Photo-realistic Rendering and Global Illumination in Computer Graphics Spring 2012 Material Representation K. H. Ko School of Mechatronics Gwangju Institute of Science and Technology
Dec 13, 2015
Photo-realistic Rendering and Global Illumination in Computer Graphics
Spring 2012
Material Representation
K. H. Ko
School of MechatronicsGwangju Institute of Science and Technology
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Interaction of Light with Surfaces Materials interact with light in different
ways. The appearance of materials differs given the
same lighting conditions. The reflectance properties of a surface
affect the appearance of the object. The interaction of light with surfaces can
be represented as a function of diverse quantities such as the incident light, exitant light, surface conditions, etc.
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Illustration
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 12D
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 11D
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 10D
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 9D
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 8D
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Generalization – 6D (Spatially Varying BRDF – 6D)
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
fr(x;(wiwo))
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Generalization – 6D (Homogeneous Material BSSRDF – 6D)
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
fr(Δx;(wiwo))
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Generalization – 4D (BRDF – 4D)
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Reflection of an Opaque Surface
Interaction of Light with Surfaces
Images obtained from SIGGRAPH 2005 Course Notes
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Materials interact with light in different ways. The appearance of materials differs given the
same lighting conditions. Some materials appear as mirrors. Others appear as diffuse surfaces.
The reflectance properties of a surface affect the appearance of the object.
BRDF Assume that light incident at a surface exits at
the same wavelength and same time. Ignore effects such as fluorescence and
phosphorescence.
BRDF
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In the most general case, light can enter some surface at a point p and incident direction Ψ and can leave the surface at some other point q and exitant direction Θ.The function defining this relation between
the incident and reflected radiance is called the bidirectional surface scattering reflectance distribution function.
BRDF
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Additional assumptionThe light incident at some point exits at
the same point. Do not discuss subsurface scattering. BRDF (bidirectional reflectance distribution
function)
BRDF
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BRDF
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The BRDF is defined over the entire sphere of directions (4π steradians) around a surface point.This is important for transparent
surfaces, since these surfaces can reflect light over the entire sphere.
BRDF
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Properties of BRDF Range: The BRDF can take any positive value
and can vary with wavelength. Dimension: The BRDF is a four-dimensional
function defined at each point on a surface. Two dimensions correspond to the incoming
direction, and two dimensions correspond to the outgoing directions.
Generally, the BRDF is anisotropic. If the surface is rotated about the surface normal, the
value of BRDF will change. But In general isotropic materials are considered.
BRDF
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BRDF
Properties of BRDF Helmholtz Reciprocity
Images obtained from SIGGRAPH 2005 Course Notes
)( oirf =
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Properties of BRDF Relation between incident and reflected
radiance The value of the BRDF for a specific incident direction
is not dependent on the possible presence of irradiance along other incident angles.
The BRDF behaves as a linear function with respect to all incident directions.
BRDF
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BRDF
Energy Conservation The sum of energy reflected into all directions
has to be smaller or equal than the incident energy.
Images obtained from SIGGRAPH 2005 Course Notes
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BRDF
Global illumination algorithms often use empirical models to characterize the BRDF. Great care must be taken to make certain
that these empirical models are a good and acceptable BRDF.
Energy conservation Helmholtz reciprocity: A particularly important
constraint for bidirectional global illumination algorithms.
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BRDF
Diffuse Surfaces Some materials reflect light uniformly over the
entire reflecting hemisphere. Given an irradiance distribution, the reflected
radiance is independent of the exitant direction.
The value of the BRDF is constant for all values of Θ and Ψ.
To an observer, a diffuse surface point looks the same from all possible directions.
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BRDF
Diffuse Surfaces The reflectance ρd represents the fraction of
incident energy that is reflected at a surface. ρd varies from 0 to 1.
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BRDF
Specular Surfaces Perfect specular surfaces only reflect or refract light in
one specific direction. Specular Reflection
The direction of reflection can be found using the law of reflection.
The incident and exitant light direction make equal angles to the surface’s normal, and lie in the same plane as the normal.
Given that light is incident to the specular surface along direction vector Ψ, and the normal to the surface is N, the incident light is reflected along the direction R
R = 2(N ·Ψ)N – Ψ.
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BRDF
Specular Reflection A perfect specular reflector has only one exitant
direction for which the BRDF is different from 0. The value of the BRDF along that direction is infinite.
It can be described with the proper use of delta functions. There exists no ideal reflectors.
Specular Refraction The direction of specular refraction is computed
using Snell’s law.
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BRDF
Specular Refraction Consider the direction T along
which light that is incident from a medium with refractive index η1 to a medium with refractive index η2 is refracted.
Snell’s law specifies the invariant between the angle of incidence and refraction and the refractive indices of the media.
η1sinθ1 = η2sinθ2
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BRDF
Specular Refraction The transmitted ray T is
given as
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BRDF
Total Internal Reflection When light travels from a dense medium to a
rare medium, it could get refracted back into the dense medium.
The critical angle θc can be computed by Snell’s law:
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BRDF
Reciprocity for Transparent Surfaces One has to be careful when assuming
properties about the transparent side of the BSDF.
Some characteristics such as reciprocity, may not be true with transparent surfaces.
When computing radiance in scenes with transparent surfaces, a weighting factor (η2/η1)2 should be considered.
When a pencil of light enters a dense medium from a less dense medium, it gets compressed. Therefore, the light energy per unit area perpendicular to the pencil direction becomes higher; i.e. the radiance is higher.
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BRDF
Fresnel Equations It specify the amount of light energy that is reflected
and refracted from a perfectly smooth surface. When light hits a perfectly smooth surface, the light
energy that is reflected depends on the wavelength of light, the geometry at the surface, and the incident direction of the light.
Fresnel equations specify the fraction of light energy that is reflected.
These equations take the polarization of light into consideration.
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BRDF
Fresnel Equations Two components of the polarized light, rp and
rs, referring to the parallel and perpendicular components are given as:
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BRDF
Fresnel Equations For unpolarized light,
The Fresnel equations assume that light is either reflected or refracted at a purely specular surface.
Since there is no absorption of light energy, the reflection and refraction coefficients sum to 1.
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BRDF
Glossy Surfaces Most surfaces are neither ideally diffuse nor
ideally specular but exhibit a combination of both reflectance behaviors.
The BRDF is often difficult to model with analytical formulae.
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BRDF
Shading Models Real materials can have fairly
complex BRDFs. Various models have been
suggested in computer graphics to capture the complexity of BRDFs.
Notations Ψ: the direction of the light (the
input direction) Θ: the direction of the viewer (the
outgoing direction)
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BRDF
Lambert’s model For idealized diffuse materials. The BRDF is a constant in all direction. ρd : diffuse reflectance
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BRDF
Phong model The most popular model. The BRDF for the Phong model is
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BRDF
Blinn-Phong model It uses the half-vector H.
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BRDF
Modified Blinn-Phong model The simplicity of the Phong model is
appealing. But it has some serious limitations:
It is not energy conserving. It does not satisfy Helmholtz’s reciprocity. It does not capture the behavior of most real
materials. The modified Blinn-Phong model addresses
some of these problems.
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BRDF
Cook-Torrance Model One of the physically based shading models It includes a microfacet model that assumes that a
surface is made of a random collection of small smooth planar facets.
The assumption is that an incoming ray randomly hits one of these smooth facets.
Given a specification of the distribution of microfacets for a material, this model captures the shadowing effects of these microfacets.
It also includes the Fresnel reflection and refraction terms.
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BRDF
Cook-Torrance Model
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BRDF
Empirical Models Ward model