Welcome back Lots of logistics to take care of: Readings Grad - - PDF document

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Material Properties 2

Welcome back

 Lots of logistics to take care of:

 Readings  Grad Report  Assignments  Projects

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Readings

 All readings up to week 3 graded

 Comments/grades on mycourses

 Remember to place this weeks in the

dropbox.

Grad Report

 Topic due tonight.

 Please place short description in dropbox.

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Projects

 Proposals

 Proposal due before break (please get

yours in if not submitted)

 Feedback on proposals -- mycourses  Web sites please.  23 projects (4-5 more expected)

Projects

 Presentations:

 Dates:

 Week 10: Mon, Feb 18  Week 10: Wed, Feb 20  Finals Week / Week 11: Mon, Feb 25

 WE WILL NEED AN EXTRA DAY  Week 11 or Week 9?  15 minutes / presentation  Schedule on Web by next class  Please send me choice of time/day

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Assignments

 Checkpoint 1 - Setting the scene

 All graded

 Checkpoint 2 - Camera

 Due tonight.

 Checkpoint 3 - Basic shading

 To be given tonight.

Plan for today

 Material Properties

 Bi-directional reflectance distribution functions

(BRDFs)

 Advanced Illumination Models  Beyond BRDFs

 Checkpoint 3 of the ray tracer  Ray tracer help  Questions

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Computer Graphics as Virtual Photography

camera (captures light) synthetic image camera model (focuses simulated lighting)

processing

photo processing tone reproduction real scene 3D models Photography: Computer Graphics: Photographic print

Shading

 Computing the light that leaves a point  Shading point - point under investigation  Illumination model - function or algorithm

used to describe the reflective characteristics of a given surface.

 Shading model – algorithm for using an

illumination model to determine the color of a point on a surface.

 For efficiency’s sake, most illumination models

are approximations.

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BRDF

 Bi-directional Reflectance Function

) , , , (

r r i i r

f BRDF

• =

At a given point, gives relative reflected illumination in any direction with respect to incoming illumination coming from any direction; Note: The θ’s are elevation, ϕ’s are measured about the surface normal. The i’s refer to the incident ray; the r’s to the reflected ray.

BRDF Geometry

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BRDF

 Can return any positive value.  Generally wavelength specific.

) , , , , (

• r

r i i r

f BRDF =

Anisotropic Models

 Anisotropy

 Isotropic - surfaces reflect equally from any

direction of view

 Anisotropic - reflection varies not only with angle

• f incidence, but also with the angle of the

incident light w.r.t some viewing angle.

 Surfaces considered to possess an intrinsic grain  Examples: satin, velvet, hair, brushed aluminum

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Ansiotropic Models

 anisotropic (adj.) an·i·so·trop·ic 1.

• Physics. of unequal physical properties

along different axes.

 http://www.neilblevins.com/cg_educatio

n/aniso_ref/aniso_ref.htm

Anisotropic Models

 Anisotropic reflection -- example

Ward Blevins

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Why does ansiotropic reflection occur?

 Occurs on objects with fine grain in a

given direction.

Blevins

Anisotropic Models

 Ward Model [Ward92]

 Designed for both accuracy and ease of

use

 Includes model for anisotropic reflection

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Anisotropic Models

 Ward Model - Isotropic

specular 2 / ) (tan diffuse

) 4 cos cos 1 (

2 2

πα δ θ ρ π ρ ρ

α γ −

• +

= e

s d

Anisotropic Model

 Ward Model

 ρd - Diffuse reflectance coefficient (can

vary with wavelength)

 ρs - Specular reflectance coefficient (can

vary with wavelength)

 α - Standard deviation of surface slope

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Anisotropic Models

 Ward Model -- anisotropic

specular )) / sin / (cos (tan diffuse

) 4 cos cos 1 (

2 2 2 2 2

y x s d

y x

e α πα δ θ ρ π ρ ρ

α φ α φ γ + −

• +

=

Anisotropic Models

 Ward Model w/ ansiotropy

 αx - Standard deviation of surface slope in

x-direction

 αy - Standard deviation of surface slope in

y-direction

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Ward’s Anisotropic Model Anisotropic Models

 Ward Model - example

Photo Isotropic Anisotropic

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Anisotropic Models

 Other anisotropic models (all based on

physics)

 [Kajia85]  [Poulin90]  [He91]

BRDF

 Simplifying Assumptions wrt the BRDF

 Light enters and leaves from the same point.

 Not necessarily true  Subsurface scattering  Skin, marble

 Light of a given wavelength will only reflect back light

• f that same wavelength

 Not necessarily true  Light Interference  Oily patches, peacock feathers

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Subsurface Scattering

Jensen, et al 2001

Subsurface Scattering

 Example: Skin

Blevins,2001

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bidirectional surface scattering distribution function (BSSDF)

 Relates outgoing reflectance in a given

direction (at a given point) to the incoming luminance arriving at another point.

bidirectional surface scattering distribution function (BSSDF)

Outgoing luminance at xo in the direction

• f wo

incoming luminance at xi in the direction

• f wi

BSSDF When xo == xi the BSSDF is simply a BRDF

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BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

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BSSDF -- Examples

Jensen, et al 2001

Using BRDF Using BSSDF

BSSDF Modeling

 Won Henrik Wann Jensen an academy

award in 2004.

 Practical model described in [Jensen, et.

• al. 2001]

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Using BSSRDF

[Hao, 2004]

Light transport functions

 BSSRDF (Bidirectional surface scattering

reflectance distribution function) describes the relation between outgoing radiance and the incident flux, including the phenomena like subsurface scattering (SSS).

 BRDF (Bidirectional reflectance distribution

function) is a simplified BSSRDF, assuming that light enters and leaves at the same point

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Light Transport Functions

Wikipedia

Light transport functions

 BTDF (Bidirectional transmittance distribution

function) is similar to BRDF but for the

• pposite side of the surface. (see the top

image).

 BSDF (Bidirectional scattering distribution

function) is the most general function.

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Light transport functions Summary

 Advanced models of reflection

 Anisotropic Models  BSSDF – subsurface scattering  Complete transport functions.  Adding to ray tracer.  Break.