Shading, lighting, & BRDF Theory. Cliff Lindsay, PHD

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1 Shading, lighting, & BRDF Theory Cliff Lindsay, PHD

2 Overview of today s lecture BRDF Characteristics Lights in terms of BRDFs Classes of BRDFs Ambient light & Shadows in terms of BRDFs

3 Decomposing Reflection Phong = Amb + Diff + Spec Don t Confuse Phong Shading

4 Refresher on lighting Diffuse component : idiff i=iamb+idiff+ispec Diffuse is Lambert s law: i diff nl Photons are scattered equally in all directions i diff ( nl) m diff s diff cos

5 Lighting Specular component : ispec Diffuse is dull (left) Specular: simulates a highlight

6 Specular component: Phong Phong specular highlight model Reflect l around n: r l 2(n l)n m shi m i ( r v) (cos ) shi spec ( n l) n r -l n l nl i spec mshi max(0,( r v) ) m spec s spec Read about Blinns highlight formula: (n. h) m

7 Ambient component: iamb Ad-hoc tries to account for light coming from other surfaces Just add a constant color: i amb m amb s amb

8 Lighting i=iamb+idiff+ispec + + = This is just a hack! Has little to do with how reality works!

9 What s lighting and what s shading? Lighting: the interaction between light and matter Shading: do lighting (at vertices) and determine pixel s colors from these Three types of shading: Flat, Goraud, and Phong

10 Now Some Info About Lights

11 Additions to the lighting equation Depends on distance: 1/(a+bt+ct ) Can have more lights: just sum their respective contributions Different light types: 2

12 Omni r l E L Lights pl pl I r r L 2 ps ps Directional Omni with falloff Spotlight

13 Falloff OpenGL way f dist s c s l 1 r s q r 2 Typical for Games f dist r r end end 1, r r 0 start,

14 Spotlights I L ( l) I L *( s 0 l) s exp S- angle P-penumbra U - cutoff

15 BRDF Theory Ratio between incoming and outgoing light Outgoing Incoming f ( l, v) Lo ( v) E( l)cos( ) i Think of f(l,v) as a function l v

16 BRDFs Better Modeling Better Modeling: Diffuse define better diffuse Specular different types of specular Ambient beyond just simple Phong ambient

17 What We ve Done Already For Phong Reflectance We calculate L o = f(l,v)*e(l)*cos( i ) Phong = i*mat+i*nl*mat+i*(nr) m *mat E(l) E(l) f(l,v) E(l) f(l,v) f ( l, v) Lo ( v) E( l)cos( ) i

18 BRDF Theory Generally Parameterized by: i - incoming o outgoing n Normal V View Vector L Light Vector Easy to param based on two quantities

19 BRDF Characteristics Helmholtz Reciprocity f ( l, v) f ( v, l) Conservation of Energy What comes in, must go? - Out - Absorbed - Scattered

20 Light Material Interaction When Light Hits Material: Interacts with surface Goes through surface an interacts below surface Independent of color (most of time for us) Sub-Surface Interaction Surface Interaction

21 Fresnel Reflectance Governs interface between two surfaces r i is the ideal reflection (look familiar?) t is the ideal refraction Snell s Law (n 1 sin( i ) = n 2 sin( t ) ) i = 90, glancing angle produces white color

22 Fresnel Example

23 Which Would You Drink?

24 Subsurface Scattering Very Important for flesh Most organic materials exhibit Lots of other materials too Without With

25 Micro-Geometry

26 Micro-geometry A. Self Shadowing B. Masking C. Interreflection (self) A B C

27 Example: Micro-Geometry Retro-Reflection

28 Micro-facet Special Case Micro-geometry Facets Assumed to be ideal mirrors Uses Half-vector h (half-way vector) NDF: Normal Distribution Function p(h) Introduces Geometry Factor G(l,v)

29 Micro-facet Incorporates: NDF distribution of facets on surface Geometry surface geometry Fresnel f ( l, v) p( h) G( l, v) Rf ( h) 4k cos( )cos( ) p i o

30 Example BRDFs Modified Phong Old Phong Physically Accurate Phong mat f ( l, v) mat f ( l, v) mat *cos( r ) cos( i ) 0 mat *cos( r ) m m,,

31 Simple Visibility Many BRDFs (especially game ones) have no visibility term at all This means the visibility term = 1 Implies geometry factor = nl * nv.

32 Torrance Sparrow Geometry invented by Blinn in 1975 as a reformulation of the Torrance- Sparrow based on an micro-geometry model not affected by roughness

33 More Geometry Factors Kelemen-Szirmay-Kalos Geometry Factor Has cheap and effective approximation

34 Rougher = Blurrier

35 Smith Geometry Factor Gsmith cos i cos (1 k) i k cos o cos (1 k) o k Incorporates roughness into Geometry Term k=(2m 2 /) Roughness

36 Many Different Things To Consider

37 Samples from real-world materials

38 Demo

39 More Geometry Factor Phong Ambient Ambient Occlusion AO + GI Light Instead of general inclusion within the BRDF We can account for geometry for each geometry specifically

40 Ambient Occlusion At surface points P shoot out rays If we hit something shelf-shadow If not, calculate lighting (NL) or something Incorporate into reflectance function

41 AO Light = local hemisphere Centered at current surface point Radius = user parameter Can be rendered with ray tracing Gives perceptual clues of depth, curvature and spatial proximity Lots of techniques (For Games: Screen Space, Horizon-Based, Image-Space)

42 Example

43 Other Illumination Models Cliff Lindsay

44 Overview of today s lecture Refresher on simple lighting models Plus some new stuff More Advanced Illumination Models

45 Additions to the lighting equation Depends on distance: 1/(a+bt+ct ) Can have more lights: just sum their respective contributions Different light types: 2

46 What s lighting and what s shading? Lighting: the interaction between light and matter Shading: do lighting (at vertices) and determine pixel s colors from these Three types of shading: Flat, Goraud, and Phong

47 Global Models You have seen: Local illumination model: Phong Ambient Diffuse Specular Point light sources No: shadows, inter-object light reflection. More global illumination model: Ray Tracing Shadows Area light sources (via distributed ray tracing) inter-object light reflection Tradeoffs: Improvements in fidelity come at the expense of computational complexity.

48 Realistic rendering For each visible point p in the scene How much light is reflected towards the camera

49 Direct + Indirect p

50 Local vs. Global

51 Indirect Light Direct-only 1-bounce indirect 2-bounce indirect

52 Ray Tracing

53 Different Ways to Achieve GI Ray Tracing Path Tracing Photon Mapping Radiosity Metropolis Light Transport

54 Put it all together

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