159.235 Graphics & Graphical Programming

159.235 Graphics & Graphical Programming Lecture 30 - Colour, Physics and Light - Part 2 Graphics

Radiometry : Radiance Radiometry is the science of light energy measurement Definition: The radiance (luminance) is the power per unit area per unit solid angle. Properties: 1. Fundamental quantity 2. Stays constant along a ray 3. Response of a sensor proportional to radiance Graphics

Radiometry: Irradiance and Radiosity Definition: The irradiance (illuminance) is the power per unit area incident on a surface. Definition: The radiosity (luminosity) is the power per unit area leaving a surface. Graphics

Irradiance: Distant Source Graphics

Irradiance: Point Source • Inverse square law fall off • Still has cosine dependency. Graphics

What does Irradiance look like? Graphics

The Reflection Equation • Linear response • 2. Bidirectional reflectance distribution function (BRDF) defines outgoing radiance for a given incoming irradiance – characteristic property of surface. Graphics

Approximating the BRDF • All illumination models in graphics are approximations to the BRDF for surfaces. • Frequently chosen for their visual effect, and ease of implementation, rather than on physical principles. • BRDF is approximated by reflection functions. • Usually a total hack ! Graphics

Types of Reflection Functions • Ambient. • Ideal Specular • Mirror • Reflection Law • Ideal Diffuse • Matte • Lambert’s Law • Specular • Glossiness and Highlights • Phong and Blinn Models Graphics

Ambient Reflection. • Simplest illumination model. • There is assumed to be global ambient illumination in the scene, Ia • Amount of ambient light reflected from a surface defined by ambient reflection coefficient, ka. • Ambient term is I = Ia.ka • No physical basis whatsoever ! Graphics

Mirror: Ideal Specular Surface Calculation of the reflection vector involves mirroring L about N. Law of Reflection i r r=i Graphics

Matte: Ideal Diffuse Reflection • Dull surfaces such as chalk exhibit diffuse or Lambertian reflection. • Reflect light with equal intensity in all directions. • For a given surface, brightness depends only on the angle between the surface normal and the light source. Graphics

Matte: Ideal Diffuse Reflection • 2 effects to consider : • The amount of light reaching the surface. • Beam intercepts an area dA/ cos  • cos  dependence. • The amount of light seen by the viewer. • Also cos  dependence per unit surface area • BUT amount of surface seen by viewer also has cos  dependence. Ip   dA Graphics

Matte: Ideal Diffuse Reflection Ip The diffuse lighting equation is :   dA Graphics

Matte: Ideal Diffuse Reflection • Diffuse coefficient defined for each surface. • Diffusely lit objects often look harshly lit • Ambient light often added. • Poor physical basis for diffuse reflection. • Internal reflections inside the material etc… Graphics

Specular reflection • Can be observed on a shiny surface, e.g nice red apple lit with white light. • Observe highlights on surface. • Highlight appears as the colour of the light, rather than of the surface. • Highlight appears in the direction of ideal reflection. Now view direction important. • Materials such as waxy apples, shiny plastics have transparent reflective surface. Graphics

The Phong model • Assume specular highlight is at a maximum when  = 0 , and falls off rapidly with larger values of  • Fall-off depends on cosn . • n referred as specular exponent. • For perfect reflector, n is infinite.    Graphics

The Phong model • An alternative formulation uses halfway vector, H • It’s direction is halfway between viewer and light source. • If the surface normal was oriented at H, viewer would see brightest highlights. • Note    , both formulations are approximations.     Graphics

Rough Surface : Microfacet distribution Physical justification for Phong model is that the surface is rough and consists of microfacets which are perfect specular reflectors. Distribution of microfacets determines specular exponent. Graphics

Material Selection Ambient 0.52 Diffuse 0.00 Specular 0.82 Shininess 0.10 Light intensity 0.31 Ambient 0.39 Diffuse 0.46 Specular 0.82 Shininess 0.75 Light intensity 0.52 Graphics

Choosing “shininess” n 0 is dull, infinity is perfect reflector Graphics

Colour, Physics & Light - Summary • Surface reflection specified by BRDF. • BRDF approximated by ambient, diffuse and specular reflection. • Lambertian reflection. • Phong Lighting model • Acknowledgments - thanks to Eric McKenzie, Edinburgh, from whose Graphics Course some of these slides were adapted. Graphics

159.235 Graphics & Graphical Programming