bi-directional reflectance distribution functions (brdf’s)
Post on 10-Feb-2016
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Bi-Directional Reflectance Distribution Functions
(BRDF’s)
Matthew McCrory
What is a BRDF?
Must know something about light and how it interacts with matterWhen light interacts with matter:
Complicated light-matter dynamic occursDependent on characteristics of both the light and the matterExample, sandpaper vs. a mirror
What is a BRDF?
Typical light-matter interaction scenario:Incoming Light
Transmitted Light
Reflected Light
Scattering and Emission Internal Reflection Absorption
3 types of interaction: transmission, reflection, and absorbtionLight incident at surface = reflected + absorbed + transmittedBRDF describes how much light is reflected
What is a BRDF?
Viewer/light position dependency (incoming/outgoing rays of light)
Example – Shiny plastic teapot with point lightDifferent wavelengths (colors) of light may be absorbed, reflected, transmitted differentlyPositional variance – light interacts differently with different regions of a surface, e.g. woodBRDF must capture this view and light dependent nature of reflected light
What is a BRDF?In functional notation:
Or
For position invariant BRDF’s
vuooii ,,,,,BRDF
ooii ,,,BRDF
Differential Solid AnglesMore appropriate to speak of light in terms of quantity of light arriving at or passing through a certain area of spaceLight doesn’t come from a single direction
More appropriate to consider a small region of directions
Small surface element
Normal
Small area
Incoming light direction
wi
Neighborhood of directions
Differential Solid Angles
Patch formed at intersection of pyramid and unit sphereDifferential Solid Angle defined as surface area of path
sin
d
d
sphere of radius 1
dddwdddwwidthheightdw
sin))(sin(
))((
Definition of a BRDFGiven:
Incoming light direction wi, and an outgoing reflected direction wo, each defined relative to a small surface element
BRDF defined as: the ratio of the quantity of reflected light in direction wo, to the amount of light that reaches the surface from direction wi.
n wi
light source
Small surface element
Differential solid angle dwi
θii
o
EL
BRDF
Definition of a BRDFLight arriving from direction wi proportional to the amount arriving at the differential solid angle.Given light source Li, total light arriving through the region is Li*dw
Incoming light must be projected onto surface element. Accomplished by modulating by (= N.wi)
BRDF given by:
icos
iii
o
dwLL
BRDFcos
Classes and Properties of BRDF’s
2 classesIsotropicAnistropic
2 important propertiesReciprocity
Conservation of energy
=
Surface
Incoming lightReflected light
1cos,,,BRDF
ooooii dw
The BRDF Lighting EquationGoal:
Define a general lighting equation that expresses how to use BRDF’s for computing the illumination produced at a surface point
Light arrives from > 1 point
Surface
Outgoing light
Incoming lightE
The BRDF Lighting EquationAmount of light reflected in outgoing direction is the integral of the amount of light reflected in the outgoing direction from each incoming direction
More convenient to think discreetly
ioiioo dwwwLL ),( todue
in
oiioo wwLL ),( todue
The BRDF Lighting EquationFor each incoming direction, the amount of reflected light in the outgoing direction is defined in terms of the BRDF.Given:
Li is the light intensity from direction wi. Ei is the amount of light arriving from direction wi:
Ei must take into account surface area intensity instead of differential solid angle
iooiiio EBRDFL ),,,( todue
iiii dwLE cosiiooiiio LBRDFL cos),,,( todue
in
iiooiio LBRDFL cos),,,(
The BRDF Lighting EquationFinally! The general BRDF lighting equation for a single point light source is:
For multiple light sources, each light must be used in the equation and the sum is the amount of outgoing light
iiooiio LBRDFL cos),,,(
Analytical Models and Acquired BRDF Data
How can we compute BRDFs for use in the general BRDF lighting equation?
Evaluate mathematical functions derived from analytical modelsResample BRDF data acquired by empirical measurements of real-world surfaces
Some ExamplesFrom the National Institute of Standards and TechnologyCourse and fine metallic paint on vases
Some ExamplesTwo tiles rendered using BRDFs obtained from the measured surface topology of actual tile samples
Improvements on BRDFBRDF assumes light enters and leaves a surface at the same point, which isn’t true in real lifeLight scatters beneath a surface and leaves at different places than where it enteredBi-direction Scattering Surface Reflection Distribution Functions (BSSRDFs) account for just that
Comparison
BRDF vs BSSRDF
Real-time BRDFSome hardware vendors like Nvidia are making BRDF lighting doable in real-time
That’s it!
Questions?
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