CSCE 641 Computer Graphics: Reflection Models. Jinxiang Chai. Motivation. How to model surface properties of objects?. Reflection Models.

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CSCE 641 Computer Graphics: Reflection Models

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Motivation • How to model surface properties of objects?

Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

Materials Plastic Metal Matte From Apodaca and Gritz, Advanced RenderMan

Mathematical Reflectance Models • How can we mathematically model reflectance property of an arbitrary surface? • - what’s the dimensionality? • - how to use it to compute outgoing radiance given incoming radiance?

Photons • The basic quantity in lighting is the photon • The energy (in Joule) of a photon with wavelength λ is: qλ = hc/λ - c is the speed of light In vacuum, c = 299.792.458m/s - h ≈ 6.63*10-34Js is Planck’s constant

(Spectral) Radiant Energy • The spectral radiant energy, Qλ, in nλ photons with wavelength λ is • The radiant energy, Q, is the energy of a collection of photons, and is given as the integral of Qλ over all possible wavelengths:

Radiant Intensity • Definition: the radiant power radiated from a point on a light source into a unit solid angle in a particular direction. • - measured in watt per steradian

Radiance • Definition: the radiant power per unit projected surface area per solid angle

Radiance Per unit projected surface area - radiance varies with direction - incidence radiance and exitant radiance

Radiance • Ray of light arriving at or leaving a point on a surface in a given direction Radiance (arriving) Radiance (leaving)

Irradiance • Definition: the power per unit area incident on a surface.

Radiant Exitance • Definition: The radiant (luminous) exitance is the • energy per unit area leaving a surface. • In computer graphics, this quantity is often • referred to as the radiosity (B)

Reflection Models • Outline - Types of reflection models - The BRDF and reflectance - The reflection equation - Ideal reflection - Ideal diffuse - Cook-Torrance Model

Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

Reflection Models • Definition: Reflection is the process by which light incident on a surface interacts with the surface such that it leaves on the incident side without change in frequency.

Types of Reflection Functions • Ideal Specular • Reflection Law • Mirror • Ideal Diffuse • Lambert’s Law • Matte • Specular • Glossy • Directional diffuse

Mathematical Reflectance Models • How can we mathematically model reflectance property of an arbitrary surface? • - what’s the dimensionality? • - how to use it to compute outgoing radiance given incoming radiance?

The Reflection Equation How to model surface reflectance property? for a given incoming direction, the amount of light that is reflected in a certain outgoing direction

The BRDF • Bidirectional Reflectance Distribution Function

Dimensionality of the BRDF • This is 6-D function • - x: 2D position • - (θi,φi): incoming direction • - (θr,φr): outgoing direction • Usually represented as 4-D • - ignoring x • - homogenous material property