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

Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao Computer Science Department University of California, Irvine CS295, Spring 2017 Shuang Zhao 1

Today’s Lecture • Radiometry • Physics of light • BRDFs • How materials reflects light CS295, Spring 2017 Shuang Zhao 2

Radiometry CS295: Realistic Image Synthesis Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao 3

Geometric Optics • Light travels in straight lines • Unpolarized • Ray properties: • Wavelength (i.e., color) • Intensity CS295, Spring 2017 Shuang Zhao 4

Background: Solid angle, spherical coordinate Physically Based Rendering: Radiometry CS295, Spring 2017 Shuang Zhao 5

Background: Hemispheres • Hemisphere = 2D surface • Direction = point on (unit) sphere CS295, Spring 2017 Shuang Zhao 6

Background: Solid Angles 2D 3D Full circle = 2 π radians Full sphere = 4 π steradians CS295, Spring 2017 Shuang Zhao 7

Background: spherical coordinates • Direction = point on (unit) sphere For unit sphere ( r = 1 ): CS295, Spring 2017 Shuang Zhao 8

Background: spherical coordinates • Direction = point on (unit) sphere = direction vector Defines a measure over (hemi)sphere CS295, Spring 2017 Shuang Zhao 9

Background: spherical coordinates • Example: solid angle of hemisphere CS295, Spring 2017 Shuang Zhao 10

Power • Energy • Symbol: Q ; unit: Joules • Power: Energy per unit time (d Q /d t ) • Aka. “radiant flux” • Symbol: P or Ф ; unit: Watts (Joules per second) • All further quantities are derivatives of power • “flux densities” CS295, Spring 2017 Shuang Zhao 11

Irradiance & Radiosity • Power per unit area (d Ф /d A ) • i.e., area density of power • Defined with respect to a surface • Symbol: E ; unit: W / m 2 • Measureable as power on a small-area detector Irradiance Radiosity CS295, Spring 2017 Shuang Zhao 12

Intensity • Power per unit solid angle (d Ф /d ω ) • i.e., solid angle density of power • Normally used for point sources • Symbol: I ; units: W / sr • For uniform source: CS295, Spring 2017 Shuang Zhao 13

Radiance • Radiant energy at x in direction ω : • A 5D function : Power • per projected surface area • per solid angle • Unit: Watt / (m 2 sr) CS295, Spring 2017 Shuang Zhao 14

Why is radiance important? • Invariant along a straight line (in vacuum) CS295, Spring 2017 Shuang Zhao 15

Invariant of Radiance Equal! CS295, Spring 2017 Shuang Zhao 16

Invariant of Radiance • Take-home message: • is a well-defined measure on the space of lines CS295, Spring 2017 Shuang Zhao 17

Projected Area and Solid Angle θ CS295, Spring 2017 Shuang Zhao 18

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 CS295, Spring 2017 Shuang Zhao 19

Wavelength Dependencies • All radiometric quantities depend on wavelength λ • E.g., spectral radiance: • Radiance: CS295, Spring 2017 Shuang Zhao 20

Relationships (Bottom-Up) • Radiance is the fundamental quantity • Power: • Irradiance/radiosity: CS295, Spring 2017 Shuang Zhao 21

Example: Diffuse Emitter • Diffuse emitter: light source with equal radiance ( L ) everywhere CS295, Spring 2017 Shuang Zhao 22

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 Larger solid angle A B Smaller solid angle CS295, Spring 2017 Shuang Zhao 23

BRDFs CS295: Realistic Image Synthesis Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao 24

Reflectance Models • The B idirectional R eflectance D istribution F unction (BRDF) CS295, Spring 2017 Shuang Zhao 25

Properties of BRDF • Reciprocity: • Therefore “bidirectional”! • Notation CS295, Spring 2017 Shuang Zhao 26

Properties of BRDF • Nonnegativity: • Conservation of energy: CS295, Spring 2017 Shuang Zhao 27

BRDF models geometry Micro- Somewhere in between (Very) rough Smooth Ideal diffuse Ideal specular More general (Lambertian) CS295, Spring 2017 Shuang Zhao 28

Ideal Diffuse BRDF CS295, Spring 2017 Shuang Zhao 29

Ideal Specular BRDF is the Dirac delta function satisfying: CS295, Spring 2017 Shuang Zhao 30

Microfacet BRDF Normal Shadowing & distrb. masking Fresnel term where CS295, Spring 2017 Shuang Zhao 31

Fresnel Reflection [www.scratchpixel.com] CS295, Spring 2017 Shuang Zhao 32

Schlick's Approximation where The material’s refractive index CS295, Spring 2017 Shuang Zhao 33

Normal Distribution Function • D( m ) controls the distrb. of micro-surface normal • Example: isotropic GGX where θ h is the angle between n and ω h , and β >0 controls surface roughness CS295, Spring 2017 Shuang Zhao 34

Shadowing and Masking • Depends on normal distribution function D ( m ) • Captures self-occlusion at the micro-surface (inter-reflection ignored) • Example: isotropic GGX where with θ x being the angle between x and n (for all x ) CS295, Spring 2017 Shuang Zhao 35

Generalization of microfacet BRDFs • Handling transmission [Walter et al. 2007] • Capturing inter-reflection [Heitz et al. 2016] No inter-reflection With inter-reflection CS295, Spring 2017 Shuang Zhao 36

BRDF Mixtures • Linear combinations of multiple BRDFs • E.g., CS295, Spring 2017 Shuang Zhao 37

More BRDFs [Montes & Ureña 2012] CS295, Spring 2017 Shuang Zhao 38

More BRDFs • http://digibug.ugr.es/bitstream/10481/19751/1/r montes_LSI-2012-001TR.pdf CS295, Spring 2017 Shuang Zhao 39