Shading

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Instructor: Christopher Rasmussen (cer@cis.udel.edu)

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Course web page:

http://goo.gl/XXHixg

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March 10, 2016 ❖ Lecture 10

Outline

• HW #2 math fix -- normalize() after cross product in Creature.cpp
• Radiometry
• Surface properties
• Diffuse vs. specular
• Bidirectional reflectance distribution function (BRDF)
• Simplified local model

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• Marschner, 10-10.2.1, 20-20.2

Shading

• Geometry of perspective projection explains location of scene point in image, but what about its intensity and color?

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• Radiometry is about the measurement of electromagnetic radiation, in this case visible light (Marschner, 20-20.2)
• Photometry quantifies camera/eye sensitivity (Marschner 20.3)

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Lighting Objects

Lighting Objects

What is Light?

• A photon is a quantum of light with a:
• 3-D position
• 3-D direction of propagation
• Wavelength λ
• Energy q carried by one photon is proportional to 1/λ
• Power is energy per unit of time; units are watts W
• Spectral power is watts per unit of wavelength
• In the following slides this is the kind of power we are talking about unless otherwise noted

Incoming and Outgoing Light at a Surface

• Irradiance E (Wm^-2)
• Light power (watts) arriving at a point on a surface from all visible directions
• An image samples the irradiance at the pinhole
• Book uses variable H
• Radiosity B (Wm^-2)
• Light leaving a surface in all directions (per patch)
• Also called “radiant exitance”

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Perspective Projection

from Forsyth & Ponce

c

Instead of single direction d characteristic of parallel projections,

rays emanating from single point c define perspective projection

Radiance

• Irradiance doesn’t tell us where light came from
• Radiance L (Wm^-2sr^-1)
• Power at a point in space in a given direction, per solid angle, foreshortened
• Can be incoming or outgoing
• Does not attenuate with distance in vacuum
• What is stored in one pixel—the light energy arriving along a particular ray at a particular point
• After photometric considerations

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Foreshortening

• The more a surface is tilted away, the larger the area light energy is distributed over (and therefore is “diluted”)
• In 2-D, received intensity is proportional to cosine of angle between light direction l and surface normal n
• Received intensity is greatest when l and n are parallel
• 3-D foreshortening factor for light coming from direction (θ, φ) is cos θ , aka dot product n ^. l

from Akenine-Moller & Haines

Object surface properties

• General
• Light/dark/color
• Reflectivity (e.g., matte/ Lambertian vs. shiny)
• Space-varying pattern
• I.e., are above characteristics different in different locations?
• We’ll get to this when we cover texture-mapping

Detailed Surface Properties: BRDF

• Bidirectional Reflectance Distribution Function (BRDF): Ratio of outgoing radiance in one direction to incident irradiance from another

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BRDF Properties

• Energy leaving ≤ Energy arriving (albedo is fraction reflected)
• For a perfectly diffuse/Lambertian surface, the BRDF is a constant—incoming light is scattered equally in all directions
• Generally, only the difference between incident and emitted angle Φ (as well as polar angles) is significant
• Dependence on absolute Φ → Anisotropy (e.g., brushed metal, fur)

Anisotropic BRDF examples

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blenderguru.com

max planck institute

Reflectance equation

• Radiance for a viewing direction given all incoming light (also called rendering equation in Marschner 20.2):

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• This is expensive to compute in general, so the standard local approach is approximation:
• Approximate incoming light as ambient (whole hemisphere) + set of point light sources
• Approximate BRDF of surface as combination of diffuse (matte) and specular (shiny) factors

Illumination models

• Interaction between light sources and objects in scene that results in perception of intensity and color at eye
• Local vs. global models
• Local illumination: Perception of a particular primitive only depends on light sources directly affecting that one primitive
• Geometry
• Material properties
• Global illumination: Also take into account indirect effects on light of other objects in the scene
• Shadows cast
• Light reflected/refracted
• More when we get to ray tracing

Light sources

• Properties
• Intensity (total radiosity)
• Color (intensity / wavelength)
• Geometry
• Point: Shoots light in all directions
• Spotlight: Angle-limited point source
• Directional: Source distant enough that light rays are roughly parallel (e.g., like the sun relative to earth)
• Area: Behaves like a continuous configuration of point sources inside, say, a polygon

from Akenine-Moller & Haines

Some light source types

Light source types: Induced shading

Standard local model for graphics

• Final perceived brightness is a combination of diffuse and specular reflectance, plus an ambient term to approximate global lighting effects

Ambient

Diffuse

Specular

Total

Reflectance equation: Total illumination

• For greater control of appearance, a different light radiance is typically specified in OpenGL for each type of reflectance

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• Actual light at a pixel is combination of three effects:

from Wikipedia