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

Technische Universität München Computer Graphics Lighting Lighting models Material properties Surface orientation (normals) Light sources 2

Technische Universität München Computer Graphics 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 3 eye

Technische Universität München Computer Graphics 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 4

Technische Universität München Computer Graphics Lighting models Scene description must contain –Geometry: surface and volumes –Light sources: position, orientation, power –Surface properties: reflection properties 5

Technische Universität München Computer Graphics Radiative transfer Simulation of the interaction between light and matter –Radiative transfer 6 Interface between materials Volumetric medium

Technische Universität München Computer Graphics 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 7

Technische Universität München Computer Graphics Radiative transfer Simulation of light-matter interaction 8

Technische Universität München Computer Graphics Radiative transfer Simulation of light-matter interaction 9

Technische Universität München Computer Graphics Radiative transfer Simulation of volumetric effects 10

Technische Universität München Computer Graphics 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=h h: Planck constant v: frequency of light wave –Given all material properties, the radiant intensity can be computed from the transfer equation 11

Technische Universität München Computer Graphics 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 12

Technische Universität München Computer Graphics 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 13

Technische Universität München Computer Graphics 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/m 2 ] Ausgehende Flussdichte: radiosity (radiant exitance ) power per area in [W/m 2 ] 14

Technische Universität München Computer Graphics Radiometric quantities Strahlungsintensität (radiant intensity) power per solid angle in [W/sr] sr (steradian): unit for solid angle A 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 = r 2 subtends one steradian. 15

Technische Universität München Computer Graphics Radiometric quantities Strahlungsintensität (radiant intensity) power per solid angle in [W/sr] 16

Technische Universität München Computer Graphics Radiometric quantities The radiant power emitted by a (differential) projected surface element in the direction of a (differential) solid angle 17

Technische Universität München Computer Graphics Radiometric quantities 18 BeschreibungDefinitionZeichenEinheitenBezeichnung Energie energy QeQe [J] JouleStrahlungsenergie radiant energy Leistung, Fluss power, flux dQ/dt ee [W= J/s]Strahlungsfluss radiant flux Flussdichte flux density dQ/dAdtEeEe [W/m 2 ]Bestrahlungsstärke irradiance Flussdichte flux density dQ/dAdtM e = B e [W/m 2 ]radiom. Emissionsvermögen radiosity Radiant density dQ/dA  d  d t LeLe [W/m 2 sr]Strahlungsdichte radiance Intensität intensity dQ/d  dt IeIe [W/sr]Strahlungsstärke radiant intensity

Technische Universität München Computer Graphics 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 19

Technische Universität München Computer Graphics Light sources Effects of different light sources 20

Technische Universität München Computer Graphics 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) 21 umbra penumbra

Technische Universität München Computer Graphics Light sources 22

Technische Universität München Computer Graphics 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 23 dAdA dA´dA´ LiLi

Technische Universität München Computer Graphics 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 24 ii ii oo oo

Technische Universität München Computer Graphics Material properties The reflection at a surface point is described by the BRDF 25 ii ii oo oo

Technische Universität München Computer Graphics Material properties Properties of the BRDF –In general, it is a 6-dimensional function 2 surface parameters, 2 x 2 direction parameters 26

Technische Universität München Computer Graphics 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 27

Technische Universität München Computer Graphics 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 28

Technische Universität München Computer Graphics The Rendering equation 29