Announcement Mike Krummhoefener Material Properties 2 RIT Alum - PDF document

Announcement  Mike Krummhoefener Material Properties 2  RIT Alum (1992)  Technical Director / Digital Artist for Pixar  will be visiting RIT:  Friday, April 13th  Gravure Press Pit (Building 7B)  9:00am (reception) / 9:30am (Q&A) Plan for today Logistics  Checkpoint 2  Material Properties  Bi-directional reflectance distribution functions  Due Today (BRDFs)  Checkpoint 3  Advanced Illumination Models  To be given today  Beyond BRDFs  Project Proposals  Checkpoint 3 of the ray tracer  All should have received e-mail feedback.  Ray tracer help Shading Computer Graphics as Virtual Photography  Computing the light that leaves a point real camera photo Photographic Photography: scene (captures processing print  Shading point - point under investigation light)  Illumination model - function or algorithm used to describe the reflective characteristics of processing a given surface.  Shading model – algorithm for using an camera Computer 3D tone synthetic illumination model to determine the color of a model Graphics: models reproduction image point on a surface. (focuses simulated  For efficiency’s sake, most illumination models lighting) are approximations. 1

BRDF BRDF Geometry  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 Anisotropic Models  Anisotropy  Can return any positive value.  Isotropic - surfaces reflect equally from any  Generally wavelength specific. direction of view  Anisotropic - reflection varies not only with angle of incidence, but also with the angle of the BRDF = f ( , , , , ) � � � � � incident light w.r.t some viewing angle. r i i r r  Surfaces considered to possess an intrinsic grain  Examples: satin, velvet, hair, brushed aluminum Ansiotropic Models Anisotropic Models  Anisotropic reflection -- example  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 Blevins Ward 2

Anisotropic Models Why does ansiotropic reflection occur?  Occurs on objects with fine grain in a  Ward Model [Ward92] given direction.  Designed for both accuracy and ease of use  Includes model for anisotropic reflection Blevins Anisotropic Models Anisotropic Model  Ward Model - Isotropic  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 2 2 ρ − (tan γ ) / α 1 e ρ = d + ρ ( • ) s π πα 2 cos θ cos δ 4 diffuse specular Anisotropic Models Anisotropic Models  Ward Model -- anisotropic  Ward Model w/ ansiotropy  α x - Standard deviation of surface slope in x-direction  α y - Standard deviation of surface slope in y-direction 2 2 2 2 2 − (tan γ (cos φ / α + sin φ / α )) ρ 1 e x y ρ = d + ρ ( • ) s π cos θ cos δ 4 πα α x y diffuse specular 3

Anisotropic Models Ward’s Anisotropic Model  Ward Model - example Photo Isotropic Anisotropic BRDF Anisotropic Models  Other anisotropic models (all based on  Simplifying Assumptions wrt the BRDF physics)  Light enters and leaves from the same point.  [Kajia85]  Not necessarily true  [Poulin90]  Subsurface scattering  Skin, marble  [He91]  Light of a given wavelength will only reflect back light of that same wavelength  Not necessarily true  Light Interference  Oily patches, peacock feathers Subsurface Scattering Subsurface Scattering  Example: Skin Jensen, et al Blevins,2001 2001 4

bidirectional surface scattering bidirectional surface scattering distribution function (BSSDF) distribution function (BSSDF)  Relates outgoing reflectance in a given direction (at a given point) to the incoming luminance arriving at another point. 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 BSSDF -- Examples BSSDF -- Examples Using BSSDF Using BRDF Jensen, et al 2001 Using BSSDF Using BRDF Jensen, et al 2001 BSSDF -- Examples BSSDF Modeling  Won Henrik Wann Jensen an academy award in 2004.  Practical model described in [Jensen, et. al. 2001] Using BSSDF Using BRDF Jensen, et al 2001 5

Using BSSRDF 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 [Hao, 2004] Light Transport Functions 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. Wikipedia Light transport functions Summary  Advanced models of reflection  Anisotropic Models  BSSDF – subsurface scattering  Complete transport functions.  Adding to ray tracer.  Break. 6