Lecture 13 - BRDFs Welcome! , = (, ) , - - PowerPoint PPT Presentation

β–Ά
lecture 13 brdfs
SMART_READER_LITE
LIVE PREVIEW

Lecture 13 - BRDFs Welcome! , = (, ) , - - PowerPoint PPT Presentation

Feb 05, 2023 46 likes β€’571 views

INFOMAGR Advanced Graphics Jacco Bikker - November 2017 - February 2018 Lecture 13 - BRDFs Welcome! , = (, ) , + , , ,

slide-1
SLIDE 1

𝑱 π’š, π’šβ€² = 𝒉(π’š, π’šβ€²) 𝝑 π’š, π’šβ€² + ΰΆ±

𝑻

𝝇 π’š, π’šβ€², π’šβ€²β€² 𝑱 π’šβ€², π’šβ€²β€² π’†π’šβ€²β€²

INFOMAGR – Advanced Graphics

Jacco Bikker - November 2017 - February 2018

Lecture 13 - β€œBRDFs”

Welcome!

slide-2
SLIDE 2

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-3
SLIDE 3

Advanced Graphics – BRDFs 3

Exam Questions

In path tracing, we can reduce variance by using cosine weighted sampling of the hemisphere, rather than uniform sampling, for diffuse surfaces. a) Why does this reduce variance? b) When using cosine weighted sampling, the result remains unbiased. What does unbiased mean?

slide-4
SLIDE 4

Advanced Graphics – BRDFs 4

Exam Questions

An exam can be seen as a Monte-Carlo process. Expain why.

slide-5
SLIDE 5

Advanced Graphics – BRDFs 5

Exam Questions

After reading the probability tutorial, answer these: a) What is a definite integral? b) What do we mean by an analytical solution? c) How is the Riemann sum defined (mathematically)? d) What is β€˜univariate’? e) What is β€˜aliasing’? f) Define, in your own words, β€˜expected value’. g) What is β€˜deviation’ in the context of probability theory? And, finally: When using importance sampling, we assume that for 𝑂 = ∞,

π‘βˆ’π‘ 𝑂 σ𝑗=1 𝑂 𝑔(π‘Œ) π‘ž(π‘Œ) = π‘βˆ’π‘ 𝑂 σ𝑗=1 𝑂

𝑔(π‘Œ), if Χ¬

𝑏 𝑐 π‘ž 𝑦 𝑒𝑦 = 1. Provide one

example for which this is not true.

slide-6
SLIDE 6

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-7
SLIDE 7

Phong

Advanced Graphics – BRDFs 7

BRDFs, Recap

Recall that a BRDF defines the relation between incoming and outgoing radiance for directions and a surface point: 𝑔

𝑠 𝑦, πœ„π‘—, πœ„π‘ = 𝑀𝑝(𝑦, πœ„π‘)

𝐹𝑗(𝑦, πœ„π‘—) = 𝑀𝑝(𝑦, πœ„π‘) 𝑀𝑗 𝑦, πœ„π‘— cos πœ„π‘—

π‘œ

πœ„π‘ πœ„π‘—

𝑦 π‘œ π‘œ What about materials that are not purely specular, nor diffuse?

slide-8
SLIDE 8

Phong

Advanced Graphics – BRDFs 8

BRDFs, Recap

We already know how to do materials that are diffuse and shiny. But that gets us good looking marble floors, not glossy reflections.

50% diffuse, 50% specular, 50% diffuse, 50% glossy (or: 100% glossy)

slide-9
SLIDE 9

Phong

Advanced Graphics – BRDFs 9

Glossy Reflection

Glossy reflections: sending out rays in random directions close to the reflected vector.

Simple solution: 𝑆 = π‘ π‘“π‘”π‘šπ‘“π‘‘π‘’(π‘Š, 𝑂); 𝑄 = 𝐽 + 𝑆 + π‘‘π‘‘π‘π‘šπ‘“(π‘ π‘π‘œπ‘’π‘π‘›π‘„π‘π‘—π‘œπ‘’π½π‘œπ‘‡π‘žβ„Žπ‘“π‘ π‘“(), π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘ π‘—π‘’π‘§) 𝑆 = π‘œπ‘π‘ π‘›π‘π‘šπ‘—π‘¨π‘“(𝑄 βˆ’ 𝐽); Or: 𝑆 = π‘ π‘“π‘”π‘šπ‘“π‘‘π‘’(π‘Š, 𝑂); 𝑄 = 𝐽 + 𝑆 + π‘‘π‘‘π‘π‘šπ‘“(π‘ π‘π‘œπ‘’π‘π‘›πΈπ‘—π‘ π‘“π‘‘π‘’π‘—π‘π‘œπ½π‘œπΌπ‘“π‘›π‘—π‘‘π‘žβ„Žπ‘“π‘ π‘“π·π‘π‘‘π‘—π‘œπ‘“π‘‹π‘“π‘—π‘•β„Žπ‘’π‘“π‘’(𝑆), π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘ π‘—π‘’π‘§) 𝑆 = π‘œπ‘π‘ π‘›π‘π‘šπ‘—π‘¨π‘“(𝑄 βˆ’ 𝐽); 𝑢

slide-10
SLIDE 10

Phong

Advanced Graphics – BRDFs 10

Glossy Reflection

In OpenGL, shading is defined as follows*: 𝐽𝑦 = π‘™π‘π‘›π‘π‘—π‘“π‘œπ‘’π½π‘π‘›π‘π‘—π‘“π‘œπ‘’ + ෍

π‘›βˆˆπ‘šπ‘—π‘•β„Žπ‘’π‘‘

𝑙𝑒𝑗𝑔𝑔𝑣𝑑𝑓 𝑂 βˆ™ 𝑀𝑛 + π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  𝑆𝑛 βˆ™ π‘Š

π‘“π‘¦π‘žπ‘π‘œπ‘“π‘œπ‘’

𝐽𝑛

*: Bui-Tuong Phong, Illumination for Computer Generated Images, 1975.

𝑆𝑛 𝑀𝑛 π‘Š

𝑦 where

  • π‘™π‘π‘›π‘π‘—π‘“π‘œπ‘’, 𝑙𝑒𝑗𝑔𝑔𝑣𝑑𝑓 π‘π‘œπ‘’ π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  are

material properties (typically: rgb);

  • 𝑆𝑛 is the vector 𝑀𝑛 reflected in the

normal 𝑂;

  • 𝐽𝑛 is the illumination from light 𝑛.

𝑂 ΰΆ±

𝛻

cos πœ„ = 𝜌 ΰΆ±

𝛻

π‘‘π‘π‘‘π‘“π‘¦π‘žπœ„ =?

slide-11
SLIDE 11

Phong

Advanced Graphics – BRDFs 11

Blinn-Phong BRDF (images: Disney BRDF Explorer)

slide-12
SLIDE 12

Phong

Advanced Graphics – BRDFs 12

Modified Phong BRDF

slide-13
SLIDE 13

Phong

Advanced Graphics – BRDFs 13

Fixing Phong

Recall the requirements for a proper BRDF:

  • Should be positive: 𝑔

𝑠 πœ•π‘, πœ•π‘— β‰₯ 0

  • Helmholtz reciprocity should be obeyed: 𝑔

𝑠 πœ•π‘, πœ•π‘— = 𝑔 𝑠 πœ•π‘—, πœ•π‘

  • Energy should be conserved: Χ¬

𝛻 𝑔 𝑠 πœ•π‘, πœ•π‘— cos πœ„π‘ π‘’πœ•π‘ ≀ 1

BRDFs obeying these rules are called physically plausible. For a path tracer, we have additional requirements:

  • 1. It β€˜would be nice’ if we could generate a random direction proportional to the BRDF (IS)
  • 2. We need to be able to calculate the probability density (importance) for a given direction

(for MIS).

slide-14
SLIDE 14

Phong

Advanced Graphics – BRDFs 14

Fixing Phong

  • 1. Sampling the specular lobe proportional to the BRDF:

Sampling proportional to 𝑂 βˆ™ 𝑀, according to the G.I.C. : 𝑦 = cos 2πœŒπ‘ 

1

1 βˆ’ 𝑠2 𝑧 = sin 2πœŒπ‘ 

1

1 βˆ’ 𝑠2 𝑨 = 𝑠

2

𝑆 βˆ™ π‘Š 1 𝑆 βˆ™ π‘Š 2 𝑆 βˆ™ π‘Š 10 𝑆 βˆ™ π‘Š 50

Sampling proportional to 𝑆 βˆ™ π‘Š 𝛽, according to the G.I.C. : 𝑒 = 𝑠

2

2 𝛽+1, 𝑦 = cos 2πœŒπ‘ 

1

1 βˆ’ 𝑒 𝑧 = sin 2πœŒπ‘ 

1

1 βˆ’ 𝑒 𝑨 = 𝑒

𝑨 𝑦 𝑧

slide-15
SLIDE 15

Phong

Advanced Graphics – BRDFs 15

Tangent / Local Space

Setting up a local coordinate system in 2D:

  • First axis is the normal;
  • Second axis is perpendicular to normal.

𝑂 = π‘œ π‘ˆ = βˆ’π‘œ. 𝑧 π‘œ. 𝑦 Setting up a local coordinate system in 3D: 𝑂 = π‘œ π‘ˆ = π‘œπ‘π‘ π‘›π‘π‘šπ‘—π‘¨π‘“(𝑂 Γ— 𝑋) 𝐢 = π‘ˆ Γ— 𝑂 where 𝑋 is a random unit vector; 𝑋 β‰  𝑂.

𝑨 𝑦 𝑧

Good choice for 𝑋: 𝑋 = (0,1,0) if abs(π‘œπ‘¦) > 0.99; 𝑋 = 1,0,0 otherwise.

𝑢 𝑼 π‘ͺ

slide-16
SLIDE 16

Phong

Advanced Graphics – BRDFs 16

Tangent / Local Space

Converting a vector from world space to local space: 𝑄

𝑦

𝑄

𝑧

𝑄

𝑨

= 𝑄 βˆ™ π‘ˆ 𝑄 βˆ™ 𝐢 𝑄 βˆ™ 𝑂 Local space to world space: 𝑄π‘₯π‘π‘ π‘šπ‘’ = 𝑁 Γ— π‘„π‘šπ‘π‘‘π‘π‘š = 𝑄

π‘¦π‘ˆ + 𝑄 𝑧𝐢 + 𝑄 𝑨𝑂

𝑢 𝑼 π‘ͺ

slide-17
SLIDE 17

Phong

Advanced Graphics – BRDFs 17

Normalizing the Lobe

A material cannot reflect more energy than it receives:  We thus scale the BRDF by the inverse of its integral over the hemisphere. For the Lambertian BRDF: π‘‘π‘‘π‘π‘šπ‘“ =

1 𝜌 (because cos πœ„ integrates to 𝜌)

For the cosine lobe, the scale is

𝛽+1 2𝜌 (*). However, there is a problem:

*: Physically Based Rendering, page 969; also see: http://www.farbrausch.de/~fg/stuff/phong.pdf

π‘œ π‘œ π‘œ

slide-18
SLIDE 18

Phong

Advanced Graphics – BRDFs 18

The Modified Phong BRDF

The Phong BRDF has problems:

  • 1. it does not doesn’t obey the Helmholtz reciprocity rule.
  • 2. We can only estimate the integral of the lobe, since it

intersects the surface. Compensating for the intersection: Modified Phong BRDF. 𝑔

𝑠 𝑦, πœ„π‘—, πœ„π‘ = 𝑙𝑒

1 𝜌 + 𝑙𝑑 𝛽 + 2 2𝜌 π‘‘π‘π‘‘π›½πœ’ where πœ’ is the angle between the view vector and the reflected light vector. For 𝑙𝑒 + 𝑙𝑑 < 1, this guarantees energy preservation*.

*: Lafortune & Willems, Using the Modified Phong Reflectance Model for Physically Based Rendering, 1994.

𝑔

𝑠 𝑦, πœ„π‘—, πœ„π‘ = 𝑙𝑒 1 𝜌 + 𝑙𝑑 𝛽+2 2𝜌 π‘‘π‘π‘‘π›½πœ’ :

Total hemispherical reflection (note: integrating over

  • utgoing directions, since these cannot exceed 1):

𝜍 𝑦, πœ„π‘ = ΰΆ±

Ξ©

𝑔

𝑠 𝑦, πœ„π‘—, πœ„π‘ cos ΞΈπ‘π‘’πœ•π‘

= ΰΆ±

Ξ©

(𝑙𝑒 1 𝜌 + 𝑙𝑑 𝛽 + 2 2𝜌 π‘‘π‘π‘‘π›½πœ’) cos ΞΈπ‘π‘’πœ•π‘ = 𝑙𝑒 + 𝑙𝑑 𝛽 + 2 2𝜌 ΰΆ±

Ξ©

π‘‘π‘π‘‘π›½πœ’ cos ΞΈπ‘π‘’πœ•π‘ The last integral is maximal when the incoming light arrives along the normal; in this case πœ’ = πœ„π‘, and the integral is 2𝜌/ (π‘œ + 2). Therefore, in this case: 𝜍 𝑦, πœ„π‘ = 𝑙𝑒 + 𝑙𝑑 and conservation of energy is guaranteed iff: 𝑙𝑒 + 𝑙𝑑 ≀ 1.

slide-19
SLIDE 19

Phong

Advanced Graphics – BRDFs 19

The Modified Phong BRDF

Despite the kludges, we now have a decent BRDF for glossy materials. We can sample it: 𝑒 = 𝑠

2

2 𝛽+1, 𝑦 = cos 2πœŒπ‘ 

1

1 βˆ’ 𝑒 𝑧 = sin 2πœŒπ‘ 

1

1 βˆ’ 𝑒 𝑨 = 𝑒 Normalize it: 𝛽 + 2 2𝜌 π‘‘π‘π‘‘π›½πœ’ We have a PDF: 𝛽 + 2 2𝜌 π‘‘π‘π‘‘π›½πœ’

And finally, we can blend it with the Lambertian BRDF:

  • Define a probability π‘ž of sampling Phong;
  • Draw a random number 𝑠0;
  • Sample Phong if 𝑠0 < π‘ž, Lambert otherwise;
  • Combine PDFs: 𝑄𝐸𝐺 = π‘ž π‘„πΈπΊπ‘žβ„Žπ‘π‘œπ‘• + 1 βˆ’ π‘ž 𝑄𝐸𝐺𝑒𝑗𝑔𝑔
slide-20
SLIDE 20

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-21
SLIDE 21

Microfacet

Advanced Graphics – BRDFs 21

BRDFs Without Issues

We now have two BRDFs without problems:

  • 1. The Lambertian BRDF
  • 2. The pure specular BRDF

These are plausible and can be sampled. The PDF is also clear. And, we have the somewhat kludged modified Phong BRDF.

slide-22
SLIDE 22

Microfacet

Advanced Graphics – BRDFs 22

Microfacet BRDFs*

We can simulate a broad range of materials if we assume: at a microscopic level, the material consists of tiny specular fragments.

  • If the fragment orientations are chaotic, the material appears diffuse.
  • If the fragment orientations are all the same, the material appears specular.
  • Different but similar orientations yield glossy materials.

*: Torrance & Sparrow, Theory for Off-Specular Reflection from Roughened Surfaces. 1967.

slide-23
SLIDE 23

Microfacet

Advanced Graphics – BRDFs 23

Microfacet BRDFs*

The Microfacet BRDF: 𝑔

𝑠 𝑀, π‘Š = 𝐺 𝑀, π‘Š 𝐻 𝑀, π‘Š, 𝐼 𝐸 𝐼

4 𝑂 βˆ™ 𝑀 𝑂 βˆ™ π‘Š Ingredients:

  • 1. Normal distribution D
  • 2. Geometry term G
  • 3. Fresnel term F
  • 4. Normalization
slide-24
SLIDE 24

Microfacet

Advanced Graphics – BRDFs 24

Normal Distribution

Microfacet BRDF, ingredient 1: 𝐸(𝐼)  the normal distribution function. Parameter 𝐼: the halfway vector: 𝑔

𝑠 π‘Š, 𝑀 = β‹―

A microfacet that reflects 𝑀 towards π‘Š must have a normal halfway π‘Š and 𝑀:

H = normalize(V + L).

𝑔

𝑠 𝑦, πœ„π‘—, πœ„π‘ =

𝑀𝑝(𝑦, πœ„π‘) 𝑀𝑗 𝑦, πœ„π‘— cos πœ„π‘—

𝑾 𝑴

𝑰

slide-25
SLIDE 25

Microfacet

Advanced Graphics – BRDFs 25

Normal Distribution

Intuitive choices for D: 𝐸 𝐼 = 𝐷: microfacet normals are equally distributed  diffuse material. 𝐸 𝐼 = ∞, 𝑔𝑝𝑠𝐼 = 0,0,1 0, π‘π‘’β„Žπ‘“π‘ π‘₯𝑗𝑑𝑓 : all microfacet normals are (0,0,1)  pure specular. Good practical choice for D: the Blinn-Phong distribution; 𝐸 𝐼 = 𝛽 + 2 2𝜌 𝑂 βˆ™ 𝐼

𝛽

slide-26
SLIDE 26

Microfacet

Advanced Graphics – BRDFs 26

Geometry Term

Microfacet BRDF, ingredient 2: 𝐻(π‘Š, 𝑀, 𝐼)  the geometry term.

slide-27
SLIDE 27

Microfacet

Advanced Graphics – BRDFs 27

Geometry Term

Intuitive choice for G: 𝐻(π‘Š, 𝑀, 𝐼) = 1: no occlusion. Good practical choice for G*: 𝐻 π‘Š, 𝑀, 𝐼 = min(1, min 2 𝑂 βˆ™ 𝐼 𝑂 βˆ™ π‘Š π‘Š βˆ™ 𝐼 , 2 𝑂 βˆ™ 𝐼 𝑂 βˆ™ 𝑀 π‘Š βˆ™ 𝐼

*: Physically Based Rendering, page 455

slide-28
SLIDE 28

Microfacet

Advanced Graphics – BRDFs 28

Fresnel Term

Microfacet BRDF, ingredient 3: 𝐺(𝑀, 𝐼)  the Fresnel term. So far, we assumed that the light reflected by a specular surface is only modulated by the material color. This is not true for dielectrics: here we use the Fresnel equations to determine reflection. In nature, Fresnel does not just apply to dielectrics.

𝒐 𝝏𝒑 𝝏𝒋

slide-29
SLIDE 29

Microfacet

Advanced Graphics – BRDFs 29

From β€œReal-time Rendering, 3rd edition, A. K. Peters.

Fresnel Term

Iron is specular, but reflectivity differs depending on incident angle. Aluminum is even more interesting: reflectivity depends on wavelength. The three lines in the graph: Top: blue, middle: green, bottom: red. Copper takes this to extremes: at grazing angles, it appears white. The lines in the graph: Top: red, middle: green, bottom: blue.

(hence its reddish appearance)

slide-30
SLIDE 30

Microfacet

Advanced Graphics – BRDFs 30

Fresnel Term

For Fresnel, we once again use Schlick’s approximation: 𝐺

𝑠 = π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  + (1 βˆ’ π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘ )(1 βˆ’ 𝑀 βˆ™ 𝐼 )5

Note that this is calculated per color channel (π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  is an rgb triplet). Values for π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  for various materials: Iron 0.56, 0.57, 0.58 Copper 0.95, 0.64, 0.54 Gold 1.00, 0.71, 0.29 Aluminum 0.91, 0.92, 0.92 Silver 0.95, 0.93, 0.88

slide-31
SLIDE 31

Microfacet

Advanced Graphics – BRDFs 31

Bringing it All Together

The Microfacet BRDF: 𝑔

𝑠 𝑀, π‘Š = 𝐺 𝑀, π‘Š 𝐻 𝑀, π‘Š, 𝐼 𝐸 𝐼

4 𝑂 βˆ™ 𝑀 𝑂 βˆ™ π‘Š 𝐺

𝑠 = π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘  + (1 βˆ’ π‘™π‘‘π‘žπ‘“π‘‘π‘£π‘šπ‘π‘ )(1 βˆ’ 𝑀 βˆ™ 𝐼 )5

𝐻 π‘Š, 𝑀, 𝐼 = min(1, min 2 𝑂 βˆ™ 𝐼 𝑂 βˆ™ π‘Š π‘Š βˆ™ 𝐼 , 2 𝑂 βˆ™ 𝐼 𝑂 βˆ™ 𝑀 π‘Š βˆ™ 𝐼 𝐸 𝐼 = 𝛽 + 2 2𝜌 𝑂 βˆ™ 𝐼

𝛽

For a full derivation of the denominator of the BRDF, see Physically Based Rendering, section 8.4.2.

slide-32
SLIDE 32

Microfacet

Advanced Graphics – BRDFs 32

Lambertian BRDF

slide-33
SLIDE 33

Microfacet

Advanced Graphics – BRDFs 33

Blinn-Phong Microfacet BRDF, Ξ±=1

slide-34
SLIDE 34

Microfacet

Advanced Graphics – BRDFs 34

Blinn-Phong Microfacet BRDF, Ξ±=10

slide-35
SLIDE 35

Microfacet

Advanced Graphics – BRDFs 35

Blinn-Phong Microfacet BRDF, Ξ±=50

slide-36
SLIDE 36

Microfacet

Advanced Graphics – BRDFs 36

Blinn-Phong Microfacet BRDF, Ξ±=500

slide-37
SLIDE 37

Microfacet

Advanced Graphics – BRDFs 37

Blinn-Phong Microfacet BRDF, Ξ±=50000

slide-38
SLIDE 38

Microfacet

Advanced Graphics – BRDFs 38

Specular BRDF

slide-39
SLIDE 39

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-40
SLIDE 40

Advanced Graphics – BRDFs 40

Tricks & Tips

Picking the best light:

  • For each light, calculate potential contribution, store in array
  • Calculate the summed potential contribution
  • Pick a random number between 0 and this sum
  • Walk the array until the prefix sum exceeds the random number.

Demo

10 10 22 22 4 20 20 56 30

slide-41
SLIDE 41

Advanced Graphics – BRDFs 41

Tricks & Tips

Multi-layer Microfacet:

  • Plastic is partially diffuse, partially purely reflective.

 Sample one random layer. When evaluating (for MIS):  Evaluate both layers, scale each sub-PDF

Demo

slide-42
SLIDE 42

Advanced Graphics – BRDFs 42

Tricks & Tips

Material interface: In general, you need two methods:

  • 1. SampleBRDF: produces a random direction proportional to the PDF. In: 𝑀𝑝, out: 𝑀𝑗 and the

probability density for the generated direction.

  • 2. EvaluatePDF: determines the probability density for a pair of directions. In: 𝑀𝑝 and 𝑀𝑗. Out:

the probability density for the generated direction. The first is commonly used for extending the random path. The second is used for next event estimation.

Demo

slide-43
SLIDE 43

Advanced Graphics – BRDFs 43

Tricks & Tips

Russian Roulette: Any termination probability is good. However: we don’t want really bright paths. Consider this probability: min( 1.0f, max( max( diffuse.x, diffuse.y ), diffuse.z ) ); Effect:

  • The brightest component determines the survival probability.
  • This component will become 1 (why?).

This is THE BEST. It’s genius and stable.

Demo

slide-44
SLIDE 44

Advanced Graphics – BRDFs 44

Tricks & Tips

On Random Number Generators: Noise is annoying, but its effects can be reduced somewhat. Each pixel uses for its seed:

  • 1. The pixel index
  • 2. The frame index

Replace β€˜2’ by a counter which is reset each time the camera moves. Now noise will be stationary during movement, which is a lot easier on the eyes.

Demo

slide-45
SLIDE 45

Advanced Graphics – BRDFs 45

Tricks & Tips

Fireflies: You want your path tracer to be unbiased. However: Some pixels will be extremely bright, and it takes ages for them to β€˜average out’. Solution: clamp.

  • 1. Calculate the β€˜length’ of the color. If this exceeds the maximum magnitude:
  • 2. Divide the color by its length to normalize it.
  • 3. Multiply by the maximum magnitude.

Demo

slide-46
SLIDE 46

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-47
SLIDE 47

Quo Vadis

Advanced Graphics – BRDFs 54

Quo Vadis

Anisotropic materials:

slide-48
SLIDE 48

Advanced Graphics – BRDFs 55

Quo Vadis

The Other Side: BSSRDF*

*: Jensen et al., 2001. A Practical Model for Subsurface Light Transport.

Quo Vadis

slide-49
SLIDE 49

Advanced Graphics – BRDFs 56

Quo Vadis

Variance Reduction for BSSRDFs:

Quo Vadis

slide-50
SLIDE 50

Advanced Graphics – BRDFs 57

Quo Vadis

Measured BRDFs:

Quo Vadis

slide-51
SLIDE 51

Today’s Agenda:

  • Exam Questions: Sampler (3)
  • Phong BRDF
  • Microfacets
  • Demo Time
  • Quo Vadis
slide-52
SLIDE 52

INFOMAGR – Advanced Graphics

Jacco Bikker - November 2017 - February 2018

END of β€œBRDFs”

next lecture: β€œGradient Domain Path Tracing” (guest)