Physically-based Illumination Models (2) CPSC 591/691

Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance

Phong Lighting Model

Cook-Torrance Lighting Model

Cook-Torrance Illumination Model (summary) A linear combination of a number of completely different models and approximations AMBIENT term  to approximate global illumination Lambertian DIFFUSE term  model color SPECULAR term: 1.Fresnel term  gives dependence of specular intensity and color on incidence angle 2.Microfacet model term  spreads the specular intensity, giving an “off-specular bump”

D  statistical distribution function of the microfacets slope G  geometric attenuation term, which deals with how the individual microfacets shadow and mask each other. F  Fresnel term deals with the amount of light that is reflected versus absorbed as the incident angle changes (an example of this is often seen when driving on a straight road, and the road appearing mirror-like when viewed from grazing angles).

Lambertian Lighting Model (diffuse)

Attenuation Term The fraction of light that reaches the surface as an effect of light attenuation. c1, c2, c3: The coefficients for constant, linear and quadratic attenuation of the light source, respectively. d: the distance to the light

Lambertian Lighting Model (diffuse)

Oren-Nayar Lighting Model

"Generalization of the Lambertian Model and Implications for Machine Vision," S. K. Nayar and M. Oren, International Journal of Computer Vision, Vol. 14, pp , Oren-Nayar Lighting Model

BRDF to ‘generalize’ the Lambertian diffuse lighting model. This BRDF can reproduce several rough surfaces very well, including wall plaster, sand, sand paper, clay, and others. Very computationally expensive, and it requires the calculation of azimuth and zenith angles.

Minnaert Lighting Model

Minnaert added darkening limbs to the lighting equations to make the surface seem darker from certain viewing/lighting directions. This effect is seen in some types of clothing (such as velvet). Minnaert Lighting Model Lambertian lightingDarkening factor

Phong Lighting Model

Cook-Torrance Lighting Model

Blinn Lighting Model

BRDF to ‘generalize’ the Lambertian diffuse lighting model. This BRDF can reproduce several rough surfaces very well, including wall plaster, sand, sand paper, clay, and others. Very computationally expensive, and it requires the calculation of azimuth and zenith angles.

Remaining Hard Problems Reflective Diffraction Effects thin films feathers of a blue jay oil on water CDs Anisotropy brushed metals strands pulled materials Satin and velvet cloths

Cook-Torrance Illumination Model (summary) Microfacet model term  spreads the specular intensity, giving an “off-specular bump” NOT entirely satisfactory It is based on a one-dimensional “cross-sectional” model

Isotropic, Anisotropic Surfaces An isotropic surface has the property that for any given point on the surface, the light reflected does not change when the surface is rotated about the normal This is the case for many materials, but some materials such as brushed metal or hair this is not the case. The reason for these anisotropic surfaces is that the micro facets that make up the surface have a preferred direction in the form of parallel grooves or scratches

Tiny random bumps in the surface of the floor, bumps possibly so small that you may not notice the bumps, but you will notice their affect on the reflection. Isotropic Surfaces

So now, what happens if these tiny bumps are in a regular pattern? For example, brushed metals are metals that have small grooves that all head in the same direction. This causes reflections to blur in a specific direction. Anisotropic Surfaces

Real world brushed metal

Real world example of a Christmas ornament that's made up of fine synthetic hairs that all travel in one direction

Wards Anisotropic Lighting Model

The X and Y terms are two perpendicular tangent directions on the surface. They give represent the direction of the grooves in the surface. The  terms are the standard deviations of the slope in the X and Y direction (given by their respective subscripts).

Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance

An Explicit Microfacet Model Cabral, B., Max, N., Springmeyer, R., Bidirectional Reflection Functions From Surface Bump Maps, SIGGRAPH `87, pp Construction of a surface of triangular microfacets Reflection model: –Pre-calculation (rather than simulation by a parametric distribution or function) –Table of reflectivities

Explicit Microfacet Model (Cabral et al 87) Any surface whose microstructure can be represented can be modeled Microstructure: isotropic or anisotropic Less restricted than using statistical distribution (Cook and Torrance)

Nature of the Microstructure Controlled by varying size and vertex perturbation of triangular microfacets Triangular microfaces construction: bump map or height field (2D array of vertex heights) Heights can be distributed in any desired way

Bump Mapping Map texture values to perturbations of surface normals

Bump Mapping Map texture values to perturbations of surface normals Straight Phong Shading  approximates smoothly curved surface Straight Phong Shading  approximates smoothly curved surface Phong with bump mapping approximates bumpy surface

Irradiated Surface Element Area Normal Mirror direction

Reflectivity Function Contribute a ‘delta function’  sum of delta functions

Reflectivity Function: How to Build the Information?

Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

Illuminating flux density Fresnel factor Energy incident on a microfacet Max, N., "Horizon mapping: shadows for bump-mapped surfaces“ Visual Computer, 1988

How About for ALL microfacets?

N = 24

Energy flowing through one cell

returns the index of the cell hit by a ray fired in direction R. Mirror direction Kronecker delta function

More than one microfacet is likely to contribute energy to cell k

Energy flowing through one cell Energy incident to a microfacet Solid angle of cell k

Finally…Table of Reflectivities

Reflectivity:

The fraction of incoming flux reflected by facet S i

G i  the fraction of incoming flux reflected by facet S i Energy incident on a microfacet

Energy flowing through one cell Energy incident to a microfacet Solid angle of cell k

Energy flowing through one cell Energy incident to a microfacet

Better (Realistic) Local Illumination Models Blinn-Torrance-Sparrow (1977) –isotropic reflectors with smooth microstructure Cook-Torrance (1982) –wavelength dependent Fresnel term Kajiya (1985) Cabral-Max-Springmeyer (1987) –Anisotropic surfaces Wolff (1990) –adds polarization He-Torrance-Sillion-Greenberg (1991) –adds polarization, statistical microstructure, self-reflectance