Paper Summaries Any takers? Material Properties Assignments - PDF document

Paper Summaries • Any takers? Material Properties Assignments Projects • Project feedback • Approx 22 projects • Checkpoint 2 • Listing of projects now on Web – Due next Wednesday • Presentation schedule – Any questions? – Presentations (15 min max) – Last 3 classes (week 10 + finals week) – Having trouble? Stick around after lecture. – Sign up • Email me with 1 st , 2 nd , 3 rd choices • First come first served. 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) – Illumination Models processing – Using Empirical Data camera Computer 3D synthetic tone model Graphics: models reproduction image (focuses simulated lighting) 1

Reflections Shading • Ambient – light uniformly incident from the • Computing the light that leaves a point environment • Shading point - point under investigation • Diffuse – light scattered equally in all directions • Illumination model - function or algorithm used to describe the reflective characteristics of a given • Ambient and Diffuse – color of material plays a surface. part • Shading model – algorithm for using an illumination model to determine the color of a point on a surface. • Specular – highlights connected with mirrorness • For efficiency’s sake, most illumination models are • Specular – mostly color of light approximations. Bi-directional Reflectance Functions (BRDF) BRDF Example Note: Hidden shadows Sun behind observer Sun opposite observer BRDF Example BRDF Example Note: Note: Note: Specular Hidden Specular highlights shadows highlights Sun behind observer Sun opposite observer Sun behind observer Sun opposite observer 2

BRDF BRDF Geometry • Bi-directional Reflectance Function = φ θ φ θ 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 BRDF • Can return any positive value. • Simplifying Assumptions wrt the BRDF • Generally wavelength specific. – Light enters and leaves from the same point. • Not necessarily true BRDF = φ θ φ θ λ • Subsurface scattering f ( , , , , ) • Skin, marble r i i r r – Light of a given wavelength will only reflect back light of that same wavelength • Not necessarily true • Light Interference • Oily patches, peacock feathers Illumination Models Illumination Models • Illumination model - function or algorithm • Illumination Models and Viewing Direction used to describe the reflective – Generally, BRDFs are independent of viewing characteristics of a given surface. direction – Most Illumination models take viewing • Revise to… direction into consideration – function or algorithm used in approximating the BRDF. 3

Illumination Models Illumination Models • Geometry • Geometry – N - normal vector N V H – S - direction of incoming light viewer normal – R - direction of perfect mirror reflection Half-way – H - halfway between light direction and R S viewing direction. reflection source – V - viewing direction. Illumination Models Illumination Models • Recall from Linear Algebra • Lambertian • Phong u • Cook-Torrance θ • Ward v • Many others! • = θ u v u v cos Just one reason to normalize! Illumination Models Lambertian Model • BRDF Viewer • Lambert Model – bv by Szymon Rusinkiewicz (Princeton) – Perfectly diffuse surface – http://graphics.stanford.edu/~smr/brdf/bv – reflection is constant in all directions (k d ) – SGI, Linux, and Java versions although not – Independent of viewer direction readily available for Java. I have it, if you want it, and you’ll need to load Java3D as well! 4

Lambertian Model Lambertian Model • Lambert Model • Lambert Model – why cos θ ? – Surface has differential area dA – Intensity varies with projected area on surface – Projected area = cos θ = θ = • L ( V ) L S k cos L ( V ) L k ( N S ) d S d Lambertian Model Phong Model • BRDF Viewer • Phong Model – introduces specular (mirror-like) reflections http://graphics.stanford.edu/~smr/brdf/bv – Viewer direction becomes more important – three components • ambient - background light (k a ) • diffuse - Lambertian reflection (k d ) • specular – mirror-like reflection(k s ) Phong Model Phong-Blinn Model – Uses halfway angle rather than reflected ∑ ∑ = + • + • k L ( V ) k L k L ( S N) k L ( R V) e a a d i i s i i i i ∑ ∑ = + • + • ambient k diffuse specular L ( V ) k L k L ( S N) k L ( H V) e a a d i i s i i i i ambient diffuse specular Note: L n are radiance terms, include both light and material info 5

Phong-Blinn Model Cook-Torrance Model – based on physics of a surface • BRDF Viewer • Actually developed by Torrance & Sparrow, http://graphics.stanford.edu/~smr/brdf/bv physicists. • Jim Blinn was the first to apply to CG • Cook & Torrance’s was the first complete implementation – components • microfacet model - describes geometry of surface • Fresnel term - describes reflectance • Roughness - describes microfacet distribution. Cook-Torrance Model Cook-Torrance Model • Microfacets • Microfacets – surface is composed of V shaped grooves (microfacets) – Light interactions with microfacets • Reflect - causes specular reflections • Scatter - causes diffuse reflections Cook-Torrance Model Cook-Torrance Model • Microfacets – GeometryTerm • Fresnel Equation for polarized light – Some microfacets may shadow others – Describes reflectance as a function of: • Wavelength of incident light ( λ ) • Index of refraction ( η ( λ )) • Extinction coefficient (ease at which wave can penetrate a surface) ( κ ( λ )) • Angle of incidence ( θ ) ⎧ • • • • ⎫ 2 ( N H)(N V) 2 ( N H)(N S) = ⎨ ⎬ G min 1 , , • • ⎩ ⎭ (V H) (V H) Note: S from before is the L in these diagrams 6

Cook-Torrance Model Cook-Torrance Model • Fresnel equations for polarized light • Fresnel + − θ + θ 2 2 2 a b 2 a cos cos = Perpendicular component – If all quantities known, use Fresnel equations Fs + + θ + θ 2 2 2 a b 2 a cos cos – If not, approximate using reflectance off normal • See [Glassner] or [Cook/Torrance81] for details + − θ θ + θ θ 2 2 2 2 a b 2 a sin tan sin tan Parallel component = F F p s + + θ θ + θ θ 2 2 2 2 a b 2 a sin tan sin tan a, b are functions 1 1 = + of η , κ , and θ F F F s p 2 2 η , κ are functions F is total reflectance of λ Cook-Torrance Model Cook-Torrance Model • Roughness • Roughness – Characterizes the distribution of the slopes of the microfacets – Roughness parameter, m • m between 0 -1 • small m - smooth surface, specular reflectance − α − α 2 = 2 ((tan ) / m ) ( / m ) e • large m - rough surface, diffuse reflectance D ce = D α 2 4 m cos – Statistical models Gaussian Model Beekman Model c is arbitrary constant Cook-Torrance Model Cook-Torrance Model • Roughness • Putting it all together = + f sf df r s d specular diffuse total reflectance × × 1 1 F D G = = f f s π d π • • ( N S)(N V) Where D is the roughness function, F is the Fresnel function, and G is the geometrical attenuation factor from previous pages 7

Cook-Torrance Model Cook-Torrance Models • Complete Cook-Torrance Model • examples ∑ = + • ϖ L L R L ( N S i )( f ) d r a a i r i i � Parameters for f r : � m – roughness value � Type of material (determines terms for Fresnel eqn) � Wavelength of incident light (determines terms for Fresnel eqn) � Diffuse / specular contribution constants � L a R a is the ambient radiance reflected by R a � L i is the light’s radiance Cook-Torrance Models Cook-Torrance Model • Summary • BRDF Viewer – Complicated model based on physics http://graphics.stanford.edu/~smr/brdf/bv – Components • Microfacets • Fresnel equation • Roughness – Want accuracy? Go to the source! • Break. 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 8