# Illumination. Illumination CMSC 435/634

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1 Illumination CMSC 435/634

2 Illumination Interpolation

3 Illumination Illumination Interpolation

4 Illumination Illumination Effect of light on objects Mostly look just at intensity Apply to each color channel independently Good for most objects Not fluorescent Not phosphorescent

5 Illumination Local vs. Global Local Light sources shining directly on object Global Lights bouncing from objects onto other objects Ambient Illumination Approximate global illumination as constant color Typically 1% of direct illumination

6 Illumination BRDF Rendering Equation Models Interpolation

7 BRDF BRDF Bidirectional Reflectance Distribution Function How much light reflects from L i to L o Surface normal L o Outgoing radiance v^ n^ L i l^ x Incoming radiance

8 BRDF Physically Plausible BRDF Positive Reciprocity Same light from L i to L o as from L o to L i Conservation of Energy Don t reflect more energy than comes in Surface L i Incoming normal radiance L o Outgoing radiance v^ n^ l^ x

9 BRDF Plotting BRDFs Polar plot of reflectance strength For one view direction, showing light directions For one light direction, showing view directions Reciprocity same if you swap view and light

10 Rendering Equation Rendering Equation Integral of all Incoming Light L o (ˆv) = L i (ˆl) f r (ˆv,ˆl) ˆn ˆl dω(ˆl) Parts of this equation: Ω(ˆn) L o (ˆv) Ω(ˆn) L i (ˆl) f r (ˆv,ˆl) ˆn ˆl dω(ˆl) outgoing light in direction ˆv hemisphere above ˆn that can see this point incoming light from direction ˆl BRDF from ˆl to ˆv projection of differential solid angle onto surface

11 Rendering Equation Rendering Equation for Point Lights Sum for Each Light L o (ˆv) = i L i f r (ˆv,ˆl i ) ˆn ˆl i Parts of this equation: L o (ˆv) outgoing light in direction ˆv i lights that can see this point (where ˆn ˆl i > 0) ˆl i light direction to light i L i incoming light for light i f r (ˆv,ˆl) BRDF from ˆl i to ˆv

12 Rendering Equation Results Integrating full environment Light at one point, black elsewhere

13 Rendering Equation Decomposing BRDFs Decompose BRDF into convenient parts Typical breakdown: Diffuse (view independent) Specular (view dependent near reflection) Others less common, often ignored (e.g. retro reflection) + = L o (ˆv) = i ) L i (f d (ˆv,ˆl i ) + f s (ˆv,ˆl i ) ˆn ˆl i L o (ˆv) = i L i f d (ˆv,ˆl i ) ˆn ˆl i + i L i f s (ˆv,ˆl i ) ˆn ˆl i

14 Models Important directions ˆn: Unit surface normal

15 Models Important directions ˆv: Unit vector from surface toward viewer

16 Models Important directions ˆl: Unit vector from surface toward light

17 Models Important directions ˆR v = 2ˆn(ˆn ˆv) ˆv: Direction of mirror reflection of view

18 Models Important directions ˆR l = 2ˆn(ˆn ˆl) ˆl: Direction of mirror reflection of light

19 Models Important directions ĥ = (ˆv + ˆl)/ ˆv + ˆl : Normal direction that would reflect ˆv to ˆl

20 Models Diffuse Also called Lambertian or Matte Total reflectance: i L i Kd ˆn ˆl i BRDF: Kd

21 Models Phong Strongest where ˆR l lines up with ˆv or ˆR v lines up with ˆl Total reflectance: i L i Ks ( ˆR v ˆl i ) e Physically plausible version: i L i Ks ( ˆR v ˆl i ) e ˆn ˆl With energy-conserving Ks

22 Models Specular Microfacets Imagine random mirrored microfacets Normal Distribution Function (NDF) Probability facet has normal ĥ Only facets to reflect ˆl to ˆv Proportion of light or view blocked (geometry term) Blocked light = shadowing Blocked view = masking Fresnel term Reflection from non-metals is stronger at glancing angles

23 Models Cook-Torrance Beckmann Distribution = Gaussian distribution of slope Shadow/Mask based on symmetric V-shaped microfacets BRDF: D(ˆn, ĥ) G(ˆn,ˆv,ˆl) 4 ˆn ˆv ˆn ˆl F (ˆv,ˆl), Total reflectance: i L i Ks D(ˆn, ĥ i ) G(ˆn,ˆv,ˆl i ) 4 ˆn ˆv ˆn ˆl F (ˆv, ˆl i ) ˆn ˆl

24 Models Blinn-Phong Alternate formulation for Phong, similar behavior Strongest where ĥ lines up with ˆn Function of ĥ, behaves like NDF Total reflectance (original form): i L i Ks (ˆn ĥ i ) e As NDF: D(ˆn, ĥ i ) = e+2 2π (ˆn ĥ i ) e

25 Interpolation Illumination Interpolation

26 Interpolation When to Compute Gouraud Shading = Compute per-vertex & interpolate Lose sharp highlights Subject to Mach banding Phong Shading = Interpolate normals & compute per-pixel Gouraud Phong

27 Interpolation Phong Shading Phong shading can refer to lighting model or interpolation To save confusion: Phong lighting Phong interpolation

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