.e. radiometric, quantity– Radiometry: the measurement of electromagnetic radiation in

the visible range, ie. light– Photometry: the measurement of the visual sensation

produced by electromagnetic radiation– Photometry is like radiometry except that everything is

weighted by the spectral response of the eye


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Radiometric quantities

Strahlungsenergie: radiant energy Q in Joule [J] Strahlungsleistung oder -fluss:

radiant flux or power in Watt [W=J/s]

Einfallende Flussdichte: irradiance (incident)power per area in [W/m2]

Ausgehende Flussdichte: radiosity (radiant exitance)power per area in [W/m2]

dt

dQ

dA

dE

dA

dB


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Strahlungsintensität (radiant intensity) power per solid angle in [W/sr]

dI

d

sr (steradian): unit for solid angleA steradian can be defined as the solid angle subtended at the center of a unit sphere by a unit area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian.


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Strahlungsintensität (radiant intensity) power per solid angle in [W/sr]

dI

d

Because the surface area of a sphere is , the definition implies that a sphere measures 4π ≈ 12.56637 steradians. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr (en.wikipedia.org/wiki/Steradiant)

http://de.wikipedia.org/wiki/Steradiant




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Radiance (Strahlungsdichte)

power per solid angle per projected area element in [W/m2sr]

The radiant power emitted by a (differential) projected surface element in the direction of a (differential) solid angle


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Beschreibung Definition Zeichen Einheiten Bezeichnung

Energieenergy

Qe [J] Joule Strahlungsenergieradiant energy

Leistung, Flusspower, flux

dQ/dt e [W= J/s] Strahlungsflussradiant flux

Flussdichteflux density

dQ/dAdt Ee [W/m2] Bestrahlungsstärkeirradiance

Flussdichteflux density

dQ/dAdt Me = Be [W/m2] radiom. Emissionsvermögenradiosity

Radiantdensity

dQ/dAddt Le [W/m2sr] Strahlungsdichteradiance

Intensitätintensity

dQ/ddt Ie [W/sr] Strahlungsstärkeradiant intensity


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Light sources

• Directional (parallel) lights– E.g. sun– Specified by direction

• Point lights– Same intensity in all directions– Specified by position

• Spot lights– Limited set of directions– Point + direction + cutoff angle


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Light sources

• Effects of different light sources


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Light sources

• Area lights– Light sources with a finite area– Can be considered a continuum of point lights– Hard to simulate (see later in course)

umbra

penumbra


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Light sources

• Quadratic falloff for isotropic point light sources– Assume light source with power – Light source’s radiant intensity: [– Flux along a (differential) solid angle:

– Irradiance on a differential surface element at distance r:

24 r

2)2(4 r


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Surface orientation

Johann Friedrich Lambert (1783):Power per unit area arriving at some object point x also depends on the angle of the surface to the light direction

dA

dA´

Li

𝜃Effectively litarea: dA

dA´= dA cos

𝜃

dLln

dLlndE

i

i

)()(

)()),(cos(

n


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Material properties

• The reflection at a surface point is described by the BRDF [1/sr]– BRDF: Bidirectional Reflection Distribution Function– Describes the fraction of the light from an incoming direction

i that is reflected into an outgoing direction r

– Color channels RGB treated separately– Directions are specified

by 2 angles• Angle to the normal• Angle around the normal

i

io

o

iω

rω

n

t

b


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Material properties

• The reflection at a surface point is described by the BRDF

( )( , )

( ) cos( )r r

r i ri i i i

dLf

L d

i

io

o

iω

rω

n

t

b


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Material properties

• Properties of the BRDF– In general, it is a 6-dimensional function

• 2 surface parameters, 2 x 2 direction parameters

( , )r i rf x


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Material properties

• It is often simplified by assuming the BRDF to be constant across an isotropic material– Isotropy implies that the BRDF is invariant under rotations

around the normal vector– Then, the BRDF is only a 3-dimensional function

• The validity of certain physical laws has to be guaranteed by the BRDF


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Material properties

• Range– 0 (Absorption) to (mirror reflections)

• Helmholtz Reciprocity– Light ray can be inverted

• Energy conservation– Sum of all outgoing energy does not exceed incoming energy

( , , ) ( , , )r i r r r if x f x

( , , ) cos 1 ,r i r i r if x θ dω x


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The Rendering equation

• Outgoing radiance at a point x into direction r

– Here, Le is the shelf-emission at the point

• This is what we have to evaluate in physics-based rendering

Documents

Technische Universität München Fakultät für Informatik Computer Graphics SS 2014 Lighting Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung