Radiometry & BRDFs CS295, Spring 2017 Shuang Zhao

Transcription

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

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

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

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

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

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

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

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

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

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

11 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 CS295, Spring 2017 Shuang Zhao 11

12 Irradiance & Radiosity Power per unit area (dф/da) 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

13 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: CS295, Spring 2017 Shuang Zhao 13

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

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

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

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

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

19 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

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

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

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

23 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

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

25 Reflectance Models The Bidirectional Reflectance Distribution Function (BRDF) CS295, Spring 2017 Shuang Zhao 25

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

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

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

29 Ideal Diffuse BRDF CS295, Spring 2017 Shuang Zhao 29

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

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

32 Fresnel Reflection [ CS295, Spring 2017 Shuang Zhao 32

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

34 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

35 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

36 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

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

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

39 More BRDFs montes_lsi tr.pdf CS295, Spring 2017 Shuang Zhao 39