A presentation I gave on 4/16/18 to students at Cal Poly Pomona on physically-based rendering.

1. Physically-Based Rendering
Theory and Practice
Koray Hagen

2. The agenda
• Lighting and shading models with live demonstration
• Theoretical basis for PBR with live demonstration
• Q & A

3. Reality and simulation
Three thousand years of research

4. A brief history
• 4th century B.C.
– Ancient Greeks incorrectly believe
vision involves emanations from the
eye to the object perceived.

5. A brief history
• 4th century B.C.
– Ancient Greeks incorrectly believe
vision involves emanations from the
eye to the object perceived.
– Euclid successfully describes the law
of reflection using geometry.

6. A brief history
• 17th century A.D.
– Kepler, Snell, Fermat, and Descartes
contribute to the law of refraction.

7. A brief history
• 17th century A.D.
– Kepler, Snell, Fermat, and Descartes
contribute to the law of refraction.
– Newton observes dispersion,proving
light is composed of component
colors.

8. A brief history
• 19th century A.D.
– Fresnel discovers the laws that
enable the intensity and polarization
of reflected and refracted light to be
calculated.

9. A brief history
• 19th century A.D.
– Fresnel discovers the laws that
enable the intensity and polarization
of reflected and refracted light to be
calculated.
– Maxwell summarizes and extends all
current empirical knowledge of
optics and electromagnetism with a
single set of equations.

10. A brief history
• 19th century A.D.
– Fresnel discovers the laws that
enable the intensity and polarization
of reflected and refracted light to be
calculated.
– Maxwell summarizes and extends all
current empirical knowledge of
optics and electromagnetism with a
single set of equations.
– Hertz discovers the photoelectric
effect.

11. A brief history
• 20th century A.D.
– Planck discovers a universalconstant
explainingthe relationship between
the energy and frequency of an
electromagnetic wave.

12. A brief history
• 20th century A.D.
– Planck discovers a universalconstant
explainingthe relationship between
the energy and frequency of an
electromagnetic wave.
– Einstein explains the photoelectric
effect based on streams of quantized
energy packets.

13. A brief history
• 20th century A.D.
– Planck discovers a universalconstant
explainingthe relationship between
the energy and frequency of an
electromagnetic wave.
– Einstein explains the photoelectric
effect based on streams of quantized
energy packets.
– Feynman makes large contributions
to quantum field theory and
quantum electrodynamics.

14. A brief history
• 21st century A.D.
– Jet Propulsion Laboratoryhires PhD
graduateJim Blinn to work on
computer graphics research and
simulations for various space
missions.

15. A brief history
• 21st century A.D.
– Jet Propulsion Laboratoryhires PhD
graduateJim Blinn to work on
computer graphics research and
simulations for various space
missions.
– These incredible visualizations were
shown all over the world.

16. Our journey to physicallybased rendering begins here.

18. Lighting and shading models
Research prior to physicallybased rendering

19. What is physically-based rendering?

20. What is physically-based rendering?
• “Many things” and “it depends”

21. What is physically-based rendering?
• “Many things” and “it depends”
• Must observe how it differs from other older rendering methods.

22. What is physically-based rendering?
• “Many things” and “it depends”
• Must observe how it differs from other older rendering methods.
• What makes PBR different is in how we reason about the behavior of light and
surfaces in computer graphics.

23. What is physically-based rendering?
• “Many things” and “it depends”
• Must observe how it differs from other older rendering methods.
• What makes PBR different is in how we reason about the behavior of light and
surfaces in computer graphics.
• By modeling physical phenomena rather than approximating observation, we can
achieve more mathematically stable and photorealistic visual fidelity.

24. Some terminology
• Lighting model – the behavior of interactions between materials and light sources.
Normally attributed to be a topic in physics.

25. Some terminology
• Lighting model – the behavior of interactions between materials and light sources.
Normally attributed to be a topic in physics.
• Shading model – the process of determining the color of a pixel. Normally
attributed to be a topic in computer graphics.

26. Some terminology
• Diffusion and reflection – also known as diffuse and specular reflection.

27. Some terminology
• Diffusion and reflection – also known as diffuse and specular reflection.
– Describe the most basic separation of light and surface interactions.

28. Some terminology
• Diffusion and reflection – also known as diffuse and specular reflection.
– Describe the most basic separation of light and surface interactions.
– Specular reflection is the behavior of light hitting a surfaceboundaryand perfectly
reflecting off of it, much like how a mirror would behave.

29. Some terminology
• Diffusion and reflection – also known as diffuse and specular reflection.
– Describe the most basic separation of light and surface interactions.
– Specular reflection is the behavior of light hitting a surfaceboundaryand perfectly
reflecting off of it, much like how a mirror would behave..
– Diffusion occurs when not all light reflects from the surface. Some will penetrate into
the interior of the illuminated object. There it will either be absorbed by the material
(usuallyconverting to heat) or scattered internally.

30. Some terminology
• Diffusion and reflection – also known as diffuse and specular reflection.
– Describe the most basic separation of light and surface interactions.
– Specular reflection is the behavior of light hitting a surfaceboundaryand perfectly
reflecting off of it, much like how a mirror would behave..
– Diffusion occurs when not all light reflects from the surface. Some will penetrate into
the interior of the illuminated object. There it will either be absorbed by the material
(usuallyconverting to heat) or scattered internally.
• The absorption and scattering of diffuselight are often quite different for different
wavelengths of light, which is what gives objects their color (e.g. if an object
absorbs most light but scatters blue, it will appear blue).

31. How was light modeled in 1977?

32. Blinn-Phong Shading Model
• Every surfaceis made of some material and each material reflects light differently.

33. Blinn-Phong Shading Model
• Every surfaceis made of some material and each material reflects light differently.
– Think of how metal objects are shiny and wooden objects are matte. We need to have a
way to specify material parameters that can control how a surfacereflects light.

34. Blinn-Phong Shading Model
• Every surfaceis made of some material and each material reflects light differently.
– Think of how metal objects are shiny and wooden objects are matte. We need to have a
way to specify material parameters that can control how a surfacereflects light.
• Every surfacecan then be approximated with three reflectivity constants, and
they control the intensity of the various reflections.
– 𝐾 𝑎 ambient reflectivity
– 𝐾𝑠 specular reflectivity
– 𝐾 𝑑 diffusereflectivity
– 𝑎 specular highlighting

35. Blinn-Phong Shading Model
• By sampling relevant spatial information from
a three dimensional scene, the light intensity
at point 𝑃 can be calculated.

36. Blinn-Phong Shading Model
• By sampling relevant spatial information from
a three dimensional scene, the light intensity
at point 𝑃 can be calculated.
– The normalvector 𝑁 to the surface
– The light vector 𝐿 from the surface
– The view vector 𝑉

37. Blinn-Phong Shading Model
• By sampling relevant spatial information from
a three dimensional scene, the light intensity
at point 𝑃 can be calculated.
– The normalvector 𝑁 to the surface
– The light vector 𝐿 from the surface
– The view vector 𝑉
• Lambert’s Law states that the diffusion at a
point is proportional to the cosine of the
angle between the incoming light ray 𝐿 and
the normal of the surface 𝑉.

38. Blinn-Phong Shading Model
• Diffusion value Ld derived from Lambert’s Law
– Ld = Kd * dot(N, L) * light source intensity
• Specular reflection value Ls
– Phong: Ls = Ks * exp(dot(R, V), a) * light source intensity
– Blinn: Ls = Ks * exp(dot(N, H), a) * light source intensity
• Ambient light value La
– La = Ka * ambient light intensity

39. Blinn-Phong Shading Model
• Diffusion value Ld derived from Lambert’s Law
– Ld = Kd * dot(N, L) * light source intensity
• Specular reflection value Ls
– Phong: Ls = Ks * exp(dot(R, V), a) * light source intensity
– Blinn: Ls = Ks * exp(dot(N, H), a) * light source intensity
• Ambient light value 𝐿 𝑎
– 𝐿 𝑎 = 𝐾𝑎 ∙ 𝑎𝑚𝑏𝑖𝑒𝑛𝑡 𝑙𝑖𝑔ℎ𝑡 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦
• Light intensity at a pixel equals the sum of 𝐿 𝑎 + 𝐿 𝑠 + 𝐿 𝑑
• shadertoy example

40. Blinn-Phong is far from perfect
• Does not respect conversation of energy. As specular power is increased, more
energy is lost from the system.

41. Blinn-Phong is far from perfect
• Does not respect conversation of energy. As specular power is increased, more
energy is lost from the system.
• Isn’t expressive enough to simulate more complex materials due to crude
approximations of diffusion and reflective properties.

42. Blinn-Phong is far from perfect
• Does not respect conversation of energy. As specular power is increased, more
energy is lost from the system.
• Isn’t expressive enough to simulate more complex materials due to crude
approximations of diffusion and reflective properties.
• Ambient lighting completely ignores diffusion properties of environment.

43. Blinn-Phong is far from perfect
• Does not respect conversation of energy. As specular power is increased, more
energy is lost from the system.
• Isn’t expressive enough to simulate more complex materials due to crude
approximations of diffusion and reflective properties.
• Ambient lighting completely ignores diffusion properties of environment.
• Terrible workflow for artists, due to final visuals being dependent on physically
incorrect “tweaks” on both lighting and art assets. Errors or discrepancies in
lighting can propagate to other assets.

44. Physically-based rendering
A modern responseto archaic problems

45. Bidirectional Reflectance Distribution Function
• A function that describes the reflectance properties of a surface. In computer
graphics, there are different BRDF models some of which are not physically
plausible.

46. Bidirectional Reflectance Distribution Function
• A function that describes the reflectance properties of a surface. In computer
graphics, there are different BRDF models some of which are not physically
plausible.
• For a BRDF to be physicallyplausible, it must be energy conserving and exhibit
reciprocity.

47. Bidirectional Reflectance Distribution Function
• A function that describes the reflectance properties of a surface. In computer
graphics, there are different BRDF models some of which are not physically
plausible.
• For a BRDF to be physicallyplausible, it must be energy conserving and exhibit
reciprocity.
• Energy conservation states that the total amount of light re-emitted by a surface
(reflected and scattered back) is less than the total amount it received.

48. Microfacet theory
• Both diffuse and specular reflection are dependent on surfaceirregularities.

49. Microfacet theory
• Both diffuse and specular reflection are dependent on surfaceirregularities.
• In practice, the effect of surface roughness on diffuse reflection is much less
prominent because of scattering happening inside the material.

50. Microfacet theory
• Both diffuse and specular reflection are dependent on surfaceirregularities.
• In practice, the effect of surface roughness on diffuse reflection is much less
prominent because of scattering happening inside the material.
– As a result, outgoing reflected light rays are fairly independentof surfaceroughness and
incident direction. The previous Lambertian model completely ignores this.

51. Microfacet theory
• An example microfacetbased specular BRDF would be Cook-Torrance:
– 𝑓(𝑙, 𝑣) 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 =
𝐷 ℎ 𝐹 𝑣,ℎ 𝐺 𝑙,𝑣,ℎ
4 𝑛∙𝑙 (𝑛∙𝑣)

52. Microfacet theory
• An example microfacetbased specular BRDF would be Cook-Torrance:
– 𝑓(𝑙, 𝑣) 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 =
𝐷 ℎ 𝐹 𝑣,ℎ 𝐺 𝑙,𝑣,ℎ
4 𝑛∙𝑙 (𝑛∙𝑣)
• Where:
– 𝑓 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 is the reflectance at normal incident
– 𝐹 is the Fresnel reflectance term
– 𝐺 is the geometry term
– 𝐷 ℎ is the normal distribution term describing how the microfacet normal are distributed
– 𝑙 is the light direction
– 𝑣 is the view direction
– 𝑛 is the surface normal
– ℎ is the half vector between l and v

53. Microfacet theory
• An example microfacetbased specular BRDF would be Cook-Torrance:
– 𝑓(𝑙, 𝑣) 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 =
𝐷 ℎ 𝐹 𝑣,ℎ 𝐺 𝑙,𝑣,ℎ
4 𝑛∙𝑙 (𝑛∙𝑣)
• Where:
– 𝑓 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 is the reflectance at normal incident
– 𝐹 is the Fresnel reflectance term
– 𝐺 is the geometry term
– 𝐷 ℎ is the normal distribution term describing how the microfacet normal are distributed
– 𝑙 is the light direction
– 𝑣 is the view direction
– 𝑛 is the surface normal
– ℎ is the half vector between l and v
• The goal is to analytically solve the BRDF.

54. Microfacet theory
• An example microfacetbased specular BRDF would be Cook-Torrance:
– 𝑓(𝑙, 𝑣) 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 =
𝐷 ℎ 𝐹 𝑣,ℎ 𝐺 𝑙,𝑣,ℎ
4 𝑛∙𝑙 (𝑛∙𝑣)
• Where:
– 𝑓 𝑚𝑖𝑐𝑟𝑜𝑓𝑎𝑐𝑒𝑡 is the reflectance at normal incident
– 𝐹 is the Fresnel reflectance term
– 𝐺 is the geometry term
– 𝐷 ℎ is the normal distribution term describing how the microfacet normal are distributed
– 𝑙 is the light direction
– 𝑣 is the view direction
– 𝑛 is the surface normal
– ℎ is the half vector between l and v
• Let’s look at what it would take to solve one of the terms.

55. Fresnel Effect
• The amount of light you see reflected from a surface depends on the viewing angle
at which you perceive it.

56. Fresnel Effect
• The amount of light you see reflected from a surface depends on the viewing angle
at which you perceive it.
• None: 𝐹𝑛𝑜𝑛𝑒 𝑣, ℎ = 𝐹0
• Schlick: 𝐹𝑆𝑐ℎ𝑙𝑖𝑐𝑘 𝑣, ℎ = 𝐹0 + 1 − 𝐹0 (1 − 𝑣 ∙ ℎ )5
• Torrance: 𝐹𝐶𝑜𝑜𝑘−𝑇𝑜𝑟𝑟𝑎𝑛𝑐𝑒 = too long to even write …

57. Fresnel Effect
• The amount of light you see reflected from a surface depends on the viewing angle
at which you perceive it.
• None: 𝐹𝑛𝑜𝑛𝑒 𝑣, ℎ = 𝐹0
• Schlick: 𝐹𝑆𝑐ℎ𝑙𝑖𝑐𝑘 𝑣, ℎ = 𝐹0 + 1 − 𝐹0 (1 − 𝑣 ∙ ℎ )5
• Torrance: 𝐹𝐶𝑜𝑜𝑘−𝑇𝑜𝑟𝑟𝑎𝑛𝑐𝑒 = too long to even write …
• Consequently, Schlick’s Approximation has become quite popular in real time
graphics due to it’s low computational cost.

58. Conclusion
• Energy conservation is handled by the shader. A reflected ray is never brighter
than the value it had when it first hit the surface.
• The BRDF is handled by the shader. No more magic lighting values, and properties
exposed to artists are based in physical reality.
• Naturally will trend to better visual fidelity and photorealism do due basis is
physical phenomena.
• Large opportunities in numerical analysis to create performant solutions for
solving the needed terms in the BRDF. Fresnel is just one example.

59. Questions?