Computer Graphics SS 2014 Lighting

1. Computer Graphics SS 2014 Lighting Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung

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

3. 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

4. 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 twopointsseeeachother) • Result: reflected light atthevisiblepoints in thesceneasilluminated (directlyandindirectly) bythe light sources

5. Lighting models • Scene description must contain • Geometry: surface and volumes • Light sources: position, orientation, power • Surface properties: reflection properties

6. Radiative transfer • Simulation oftheinteractionbetween light and matter • Radiativetransfer Interface between materials Volumetric medium

7. Radiative transfer • Simulation oflight-matter interaction • In volumes: volumerenderingusing in-volume scattering • Atsurfaces: absorption, reflectionandrefraction • Traditional computergraphics: • Surfacegraphicswithvacuum in between, nointeraction • Scatteringonly at surfaces

8. Radiative transfer • Simulation of light-matter interaction

9. Radiative transfer • Simulation of light-matter interaction

10. Radiative transfer • Simulation ofvolumetriceffects

11. Radiative transfer • Radiativetransferdescribesthechangesofradiantintensitydue toabsorption, emission and scattering • Expressedbyequationoftransfer • Photons haveenergy: E=hn • h: Planck constant • v: frequencyoflightwave • Given all material properties, theradiantintensitycanbecomputedfromthetransferequation

12. Radiative transfer • Howtosimulateradiativetransfer? • Wave-particledualismtellsusthatlightexhibits properties of both waves and of particles • Wave optics: diffraction, interference, polarization • Ray (geometric) optics: direction, position • Assumption: structuresare large withrespecttowavelengthoflight • Light as a setoflightrays • Standard in CG

13. Radiative transfer • Light istreatedas a physical, i.e. radiometric, quantity • Radiometry: themeasurementofelectromagneticradiation in thevisiblerange, ie. light • Photometry:themeasurementofthevisualsensationproducedbyelectromagneticradiation • Photometryislikeradiometryexceptthateverythingisweightedbythespectralresponseoftheeye

14. Radiometric quantities Strahlungsenergie: radiantenergyQin Joule [J] Strahlungsleistung oder -fluss: radiantfluxor power in Watt [W=J/s] Einfallende Flussdichte: irradiance (incident) power per area in [W/m2] Ausgehende Flussdichte: radiosity (radiantexitance) power per area in [W/m2]

15. Radiometric quantities Strahlungsintensität (radiantintensity) power per solid angle in [W/sr] sr (steradian): unitfor 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.

16. Radiometric quantities Strahlungsintensität (radiantintensity) power per solid angle in [W/sr] 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)

17. Radiometric quantities Radiance (Strahlungsdichte) power per solid angle per projectedareaelement in [W/m2sr] The radiant power emitted by a (differential) projected surface element in the direction of a (differential) solid angle

18. Radiometric quantities

19. 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

20. Light sources • Effects of different light sources

21. 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

22. Light sources • Quadratic falloff for isotropic point light sources • Assume light source with power • Light source’s radiant intensity: [ • Fluxalong a (differential) solid angle: • Irradiance on a differential surface element at distance r:

23. 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 Li Effectivelylit area: dA dA´= dAcos dA´ dA

24. 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 ithat 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 o i o

25. Material properties • The reflection at a surface point is described by the BRDF i o i o

26. Material properties • Properties of the BRDF • In general, it is a 6-dimensional function • 2 surface parameters, 2 x 2 direction parameters

27. Material properties • It is often simplified by assuming the BRDF to be constant across anisotropicmaterial • Isotropy implies that the BRDF is invariant under rotations around the normal vector • Then, the BRDF is only a 3-dimensionalfunction • The validity of certain physical laws has to be guaranteed by the BRDF

28. Material properties • Range • 0 (Absorption) to (mirrorreflections) • Helmholtz Reciprocity • Light raycanbeinverted • Energyconservation • Sumof all outgoingenergydoes not exceedincomingenergy

29. The Rendering equation • Outgoingradianceat a pointxintodirectionr • Here, Leistheshelf-emissionat thepoint • This iswhatwehavetoevaluate in physics-basedrendering