Shading I June 22, 1999
Motivational Film ✔ Graphic Violence – Gritz, Bergen, Darken (1991) – first use of BMRT ✔ Mr Will Goes Sailing June 22, 1999
Logistics ✔ Projects – Returned proposals – Proposal comments • Accept / Please Resubmit • Recall: Projects will be judged on what is in the proposal – Reminder: Report is bulk of project – Resubmitted proposals due next class June 22, 1999
Logistics ✔ Projects – Using Java3d/VRML/directX/…. • These are tools (much like “C”) • Need specifics of what you want to do with it. • Best way to learn is to implement something…be clear on what that something is. • I need to know what to expect from your project and presentation. June 22, 1999
Logistics ✔ Paper summaries on Shading I – Any takers? ✔ Slides on Web – Now in B&W and Color June 22, 1999
Photography and Light pho•tog•ra•phy, n ., the process or art of producing images of objects by the action of light on a sensitized surface, esp, a film in a camera. Yeah, we get it…photography, light…whatever.. June 22, 1999
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) June 22, 1999
Today’s Class ✔ Shading – Bidirectional reflectance distribution functions (BRDFs) – Shading Models – Using Empirical Data June 22, 1999
Shading ✔ Computing the light that leaves a point ✔ Shading point - point under investigation ✔ Shading model - function or algorithm used in determining the shading. ✔ For efficiency’s sake, most shading models are approximations. June 22, 1999
BDRF ✔ Bidirectional Reflectance Function ( , , , ) = φ θ φ θ BDRF 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 June 22, 1999
BDRF ✔ BDRF Geometry June 22, 1999
BDRF ✔ Can return any positive value. ✔ Generally wavelength specific. ( , , , , ) BDRF = φ θ φ θ λ f r i i r r June 22, 1999
Shading Models ✔ Shading model - function or algorithm used in determining the shading. ✔ Revise to… – function or algorithm used in approximating the BDRF. June 22, 1999
Shading Models ✔ Shading Models and Viewing Direction – Generally, BRDFs are independent of viewing direction – Most shading models take viewing direction into consideration June 22, 1999
Shading Models ✔ Geometry June 22, 1999
Shading Models ✔ Geometry – N - normal vector – S - direction of incoming light – R - direction of perfect mirror reflection – H - halfway between light direction and viewing direction. – V - viewing direction. June 22, 1999
Shading Models ✔ Recall from Linear Algebra u θ v u v u v cos • = θ June 22, 1999
Shading Models ✔ Lambertian ✔ Phong ✔ Cook-Torrance ✔ Strauss ✔ Ward June 22, 1999
Shading Models ✔ Lambert Model – Perfectly diffuse surface – reflection is constant in all directions (k d ) June 22, 1999
Shading Models ✔ Lambert Model ( ) cos ( ) ( ) = θ = • L V L S k L V L k N S d S d June 22, 1999
Shading Model ✔ Lambert Model – why cos θ ? – Surface has differential area dA – Intensity varies with projected area on surface – Projected area = cos θ June 22, 1999
Shading Models ✔ Phong Model – introduces specular (mirror like) reflections – three components • ambient - background light (k a ) • diffuse - lamberian reflection (k d ) • specular - mirror like reflection(k s ) June 22, 1999
Shading Models ✔ Phong Model ∑ ∑ ( ) ( S N) ( R V) = + • + • k L V k L k L k L e a a d i i s i i i i � � � � � � � � � � � � � � � � � ambient diffuse specular June 22, 1999
Shading Models ✔ Phong - Blinn – Uses halfway angle rather than reflected ∑ ∑ ( ) ( S N) ( H V) = + • + • k L V k L k L k L e a a d i i s i i i i � � � � � � � � � � � � � � � � � ambient diffuse specular June 22, 1999
Shading Models ✔ Any questions – diffuse vs specular reflections ✔ Move on to Cook - Torrance model. June 22, 1999
Shading Models ✔ Cook-Torrance Model – based on physics of a surface – components • microfacet model - describes geometry of surface • Fresnel term - describes reflectance • Roughness - describes microfacet distribution. June 22, 1999
Shading Models ✔ Cook-Torrance / Microfacets – surface is composed of V shaped grooves (microfacets) – Light interactions with microfacets • Reflect - causes specular reflections • Scatter - causes diffuse reflections June 22, 1999
Shading Models ✔ Cook-Torrance / Microfacets June 22, 1999
Shading Models ✔ Cook-Torrance / Microfacets - GeometryTerm 2 ( N H)(N V) 2 ( N H)(N S) • • • • min 1 , , = G (V H) (V H) • • June 22, 1999
Shading Model ✔ Cook-Torrance / Fresnel Equation – Describes reflectance – 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 ) June 22, 1999
Shading Models ✔ Fresnel Equations 2 2 2 cos cos 2 + − θ + θ a b a = F s 2 2 2 2 cos cos + + θ + θ a b a 2 2 2 2 + − 2 sin θ tan θ + sin θ tan θ a b a = F F p s 2 2 2 sin tan sin 2 tan 2 + + θ θ + θ θ a b a 1 1 a, b are functions = + F F F of η , κ , and θ s p 2 2 For unpolarized light June 22, 1999
Shading Models ✔ Cook-Torrance / Fresnel – If all quantities known, use Fresnel equations – If not, approximate using reflectance off normal • See [Glassner] or [Cook/Torrance81] for details June 22, 1999
Shading Model ✔ Cook-Torrance / Roughness – Characterizes the distribution of the slopes of the microfacets – Roughness parameter, m • m between 0 -1 • small m - smooth surface, specular reflectance • large m - rough surface, diffuse reflectance June 22, 1999
Shading Model ✔ Cook-Torrance / Roughness 2 − ((tan γ ) / ) m e 2 ( / ) − γ = m D ce = D 2 cos 4 γ m Beekman Model Gaussian Model June 22, 1999
Shading Models ✔ Cook-Torrance / Roughness June 22, 1999
Shading Models ✔ Cook-Torrance/putting it all together = + f sf df r s d � � specular diffuse 1 1 × × F D G = f = f s d π ( N S)(N V) π • • June 22, 1999
Shading Models ✔ Complete Cook-Torrance Model ∑ ( N S)( ) = + • ϖ L L R L f d r a a i r i i June 22, 1999
Shading Models ✔ Cook-Torrance -- examples June 22, 1999
Shading Models ✔ Cook-Torrance summary – Complicated model based on physics – Components • Microfacets • Fresnel equation • Roughness June 22, 1999
Shading Models ✔ Strauss Model [Strauss90] – Designed for ease of use and efficiency – Intuitive parameter set – Takes some liberty with physics. June 22, 1999
Shading Models ✔ Strauss Model - parameter set – Color – Smoothness - 0 = perfectly diffuse, 1 = perfectly specular – Metalness - 0 = dielectric, 1 = metal – Transparency – Index of Refraction. June 22, 1999
Shading Models ✔ Anisotropy – Isotropic - surfaces reflect equally from any direction of view – Ansiotropic - reflection varies not only with angle of incidence, but also with the angle of the incident light w.r.t some viewing angle June 22, 1999
Shading Models ✔ Ansiotropic reflection -- example June 22, 1999
Shading Models ✔ Ward Model [Ward92] – Designed for both accuracy and ease of use – Includes model for ansiotropic reflection June 22, 1999
Shading Models ✔ Ward Model 2 2 1 − (tan γ ) / α ρ e ( ) ρ = + ρ • d s 2 2 π πα cos cos θ δ � � � � � � � � � � � � � � diffuse June 22, 1999 specular
Shading Model ✔ Ward Model – ρ d - Diffuse reflectance coefficient (can vary with wavelength) – ρ s - Speculat reflectance coefficient (can vary with wavelength) – α - Standard deviation of surface slope June 22, 1999
Shading Models ✔ Ward Model -- w/ansiotropy 2 2 2 2 2 (tan (cos / sin / )) − γ φ α + φ α 1 ρ e x y ( ) ρ = + ρ • d s π cos cos 2 θ δ πα α x y � diffuse June 22, 1999 � � � � � � � � � � � � � � � � � specular
Shading 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 June 22, 1999
Shading Models ✔ Ward Model - example June 22, 1999
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