computer graphics iii
play

Computer graphics III Light reflection, BRDF Jaroslav Kivnek, MFF - PowerPoint PPT Presentation

Computer graphics III Light reflection, BRDF Jaroslav Kivnek, MFF UK Jaroslav.Krivanek@mff.cuni.cz Basic radiometric quantities Image: Wojciech Jarosz CG III (NPGR010) - J. Kivnek 2015 Interaction of light with a surface


  1. Computer graphics III – Light reflection, BRDF Jaroslav Křivánek, MFF UK Jaroslav.Krivanek@mff.cuni.cz

  2. Basic radiometric quantities Image: Wojciech Jarosz CG III (NPGR010) - J. Křivánek 2015

  3. Interaction of light with a surface  Absorption  Reflection  Transmission / refraction  Reflective properties of materials determine  the relation of reflected radiance L r to incoming radiance L i , and therefore  the appearance of the object: color, glossiness, etc. CG III (NPGR010) - J. Křivánek 2015

  4. Interaction of light with a surface  Same illumination  Different materials Source: MERL BRDF database CG III (NPGR010) - J. Křivánek 2015

  5. BRDF – Formal definition  B idirectional R eflectance D istribution F unction n L i ( w i ) „ o utgoing “ L r ( w o ) d w i q i q o „ i ncoming“ „ r eflected “ w d L ( )  w  w  1 f r ( ) r o [ sr ] i o w  q  w L ( ) cos d i i i i 5

  6. BRDF  Mathematical model of the reflection properties of a surface  Intuition  Value of a BRDF = probability density , describing the event that a light energy “packet”, or “photon” , coming from direction w i gets reflected to the direction w o .   w  w   f ( ) 0 ,  Range: r i o CG III (NPGR010) - J. Křivánek 2015

  7. BRDF Westin et al. Predicting Reflectance Functions from Complex Surfaces, SIGGRAPH 1992.  The BRDF is a model of the bulk behavior of light on the microstructure when viewed from distance CG III (NPGR010) - J. Křivánek 2015

  8. BRDF properties  Helmholz reciprocity (always holds in nature, a physically-plausible BRDF model must follow it) w  w  w  w f ( ) f ( ) r i o r o i CG III (NPGR010) - J. Křivánek 2015

  9. BRDF properties  Energy conservation  A patch of surface cannot reflect more light energy than it receives CG III (NPGR010) - J. Křivánek 2015

  10. BRDF (an)isotropy  Isotropic BRDF = invariant to a rotation around surface normal     q  q   q    q    f , ; , f , ; , r i i o o r i i o o    q q    f , , r i o o i CG III (NPGR010) - J. Křivánek 2015

  11. Surfaces with anisotropic BRDF CG III (NPGR010) - J. Křivánek 2015

  12. Anisotropic BRDF  Different microscopic roughness in different directions (brushed metals, fabrics , …) CG III (NPGR010) - J. Křivánek 2015

  13. Isotropic vs. anisotropic BRDF  Isotropic BRDFs have only 3 degrees of freedom  Instead of  i and  o it is enough to consider only D   i –  o  But this is not enough to describe an anisotropic BRDF  Description of an anisotropic BRDF   i and  o are expressed in a local coordinate frame ( U , V , N ) U … tangent – e.g. the direction of brushing  V … binormal  N … surface normal … the Z axis of the local coordinate frame  CG III (NPGR010) - J. Křivánek 2015

  14. Reflection equation  A.k.a. reflectance equation, illumination integral, OVTIGRE (“ outgoing, vacuum, time-invariant, gray radiance equation ”)  “How much total light gets reflected in the direction w o ?“  From the definition of the BRDF, we have w  w  w  w  q w d L ( ) f ( ) L ( ) cos d r o r i o i i i i CG III (NPGR010) - J. Křivánek 2015

  15. Reflection equation  Total reflected radiance: integrate contributions of incident radiance, weighted by the BRDF, over the hemisphere  w  w  w  w  q w L ( ) L ( ) f ( ) cos d r o i i r i o i i H ( x ) upper hemisphere over x = CG III (NPGR010) - J. Křivánek 2015

  16. Reflection equation  Evaluating the reflectance equation renders images!!!  Direct illumination Environment maps  Area light sources  etc.  CG III (NPGR010) - J. Křivánek 2015

  17. Energy conservation – More rigorous  Reflected flux per unit area (i.e. radiosity B ) cannot be larger than the incoming flux per unit surface area (i.e. irradiance E ).  w q w L ( ) cos d B r o o o    w q w E L ( ) cos d i i i i     w  w w q w q w f ( ) L ( ) cos d cos d r i o i i i i o o    w q w L ( ) cos d i i i i  1 CG III (NPGR010) - J. Křivánek 2015

  18. Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) 18 Souce: Ngan et al. Experimental analysis of BRDF models, http://people.csail.mit.edu/addy/research/brdf/

  19. Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) 19 Souce: Ngan et al. Experimental analysis of BRDF models, http://people.csail.mit.edu/addy/research/brdf/

  20. Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) 20 Souce: Ngan et al. Experimental analysis of BRDF models, http://people.csail.mit.edu/addy/research/brdf/

  21. Surface appearance and the BRDF Appearance BRDF lobe (for four different viewing directions) 21 Souce: Ngan et al. Experimental analysis of BRDF models, http://people.csail.mit.edu/addy/research/brdf/

  22. Reflectance  Ratio of the incoming and outgoing flux  A.k.a . „albedo“ ( used mostly for diffuse reflection)  Hemispherical-hemispherical reflectance  See the “Energy conservation” slide  Hemispherical-directional reflectance  The amount of light that gets reflected in direction w o when illuminated by the unit, uniform incoming radiance.   w  w  w  w q w ( ) a ( ) f ( ) cos d o o r i o i i H ( x ) CG III (NPGR010) - J. Křivánek 2015

  23. Hemispherical-directional reflectance  Nonnegative    w o  ( ) 0 , 1  Less than or equal to 1 (energy conservation)  Equal to directional-hemispherical reflectance  What is the percentage of the energy coming from the incoming direction w i that gets reflected (to any direction )?“  Equality follows from the Helmholz reciprocity CG III (NPGR010) - J. Křivánek 2015

  24. CG III (NPGR010) - J. Křivánek 2015

  25. CG III (NPGR010) - J. Křivánek 2015

  26. BRDF components General BRDF Ideal diffuse Ideal specular Glossy, (Lambertian) directional diffuse CG III (NPGR010) - J. Křivánek 2015

  27. Ideal diffuse reflection

  28. Ideal diffuse reflection CG III (NPGR010) - J. Křivánek 2015

  29. Ideal diffuse reflection  A.k.a. Lambertian reflection Johann Heinrich Lambert, „ Photometria “ , 1760.   Postulate: Light gets reflected to all directions with the same probability, irrespective of the direction it came from  The corresponding BRDF is a constant function (independent of w i , w o ) w  w  f ( ) f r , d i o r , d CG III (NPGR010) - J. Křivánek 2015

  30. Ideal diffuse reflection  Reflection on a Lambertian surface:  w  w q w L ( ) f L ( ) cos d o o r , d i i i i H ( x )  f E r , d irradiance  View independent appearance  Outgoing radiance L o is independent of w o  Reflectance (derive)     f , d r d CG III (NPGR010) - J. Křivánek 2015

  31. Ideal diffuse reflection  Mathematical idealization that does not exist in nature  The actual behavior of natural materials deviates from the Lambertian assumption especially for grazing incidence angles CG III (NPGR010) - J. Křivánek 2015

  32. White-out conditions  Under a covered sky we cannot tell the shape of a terrain covered by snow  We do not have this problem close to a localized light source.  Why? CG III (NPGR010) - J. Křivánek 2015

  33. White-out conditions  We assume sky radiance independent of direction (covered sky) w  sky L ( x , ) L i i  We also assume Lambertian reflection on snow  Reflected radiance given by:    snow snow sky L L o d i White-out!!! CG III (NPGR010) - J. Křivánek 2015

  34. Ideal mirror reflection

  35. Ideal mirror reflection CG III (NPGR010) - J. Křivánek 2015

  36. CG III (NPGR010) - J. Křivánek 2015

  37. CG III (NPGR010) - J. Křivánek 2015 Nishino, Nayar: Eyes for Relighting, SIGGRAPH 2004

  38. The law of reflection n  o q i q o  i q o  q i  o   i +  mod 2   Direction of the reflected ray (derive the formula) w  w   w 2 ( n ) n o i i CG III (NPGR010) - J. Křivánek 2015

  39. Digression: Dirac delta distribution  Definition (informal): Image: Wikipedia  The following holds for any f :  Delta distribution is not a function (otherwise the integrals would = 0) CG III (NPGR010) - J. Křivánek 2015

  40. BRDF of the ideal mirror  BRDF of the ideal mirror is a Dirac delta distribution We want: n q o  q i q   q q    L ( , ) R ( ) L ( , ) q i q o r o o i i o o Fresnel reflectance (see below)  q  q       (cos cos ) ( ) q  q   R q f ( , ; , ) ( ) i o i o r , m i i o o i q cos i CG III (NPGR010) - J. Křivánek 2015

Recommend


More recommend