Illumination

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本章节照明在计算机视觉中所起到的作用以及其他方面的应用，描述了BRDF，是入射光线经过某个表面反射后如何在各个出射方向上分布，以及关于BRDF在计算机视觉方面起的作用，另外介绍了Phong着色法（Phong shading），是三维电脑图像的绘图技巧之一。

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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

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