Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Computer - - PowerPoint PPT Presentation

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Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Computer - - PowerPoint PPT Presentation

Oct 22, 2022 972 likes •1.37k views

Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Computer Science Department University of California, Irvine CS295, Spring 2017 Shuang Zhao 1 Todays Lecture Radiometry Physics of light BRDFs How materials reflects

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Radiometry & BRDFs

CS295, Spring 2017 Shuang Zhao

Computer Science Department University of California, Irvine

CS295, Spring 2017 Shuang Zhao 1

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Today’s Lecture

  • Radiometry
  • Physics of light
  • BRDFs
  • How materials reflects light

CS295, Spring 2017 Shuang Zhao 2

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Radiometry

CS295: Realistic Image Synthesis Radiometry & BRDFs

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Geometric Optics

  • Light travels in straight lines
  • Unpolarized
  • Ray properties:
  • Wavelength (i.e., color)
  • Intensity

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Background:

Solid angle, spherical coordinate

Physically Based Rendering: Radiometry

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Background: Hemispheres

  • Hemisphere = 2D surface
  • Direction = point on (unit) sphere

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Background: Solid Angles

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2D 3D

Full circle = 2π radians Full sphere = 4π steradians

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Background: spherical coordinates

  • Direction = point on (unit) sphere

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For unit sphere (r = 1):

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Background: spherical coordinates

  • Direction = point on (unit) sphere

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= direction vector

Defines a measure over (hemi)sphere

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Background: spherical coordinates

  • Example: solid angle of hemisphere

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Power

  • Energy
  • Symbol: Q; unit: Joules
  • Power: Energy per unit time (dQ/dt)
  • Aka. “radiant flux”
  • Symbol: P or Ф; unit: Watts (Joules per second)
  • All further quantities are derivatives of power
  • “flux densities”

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Irradiance & Radiosity

  • Power per unit area (dФ/dA)
  • i.e., area density of power
  • Defined with respect to a surface
  • Symbol: E; unit: W / m2
  • Measureable as power on a small-area detector

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Irradiance Radiosity

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Intensity

  • Power per unit solid angle (dФ/dω)
  • i.e., solid angle density of power
  • Normally used for point sources
  • Symbol: I; units: W / sr
  • For uniform source:

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Radiance

  • Radiant energy at x in direction ω:
  • A 5D function

: Power

  • per projected surface area
  • per solid angle
  • Unit: Watt / (m2 sr)

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Why is radiance important?

  • Invariant along a straight line (in vacuum)

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Equal!

Invariant of Radiance

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Invariant of Radiance

  • Take-home message:
  • is a well-defined measure on the space of

lines

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Projected Area and Solid Angle

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θ

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Why is radiance important?

  • Response of a sensor (camera, human eye) is

proportional to radiance

  • Pixel values in image proportional to radiance

received from that direction

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Wavelength Dependencies

  • All radiometric quantities depend on

wavelength λ

  • E.g., spectral radiance:
  • Radiance:

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Relationships (Bottom-Up)

  • Radiance is the fundamental quantity
  • Power:
  • Irradiance/radiosity:

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Example: Diffuse Emitter

  • Diffuse emitter: light source with

equal radiance (L) everywhere

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Example: Near vs. Far

  • Two identical light sources A and B
  • The sensor receives more power from A because it

covers a greater solid angle

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A B

Larger solid angle Smaller solid angle

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BRDFs

CS295: Realistic Image Synthesis Radiometry & BRDFs

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Reflectance Models

  • The Bidirectional Reflectance Distribution

Function (BRDF)

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Properties of BRDF

  • Reciprocity:
  • Therefore “bidirectional”!
  • Notation

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Properties of BRDF

  • Nonnegativity:
  • Conservation of energy:

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BRDF models

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Ideal diffuse (Lambertian) Ideal specular More general

Micro- geometry

(Very) rough Smooth Somewhere in between

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Ideal Diffuse BRDF

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Ideal Specular BRDF

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is the Dirac delta function satisfying:

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Microfacet BRDF

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where

Fresnel term Shadowing & masking Normal distrb.

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Fresnel Reflection

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[www.scratchpixel.com]

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Schlick's Approximation

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where

The material’s refractive index

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Normal Distribution Function

  • D(m) controls the distrb. of micro-surface normal
  • Example: isotropic GGX

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where θh is the angle between n and ωh, and β>0 controls surface roughness

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Shadowing and Masking

  • Depends on normal distribution

function D(m)

  • Captures self-occlusion at the

micro-surface (inter-reflection ignored)

  • Example: isotropic GGX

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with θx being the angle between x and n (for all x) where

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Generalization of microfacet BRDFs

  • Handling transmission

[Walter et al. 2007]

  • Capturing inter-reflection

[Heitz et al. 2016]

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No inter-reflection With inter-reflection

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BRDF Mixtures

  • Linear combinations of multiple BRDFs
  • E.g.,

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More BRDFs

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[Montes & Ureña 2012]

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More BRDFs

  • http://digibug.ugr.es/bitstream/10481/19751/1/r

montes_LSI-2012-001TR.pdf

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