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 = 2π radians Full sphere = 4π 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 (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
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
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
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
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 Bidirectional Reflectance Distribution Function (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
Microgeometry BRDF models Somewhere in between (Very) rough Smooth Ideal diffuse (Lambertian) Ideal specular More general 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 Fresnel term Normal distrb. Shadowing & masking 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