Logistics Checkpoint 1 all graded Material Properties Grades / comments on mycourses Project Proposals all graded Comments in mycourses List of projects on course Web site Reminder Illumination Models / BRDFs Readings: undergrad - 1 / week Grads: - 1/ class Checkpoint 2 Due Monday Questions? Plan for today Computer Graphics as Virtual Photography BRDFs -- Reflectivity 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 Lighting vs. Shading Commonly misused terms. Computing the light that leaves a point What’s the difference? Shading point - point under investigation Lighting / Illumination designates the Illumination model - function or algorithm interaction between materials and light used to describe the reflective characteristics of sources. a given surface. Shading is the process of determining the Shading model – algorithm for using an color of a pixel. illumination model to determine the color of a point on a surface. Usually determined by lighting. Could use other methods: random color, NPR, etc. For efficiency’s sake, most illumination models are approximations. 1
Bi-directional Reflectance Functions (BRDF) Reflections Ambient – light uniformly incident from the environment Diffuse – light scattered equally in all directions Ambient and Diffuse – color of material plays a part Specular – highlights connected with mirrorness Specular – mostly color of light 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 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 Subsurface scattering BRDF = 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 2
Illumination Models Illumination Modeling Four approaches Illumination model - function or Simplistic algorithm used to describe the reflective Based on physics, abiet with many assumptions characteristics of a given surface. Heuristic Revise to… The kludge! Usually simple, yet not physically based function or algorithm used in Simulation approximating the BRDF. Employ physical model More complex than heuristic, but more accurate Empirical Use measured samples Illumination Models Reflection and color Illumination Models and Viewing Color “response” is based on color that reaches the eye or sensor Direction Generally, BRDFs are independent of http://www.cs.brown.edu/exploratories/freeS viewing direction oftware/repository/edu/brown/cs/exploratorie Most Illumination models take viewing s/applets/spectrum/reflection_guide.html direction into consideration http://www.cs.brown.edu/exploratories/freeS oftware/repository/edu/brown/cs/exploratorie s/applets/spectrum/two_materials_java_brow ser.html Reflections Illumination Models Ambient – light uniformly incident from the Geometry environment N Diffuse – light scattered equally in all directions V H Ambient and Diffuse – color of material plays a part viewer normal Half-way Specular – highlights connected with mirrorness R Specular – mostly color of light S reflection source 3
Illumination Models Illumination Models Recall from Linear Algebra Geometry N - normal vector u S - direction of incoming light θ R - direction of perfect mirror reflection v H - halfway between light direction and viewing direction. u v u v cos • = � V - viewing direction. Just one reason to normalize! Illumination Modeling Illumination Models Four approaches BRDF Viewer Simplistic bv by Szymon Rusinkiewicz (Princeton) Lamertian http://graphics.stanford.edu/~smr/brdf/bv Heuristic SGI, Linux, and Java versions although not Phong readily available for Java. I have it, if you Simulation want it, and you’ll need to load Java3D as Cook-Torrance well! Empirical Use measured samples Simplistic Lambert’s Cosine Law Lambertian Model The reflected luminous intensity in any direction from a perfectly Perfectly diffuse surface diffusing surface varies as the reflection is constant in all directions (k d ) cosine of the angle between the Independent of viewer direction direction of incident light and the Based on Lambert’s cos law. normal vector of the surface. Sometimes mistakenly attributed to Gouraud. Intuitively Gouraud didn’t introduce a new lighting model, just a cross-sectional area of shading method. the “beam” intersecting an element of surface area is smaller for greater angles with the normal. 4
Lambertian Model Lambertian Model Lambert Model BRDF Viewer http://graphics.stanford.edu/~smr/brdf/ bv L ( V ) L S k cos = � L ( V ) L k ( N S ) = • d S d Those Were the Days Phong Model (Or: how not to motivate a 21 st century Phong Model computer graphics paper.) introduces specular (mirror-like) reflections “In trying to improve the quality of the Viewer direction becomes more important synthetic images, we do not expect to be able three components to display the object exactly as it would appear ambient - background light (k a ) in reality, with texture, overcast shadows, etc. We hope only to display an image that diffuse - Lambertian reflection (k d ) approximates the real object closely enough to specular – mirror-like reflection(k s ) provide a certain degree of realism.” – Bui Tuong Phong, 1975 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 N) e a a d i i s i i i i ambient Note: L n are radiance terms, include both light and material info diffuse specular 5
Phong-Blinn Model Physically based BRDF Viewer based on physics of a surface Actually developed by Torrance & Sparrow, physicists. Jim Blinn was the first to apply to CG http://graphics.stanford.edu/~smr/brdf/ Cook & Torrance’s was the first complete implementation bv components microfacet model - describes geometry of surface And how much the microfacets shadow each other. Fresnel term - describes reflectance Roughness - describes microfacet distribution. Break? 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 2 2 2 a + b − 2 a cos θ + cos θ Perpendicular component If all quantities known, use Fresnel = Fs 2 + 2 + θ + 2 θ equations a b 2 a cos cos If not, approximate using reflectance off 2 2 2 2 a b 2 a sin tan sin tan Parallel component + � � � + � � F F normal = p s 2 2 2 2 a b 2 a sin tan sin tan + + � � + � � See [Glassner] or [Cook/Torrance81] for details a, b are functions 1 1 F F F of η , κ , and θ = + 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 2 2 − ((tan α ) / m ) − ( α / m ) e D = ce large m - rough surface, diffuse reflectance D = 2 4 m cos α 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 = 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
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