1.Illumination Rendering Equation BRDFs Interpolation Illumination CMSC 435/634 

2.Illumination Rendering Equation BRDFs Interpolation 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 

3.Illumination Rendering Equation BRDFs Interpolation 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 

4.Illumination Rendering Equation BRDFs Interpolation BRDF Bidirectional Reflectance Distribution Function How much light reflects from Li to Lo Surface L i Incoming normal radiance ^ n^ l Lo Outgoing v^ x radiance 

5.Illumination Rendering Equation BRDFs Interpolation Physically Plausible BRDF • Positive • Reciprocity • Same light from Li to Lo as from Lo to Li • Conservation of Energy • Don’t reflect more energy than comes in Surface L i Incoming normal radiance ^ n^ l Lo Outgoing v^ x radiance 

6.Illumination Rendering Equation BRDFs Interpolation 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 1.0 0.8 0.6 0.4 0.2 0.6 0.4 0.2 0.2 

7.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) 

8.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ 

9.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ Ω(ˆn) hemisphere above nˆ that can see this point 

10.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) Parts of this equation: Lo (ˆv) outgoing light in direction vˆ Ω(ˆ n) hemisphere above nˆ that can see this point ˆ Li (l) incoming light from direction lˆ 

11.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) Parts of this equation: Lo (ˆv) outgoing light in direction vˆ Ω(ˆ n) hemisphere above nˆ that can see this point ˆ Li (l) incoming light from direction lˆ fr (ˆ ˆ v , l) BRDF from lˆ to vˆ 

12.Illumination Rendering Equation BRDFs Interpolation Rendering Equation Integral of all Incoming Light Lo (ˆ v) = ˆ fr (ˆ Li (l) ˆ nˆ · lˆdω(l) v , l) ˆ Ω(ˆ n) Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ Ω(ˆ n) hemisphere above nˆ that can see this point ˆ Li (l) incoming light from direction lˆ fr (ˆ ˆ v , l) BRDF from lˆ to vˆ ˆ ˆ nˆ · l dω(l) projection of differential solid angle onto surface 

13.Illumination Rendering Equation BRDFs Interpolation Rendering Equation for Point Lights Sum for Each Light Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ 

14.Illumination Rendering Equation BRDFs Interpolation Rendering Equation for Point Lights Sum for Each Light Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ i lights that can see this point (where nˆ · lˆi > 0) 

15.Illumination Rendering Equation BRDFs Interpolation Rendering Equation for Point Lights Sum for Each Light Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ i lights that can see this point (where nˆ · lˆi > 0) lˆi light direction to light i 

16.Illumination Rendering Equation BRDFs Interpolation Rendering Equation for Point Lights Sum for Each Light Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i Parts of this equation: Lo (ˆ v) outgoing light in direction vˆ i lights that can see this point (where nˆ · lˆi > 0) lˆi light direction to light i Li incoming light for light i 

17.Illumination Rendering Equation BRDFs Interpolation Rendering Equation for Point Lights Sum for Each Light Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i Parts of this equation: Lo (ˆv) outgoing light in direction vˆ i lights that can see this point (where nˆ · lˆi > 0) lˆi light direction to light i Li incoming light for light i fr (ˆ ˆ v , l) BRDF from lˆi to vˆ 

18.Illumination Rendering Equation BRDFs Interpolation Results • Integrating full environment 

19.Illumination Rendering Equation BRDFs Interpolation Results • Integrating full environment • Light at one point, black elsewhere 

20.Illumination Rendering Equation BRDFs Interpolation 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) + = Lo (ˆ v) = v , lˆi ) nˆ · lˆi Li fr (ˆ i 

21.Illumination Rendering Equation BRDFs Interpolation 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) + = Lo (ˆ v) = Li v , lˆi ) + fs (ˆ fd (ˆ v , lˆi ) nˆ · lˆi i 

22.Illumination Rendering Equation BRDFs Interpolation 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) + = Lo (ˆ v) = v , lˆi ) nˆ · lˆi + Li fs (ˆ (Li fd (ˆ v , lˆi ) nˆ · lˆi ) i 

23.Illumination Rendering Equation BRDFs Interpolation 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) + = Lo (ˆ v) = v , lˆi ) nˆ · lˆi + Li fd (ˆ v , lˆi ) nˆ · lˆi Li fs (ˆ i i 

24.Illumination Rendering Equation BRDFs Interpolation Important directions nˆ: Unit surface normal 

25.Illumination Rendering Equation BRDFs Interpolation Important directions vˆ: Unit vector from surface toward viewer 

26.Illumination Rendering Equation BRDFs Interpolation Important directions ˆ Unit vector from surface toward light l: 

27.Illumination Rendering Equation BRDFs Interpolation Important directions Rˆv = 2ˆ n · vˆ) − vˆ: Direction of mirror reflection of view n(ˆ 

28.Illumination Rendering Equation BRDFs Interpolation Important directions Rˆl = 2ˆ ˆ − l: n · l) n(ˆ ˆ Direction of mirror reflection of light 

29.Illumination Rendering Equation BRDFs Interpolation Important directions hˆ = (ˆ ˆ v + l|: v + l)/|ˆ ˆ Normal direction that would reflect vˆ to lˆ