Transcript What is a BRDF?

An Introduction to
BRDF-Base Lighting
Chris Wynn
Presentation by Randy Rauwendaal
Review by Jaewon Jeong
Shader Study
Acronyms
 BRDF
 Bidirectional Reflectance Distribution Function
 SPDF
 Scattering Probability Density Function
 BSDF
 Bidirectional Scattering Distribution Function
 BTDF
 Bidirectional Transmission Distribution Function
 BSSRDF
 Bidirectional Scattering Surface Reflectance Distribution
Function
What is a BRDF?
 We’ll get to that later, but first we must understand
how light interacts with matter
 뒤에서 이야기할 터이니, 물질(Matter)에 조명(Light)이 어떻
게 작용하는지를 알아보자.
Light & Matter
 Interaction depends on the physical characteristics of
the light as well as the physical composition and
characteristics of the matter
 Three types of interactions when light first hits a
material
 반사(Reflection)
 흡수(Absorption)
 투과(Transmittance)
Conservation of Energy
light incident at surface = light reflected + light absorbed + light transmitted
BRDF는 조명이 물체와 접촉할 때 얼마나 반사가 일어나는지
를 기술한다.
어느 정도인지는 표면의 Normal과 Tangent에 관하여 관찰자
(Viewer)와 조명의 위치에 의존적이다.
BRDF는 빛이 반응하는 점의 지역적인(local) 방향
(orientaion)에 영향을 받는 들어오는 (incoming) 조명의 방향
과 나가는(outgoing)의 방향에 대한 함수이다.
Wavelength
 빛이 표면에 닿으면 재질 자체의 물리적인 성질에 따라 각각
의 파장이 흡수, 반사, 투과가 다른 각도로 이루어진다.
 The means that a BRDF is also a function of
wavelength
 Wavelength = Color
Position Variance
 Light interacts differently with different regions of the
surface, this is know as positional variance
 Noticeable in materials that reflect light in manner that
produces surface detail (wood, marble, etc.)
Notation
BRDFλ(θI, φI, θo, φO, u, v)
 λ is wavelength
 θI and φI, represent the incoming light direction in
spherical coordinates
 θo and φO, represent the outgoing reflected direction in
spherical coordinates
 u and v represent the surface position parameterized
in the texture space
Spherical Coordinates
 Cartesian coordinates (vx, vy, vz)
 Spherical coordinates (θ, φ)
Differential Solid Angles(미소 입체각)
 Since BRDFs measure how light reflects off a surface
when viewed we must know how much light arrives at
a surface element from a particular direction
 Light is measures as energy per-unit surface area(i.e.
Watt/meter2)
 Units are in radians squared or steradians(sr.)
 We must consider flow through a
neighborhood of directions when
determining the amount of light
that arrived at or leaves a surface
Radians and Steradians
 원의 원주
 구의 면적
 2πr
 4πr2
 1rad =
 1sr =
r
r
r
θ

r2
θ
r
전체 각: 2π rad

r
전체 입체각: 4π sr
Differential Solid Angles
 The differential solid angle is defined to be the area of
the small blue patch
 Given spherical coordinates (θ, φ) and small
differential angular changes denoted dθ, dφ, the
differential solid angle, dw, is dented to be
 The area quantity has
units of radians squared,
or steradians
Definition of a BRDF




wi = incoming light direction
wo = outgoing reflected direction
Lo = quantity of light reflected in direction wo
Ei = quantity of light arriving from direction wi
Definition of a BRDF
N
wi



방향 wi 에서 온 빛의 양은 미소 입체각에서 도착한 양에 비례
일정 영역에 들어오는 빛의 양: Li
미소 입체각에 도착하는 총 양: Li * dwi


To Determine the amount of light with respect to the surface element, the
incoming light must be projected onto the surface element by modulating by
여기에서 이뤄지는 Projection은 Lambertian diffuse lighting과 유사함

The means Ei=Licosθidwi, as a result, the BRDF is given by cosθi=N·wi
θi
θi
dwi
cosθidwi

BRDF의 단위
 sr-1
Classes and Properties of BRDFs
 There are two classes of BRDFs, isotropic BRDFs and
anisotropic BRDFs
 The importance properties of BRDFs are reciprocity(호
환성) and conservation of energy(에너지 보존)
 BRDFs that have these properties are considered to be
physically plausible
Isotropic BRDFs
 The term isotropic is used to describe BRDFs that
represent reflectance properties that are invariant with
respect to rotation of the surface around the surface
normal vector
 Smooth plastics
 Lambertian Model
Anisotropic BRDFs
 BRDFs that describes reflectance properties that do
exhibit change with respect to rotation of the surface
around the surface normal vector
 Most real world surface
 Brushed metal, satin, hair
 하지만, Isotropic BRDF도 유용하다.
 대부분의 물체는 미세한 Anisotropic BRDF를 가진다.
Helmholtz Reciprocity(호환성)
 If the incoming and outgoing directions are swapped,
the value of the BRDF does not change
Conservation of Energy(에너지 보존)
 The quantity of light reflected must be less than or
equal to the quantity of incident light
 The sum of all outgoing directions of the BRDF times
the project solid angle must be less than one
The BRDF Lighting Equation
 Outgoing light의 총 양은 각각의 Incoming light들로부터
나가는 빛의 양을 적분한 것과 같다.
 Lo dut to i(wi, wo) 는 wo 방향으로 반사되는 빛의 양을 표현함
The BRDF Lighting Equation
 Outgoing 방향으로 반사되는 빛의 Intensity

표면의 한 점에 도착하는 빛의 Intensity와 그에 상응하는 BRDF의 곱
 Where Ei is the amount of light arriving from direction wi
 빛을 다시 Projection하기 위해서 cosθi=N·wi를 곱함
 Ei=Licosθidwi, 지만 이산적인 경우
모든 incoming 방향에서 dwi 는 동일한 가중치므로
Ei=Licosθi
 Outgoing 방향으로 반사되는 빛은
The BRDF Lighting Equation
 여러 방향에서 오는 빛들을 전부 계산하여 색상을 정하는 것보다
각각의 Point 조명들을 조명 계산식을 이용하여 Intensity를 계산
하는 것이 낫다
 Where Lij is the intensity of the jth light source and
wij=(θij, θij) is the direction of the jth light source
 For a single point light source, the light reflected in the
direction of an observer is
BRDFs and the Phong Model



Notice that the final expression is very
similar to the general BRDF lighting equation
The Phong lighting model can be considered
a special case of the BRDF based lighting
The Phong model is convenient to use for
materials with reflectance properties
approximated by
Acquiring BRDF Data
 Many simple analytical models have been developed
 Cook-Torrance model
 Modified Phong model
 Ward’s model
 BRDF는 gonioreflectometer 라
불리는 장비를 통하여
물리적으로 측정하여
얻을 수도 있다
The University of Virginia
spherical gantry
Analytical models
Lambert
BRDF
(empirical model)
Cook-Torrance
(dielectric) BRDF
(physical model)
Phong
BRDF
(empirical model)
Cook-Torrance
(conductor) BRDF
(physical model)
Blinn-Phong
BRDF
(empirical model)
Schlick-Blinn-Phong
BRDF
(empirical model)
Schlick-Cook-Torrance Schlick-Cook-Torrance
(dielectric) BRDF
(conductor) BRDF
(physical model)
(physical model)
Ward
(isotroic) BRDF
(physical model)
Ashikhmin-Shirley
BRDF
(empirical model)
Ward-Duer
(isotropic) BRDF
(physical model)
Oren-Nayar
BRDF
(physical model)
Ward
(anisotropic) BRDF
(physical model)
Cook-Torrance
(anisotropic) BRDF
(physical model)
Ward-Duer
(anisotropic) BRDF
(physical model)
References
 Randy Rauwendaal. BRDFs
 Chris Wynn. An Introduction to BRDF-Base Lighting,
NVIDIA Corporation
 BRDF Analytical Models
 http://szaber.com/grafx/