Paper Summaries Any takers? Material Properties 2 Assignments - PDF document

Paper Summaries • Any takers? Material Properties 2 Assignments Projects • Proposals – Should receive feedback via e-mail by Monday. • Checkpoint 2 – Grading – Due tonight • ACCEPTED • Well….maybe Tuesday • CONDITIONALLY ACCEPTED – Any questions? • PLEASE RESUBMIT WITH MORE INFO Plan for today Computer Graphics as Virtual Photography • Material Properties real camera photo Photographic Photography: scene (captures processing print – Bi-directional reflectance distribution functions light) (BRDFs) – Advanced Illumination Models processing – Beyond BRDFs camera Computer 3D synthetic tone • Checkpoint 3 of the ray tracer model Graphics: models reproduction image (focuses simulated • Ray tracer problem session lighting) 1

Shading BRDF • Computing the light that leaves a point • Bi-directional Reflectance Function • Shading point - point under investigation = φ θ φ θ BRDF f ( , , , ) • Illumination model - function or algorithm used to r i i r r describe the reflective characteristics of a given surface. At a given point, gives relative reflected illumination in any • Shading model – algorithm for using an illumination direction with respect to incoming illumination coming from model to determine the color of a point on a surface. any direction; • For efficiency’s sake, most illumination models are Note: The θ ’s are elevation, ϕ ’s are measured about the approximations. surface normal. The i ’s refer to the incident ray; the r ’s to the reflected ray. BRDF BRDF Geometry • Can return any positive value. • Generally wavelength specific. BRDF = φ θ φ θ λ f ( , , , , ) r i i r r Anisotropic Models Anisotropic Models • Anisotropic reflection -- example • 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 2

Anisotropic Models Anisotropic Models • Ward Model [Ward92] • Ward Model - Isotropic – Designed for both accuracy and ease of use – Includes model for anisotropic reflection − γ α ρ 2 2 (tan ) / 1 e ρ = + ρ • d ( ) π πα θ δ s 2 4 cos cos diffuse specular Anisotropic Model Anisotropic Models • Ward Model -- anisotropic • 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 − γ φ α + φ α ρ 2 2 2 2 2 (tan (cos / sin / )) 1 x y e ρ = + ρ • d ( ) π πα α s θ δ cos cos 4 x y diffuse specular Anisotropic Models Ward’s Anisotropic Model • Ward Model w/ ansiotropy – α x - Standard deviation of surface slope in x- direction – α y - Standard deviation of surface slope in y- direction 3

Anisotropic Models Anisotropic Models • Ward Model - example • Other anisotropic models (all based on physics) – [Kajia85] – [Poulin90] – [He91] Photo Isotropic Anisotropic Subsurface Scattering 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 Jensen, et al • Oily patches, peacock feathers 2001 bidirectional surface scattering Subsurface Scattering distribution function (BSSDF) • Example: Skin • Relates outgoing reflectance in a given direction (at a given point) to the incoming luminance arriving at another point. Blevins,2001 4

bidirectional surface scattering BSSDF -- Examples 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 Using BSSDF Using BRDF Jensen, et al 2001 BSSDF -- Examples BSSDF -- Examples Using BSSDF Using BSSDF Using BRDF Using BRDF Jensen, et al 2001 Jensen, et al 2001 Summary • Advanced models of reflection – Anisotropic Models – BSSDF – subsurface scattering – Break. 5