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Computer Graphics SS 2014 Lighting

Computer Graphics SS 2014 Lighting. Rüdiger Westermann Lehrstuhl für Computer Graphik und Visualisierung. Lighting. Lighting models Material properties Surface orientation (normals) Light sources. Lighting models. Local

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Computer Graphics SS 2014 Lighting

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  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

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