Welcome back Lots of logistics to take care of: Readings Grad - PDF document

Material Properties 2 Welcome back  Lots of logistics to take care of:  Readings  Grad Report  Assignments  Projects 1

Readings  All readings up to week 3 graded  Comments/grades on mycourses  Remember to place this weeks in the dropbox. Grad Report  Topic due tonight.  Please place short description in dropbox. 2

Projects  Proposals  Proposal due before break (please get yours in if not submitted)  Feedback on proposals -- mycourses  Web sites please.  23 projects (4-5 more expected) Projects  Presentations:  Dates:  Week 10: Mon, Feb 18  Week 10: Wed, Feb 20  Finals Week / Week 11: Mon, Feb 25  WE WILL NEED AN EXTRA DAY  Week 11 or Week 9?  15 minutes / presentation  Schedule on Web by next class  Please send me choice of time/day 3

Assignments  Checkpoint 1 - Setting the scene  All graded  Checkpoint 2 - Camera  Due tonight.  Checkpoint 3 - Basic shading  To be given tonight. Plan for today  Material Properties  Bi-directional reflectance distribution functions (BRDFs)  Advanced Illumination Models  Beyond BRDFs  Checkpoint 3 of the ray tracer  Ray tracer help  Questions 4

Computer Graphics as Virtual Photography real camera photo Photographic Photography: scene (captures processing print light) processing camera Computer 3D synthetic tone model Graphics: models image reproduction (focuses simulated lighting) Shading  Computing the light that leaves a point  Shading point - point under investigation  Illumination model - function or algorithm used to describe the reflective characteristics of a given surface.  Shading model – algorithm for using an illumination model to determine the color of a point on a surface.  For efficiency’s sake, most illumination models are approximations. 5

BRDF  Bi-directional Reflectance Function BRDF f ( , , , ) = � � � � r i i r r At a given point, gives relative reflected illumination in any direction with respect to incoming illumination coming from any direction; Note: The θ ’s are elevation, ϕ ’s are measured about the surface normal. The i ’s refer to the incident ray; the r ’s to the reflected ray. BRDF Geometry 6

BRDF  Can return any positive value.  Generally wavelength specific. BRDF = f ( , , , , ) � � � � � r i i r r Anisotropic Models  Anisotropy  Isotropic - surfaces reflect equally from any direction of view  Anisotropic - reflection varies not only with angle of incidence, but also with the angle of the incident light w.r.t some viewing angle.  Surfaces considered to possess an intrinsic grain  Examples: satin, velvet, hair, brushed aluminum 7

Ansiotropic Models  anisotropic (adj.) an · i · so · trop · ic 1. Physics. of unequal physical properties along different axes.  http://www.neilblevins.com/cg_educatio n/aniso_ref/aniso_ref.htm Anisotropic Models  Anisotropic reflection -- example Blevins Ward 8

Why does ansiotropic reflection occur?  Occurs on objects with fine grain in a given direction. Blevins Anisotropic Models  Ward Model [Ward92]  Designed for both accuracy and ease of use  Includes model for anisotropic reflection 9

Anisotropic Models  Ward Model - Isotropic 2 2 − (tan γ ) / α ρ 1 e ρ = d + ρ ( • ) s 2 π πα θ δ 4 cos cos diffuse specular Anisotropic Model  Ward Model  ρ d - Diffuse reflectance coefficient (can vary with wavelength)  ρ s - Specular reflectance coefficient (can vary with wavelength)  α - Standard deviation of surface slope 10

Anisotropic Models  Ward Model -- anisotropic 2 2 2 2 2 − (tan γ (cos φ / α + sin φ / α )) ρ 1 e x y d ρ = + ρ ( • ) s π cos θ cos δ 4 πα α x y diffuse specular Anisotropic Models  Ward Model w/ ansiotropy  α x - Standard deviation of surface slope in x-direction  α y - Standard deviation of surface slope in y-direction 11

Ward’s Anisotropic Model Anisotropic Models  Ward Model - example Photo Isotropic Anisotropic 12

Anisotropic Models  Other anisotropic models (all based on physics)  [Kajia85]  [Poulin90]  [He91] BRDF  Simplifying Assumptions wrt the BRDF  Light enters and leaves from the same point.  Not necessarily true  Subsurface scattering  Skin, marble  Light of a given wavelength will only reflect back light of that same wavelength  Not necessarily true  Light Interference  Oily patches, peacock feathers 13

Subsurface Scattering Jensen, et al 2001 Subsurface Scattering  Example: Skin Blevins,2001 14

bidirectional surface scattering distribution function (BSSDF)  Relates outgoing reflectance in a given direction (at a given point) to the incoming luminance arriving at another point. bidirectional surface scattering distribution function (BSSDF) incoming BSSDF Outgoing luminance at x i luminance at x o in the direction in the direction of w i of w o When x o == x i the BSSDF is simply a BRDF 15

BSSDF -- Examples Using BSSDF Using BRDF Jensen, et al 2001 BSSDF -- Examples Using BSSDF Using BRDF Jensen, et al 2001 16

BSSDF -- Examples Using BSSDF Using BRDF Jensen, et al 2001 BSSDF Modeling  Won Henrik Wann Jensen an academy award in 2004.  Practical model described in [Jensen, et. al. 2001] 17

Using BSSRDF [Hao, 2004] Light transport functions  BSSRDF (Bidirectional surface scattering reflectance distribution function) describes the relation between outgoing radiance and the incident flux, including the phenomena like subsurface scattering (SSS).  BRDF (Bidirectional reflectance distribution function) is a simplified BSSRDF, assuming that light enters and leaves at the same point 18

Light Transport Functions Wikipedia Light transport functions  BTDF (Bidirectional transmittance distribution function) is similar to BRDF but for the opposite side of the surface. (see the top image).  BSDF (Bidirectional scattering distribution function) is the most general function. 19

Light transport functions Summary  Advanced models of reflection  Anisotropic Models  BSSDF – subsurface scattering  Complete transport functions.  Adding to ray tracer.  Break. 20