Illumination and Shading - II

Transcription

1 Illumination and Shading - II Computer Graphics COMP 770 (236) Spring 2007 Instructor: Brandon Lloyd 2/19/07 1

2 From last time Light Sources Empirical Illumination Shading Local vs Global Illumination 2/19/07 2

3 Today s topics Cook-Torrance illumination model Microfacets Geometry term Fresnel reflection Radiance and irradiance BRDFs Homework #2 2/19/07 3

4 OpenGL s illumination model lights I = k I + k I max((nˆ L),0) ˆ + k I max((r ˆ ),0) r a a d d s s i= 1 Problems with empirical models: What are the coefficients for copper? What are k a, k s, and n s? Are they measurable quantities? How does the incoming light at a point relate to the outgoing light? Is energy conserved? What exactly is light intensity? Is my picture accurate? 2/19/07 4 ˆV n s

5 Desiderata A model that uses physical properties that can be looked up in the CRC Handbook of Chemistry and Physics (indices of refraction, reflectivity, conductivity, etc.) Parameters that that have clear physical analogies (how rough or polished a surface is) Models that are predictive (the simulation attempts to model the real scene) Models that conserve energy Complex surface substructures (crystals, amorphous materials, boundary-layer behavior) If it was easy... everyone would do it. 2/19/07 5

6 Better reflectance models Blinn-Torrance-Sparrow (1977) isotropic reflectors with smooth microstructure Cook-Torrance (1982) wavelength dependent Fresnel term He-Torrance-Sillion-Greenberg (1991) adds polarization, statistical microstructure, self-reflectance Very little of this work has made its way into graphics H/W. Why? 2/19/07 6

7 Cook-Torrance illumination I I k I (1 k k ) (L N) k Definitions: lights λ = λ + λ ρ ˆ λ ˆ,r,a a,i + a s i s i= 1 I λ,a - Ambient light intensity (same old hack) k a - Ambient surface reflectance (hacks beget hacks) I λ,i - Luminous intensity of light source i DGF λ( θi) π(vˆ N) ˆ k s - percentage of light reflected specularly (notice terms sum to one) ρ λ - diffuse reflectivity L i - vector to light source N - average surface normal at point V - vector to viewer D - microfacet distribution function G - geometric attenuation Factor F λ (θ i ) - Fresnel reflection term 2/19/07 7

8 Microfacet distribution function Statistical model of the variation in normal direction Based on a Beckman distribution function Consistent with the surface variations of rough surfaces β - the angle between ˆN and m - the root-mean-square slope of the the microfacets. Ĥ large m indicates steep slopes and the reflections spread out over the surface 2/19/07 8

9 Beckman s distribution 2/19/07 9

10 Geometric attenuation factor There are many different ways that an incoming beam of light can interact with the surface locally. 2/19/07 10

11 Blocked reflection A portion of the out-going beam can be blocked. 2/19/07 11

12 Blocked beam A portion of the incoming beam can be blocked. 2/19/07 12

13 Geometric attenuation factor In each case, the geometric configurations can be analyzed to compute the percentage of light that actually escapes from the surface: The geometric factor, chooses the smallest amount of light that is lost as the local self-shadowing model 2/19/07 13

14 Fresnel reflection The Fresnel term results from a complete analysis of the reflection process while considering light as an electromagnetic wave. When the electric field is oriented consistent it is said to be polarized The behavior of reflection depends on the orientation of the electric field relative to the surface normal at the point of incidence 2/19/07 14

15 Fresnel reflection (dialectric) parallel perpendicular air glass glass air 2/19/07 15

16 Fresnel reflection The Fresnel reflection is wavelength dependent depends on index-of-refraction of the material Dialectrics transmit light that is not reflected Conductors absorb light that is not reflected index-of-refraction is complex to account for absorption leads to variation in colors seen in highlights This version of the equation ignores the polarization of the incoming and reflected rays. 2/19/07 16

17 Fresnel factor (conductor) 2/19/07 17

18 Results of Cook-Torrance Plastic-looking copper rendered using Phong model A Copper Vase with a more metallic appearance 2/19/07 18

19 More Cook-Torrance results 2/19/07 19

20 Energy conserving approaches Physically based models must obey the conservation of energy: Light out = Light emitted + Light in Light absorbed 2/19/07 20

21 Definitions Radiant flux (W) the rate at which light energy is emitted Irradiance (W/m 2 ) the rate of incident or incoming energy at a surface point per unit surface area. Radiant intensity (W/sr) the rate that light energy is radiated through a given solid angle a steradian (sr ) a unit of solid angle (4π steradians on a sphere) Radiance (W/(sr m 2 )) the rate of energy radiated through a given solid angle as seen reflected from a surface (i.e. the hemisphere is projected onto the surface) remains constant along a ray most important for computer graphics 2/19/07 21

22 Irradiance The irradiance function is a two dimensional function describing the incoming light energy impinging on a given point. 2/19/07 22

23 What does Irradiance look like? 2/19/07 23

24 Radiance Radiance is a two dimensional function representing the light reflected from a surface. We ve already used plots like these to visualize illumination equations for a single light direction Radiance response integrates over all incoming directions 2/19/07 24

25 BRDF The Bi-directional Reflectance Distribution Function (BRDF) describes the transport of irradiance to radiance 2/19/07 25

26 Type of BRDFs Isotropic Reflectance independent of rotation about a given surface normal Smooth plastics Random surface microstructure Anisotropic Reflectance changes with rotation around a given surface normal Brushed metal, satin, hair Patterned surface microstructure Image courtesy of Stephen Westin 2/19/07 26

27 Properties of BRDFs Hemholtz Reciprocity BDRF ( θ, φ, θ, φ ) = BDRF( θ φ θ φ ),,, i i r r r r i i From An Introduction to BRDF-Based Lighting by Wynn 2/19/07 27

28 Properties of BRDFs Conservation of Energy Ω ( ωω) BDRF, dω = 1 i r i From An Introduction to BRDF-Based Lighting by Wynn 2/19/07 28

29 Measuring BRDFs Goniphotometer One 4-D measurement at a time (slow) High-speed BRDF acquistion Homogeneous sphere w/fixed-camera and orbiting light Each photo = 1000 s of BRDF measurements Assumes isotropy 2/19/07 29

30 How to use BRDF Data? One can make direct use of acquired BRDFs in a renderer. Affine combinations of acquired BRDFs can also be used to synthesize new materials. Reciprocity? Energy Conserving? 2/19/07 30

31 BRDF approaches Table-driven obtain a set of dense samples and lookup closest entry in a table obtain data physically or by simulation fit basis functions to reduce size of the table geometry used for simulation real image rendered from tabulated data rendered with simulated BRDF 2/19/07 31

32 BRDF approaches Constraint-based models reciprocal, energy-conserving Ward, Lafortune Can be used to fit measured BRDFs 2/19/07 32

33 Remaining hard problems Reflective Diffraction Effects Thin films Irridescence Oil on water CDs Anisotropy Brushed Metals Strands - pulled materials Satin and velvet cloth image from 2/19/07 33

34 HW2 Rendering pipeline GLRenderer captures state needed for rendering provides a frame buffer in memory for rasterization calls virtual function for each stage of the pipeline uses preprocessor macros to reroute GL calls to your GLRenderer subclass #define glcolor3f( r, g, b ) \ theglrenderer->color4f( r,g,b,1 ) MyGL subclass of GLRenderer provides stubs for each stage of the pipeline can disable stages to simplify debugging 2/19/07 34

35 HW2 Rendering pipeline apply MV eye coordinates vertices Lighting to OpenGL apply P clip coordiantes Clipping divide by w and apply viewport transform window coordinates Triangulate to OpenGL to OpenGL Rasterize to OpenGL 2/19/07 35

36 Next time Illumination and shading - III Render cheats and hacks Review HW 1 and Quiz 1 2/19/07 36