Lighting

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Lighting
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Wireframe rendering
Filled regions some colouring
Smoothened curves with shading algorithm
Positional Light Note the gradient on the plane
Simple lighting and shading
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Fake shadow Immediately gives a better idea of
what the image represents (i.e. position of
sphere is more apparent)
A bit of texturing enhances the scene
considerable making it look more real-world-like
Global Illumination proper shadows, specular
reflections on objects
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Rendering

• fundamentally concerned with determining the most
  appropriate colour (i.e. RGB triple) to assign to
  a pixel associated with an object in a scene.
• The colour of an object at a point depends on
• geometry of the object at that point (normal
  direction)
• position, geometry and colour of the light
  sources (luminaires)
• position and visual response of the viewer
• surface reflectance properties of the object at
  that point
• scattering by any participating media (e.g.
  smoke, rising hot air)

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Lighting a Scene

• All surfaces considered to contribute by emitting
  light or reflecting
• The color of any point in the scene is determined
  by multiple interactions among light sources and
  reflective surfaces
• Recursive process of light transfer causes subtle
  effects such as colour bleeding between adjacent
  surfaces
• Mathematically represented as an integral
  equation the Rendering Equation

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The Rendering Equation
Kajiya 1986

• I(x, x) intensity of light passing from x to
  x
• (two point transport intensity)
• g(x, x)
• (geometry factor)
• e (x, x) intensity of light emitted by x and
  passing to x
• r (x, x, x) bi-directional reflectance
  scaling factor for light passing from x to x by
  reflecting off x
• S all surfaces in the scene

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Rendering Algorithms

• Rendering algorithms differ in the assumptions
  made regarding lighting and reflectance in the
  scene and in the solution space
• local illumination algorithms consider lighting
  only from the light sources and ignore the
  effects of other objects in the scene (i.e.
  reflection off other objects or shadowing)
• global illumination algorithms account for all
  modes of light transport
• view dependent solutions determine an image by
  solving the illumination that arrives through the
  viewport only.
• view independent solutions determine the
  lighting distribution in an entire scene
  regardless of viewing position. Views are then
  taken after lighting simulation by sampling the
  full solution to determine the view through the
  viewport.

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Local vs. Global Illumination
Global
Local
Illumination at a point can depend on any other
point in the scene
Illumination depends on local object light
sources only
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View Dependent Solution (Ray Traced)
Scene Geometry
Solution determined only for directions through
pixels in the viewport
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View Independent (Radiosity)
A single solution for the light distribution in
the entire scene is determined in advance.
Then we can take different snapshots of the
solution from different viewpoints by sampling
the complete solution for specific positions and
directions.
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Global Illumination Algorithms

• Different algorithms solve the illumination
  problem with making different assumptions to vary
  the speed/accuracy tradeoff.
• Z-Buffer Algorithms
• can compute approximate shadows and reflection
  from planar surfaces
• Ray Tracing Algorithms
• determine exact shadows, reflections and
  refractive effects (transparency) assuming point
  light sources (no volume).
• Radiosity Algorithms
• computes approximate solutions assuming no shiny
  surfaces, but light sources can be arbitrarily
  large and all surfaces polygonal.
• Path Tracing Algorithms
• currently the most powerful methods, employing an
  expensive Monte-Carlo solution to handle
  arbitrary geometries, reflectance and lighting.

Fast
Slow
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Crystal Glass Rendering using Path Tracing
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Illumination Model

• Lighting is described with models that consider
  the interaction of electromagnetic energy with
  object surfaces
• An illumination model is used to calculate the
  intensity of light that we see at a given point
  on the surface of an object in a specified
  viewing direction
• Illumination models are derived from physical
  laws that describe surface light intensities

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Illumination Variables

• Light source
• Positions
• Properties
• Object
• position relative to lights
• position relative to other objects
• material properties
• opaque/ transparent, shiny/ dull, texture surface
  patterns
• Position and orientation of view plane

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A Model for Lighting

• Follow rays from light source
• only light that reaches the viewers eye is ever
  seen
• direct light is seen as the colour of the light
  source
• indirect light depends on interaction properties

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Lighting in Computer Graphics

• For Computer graphics we replace viewer with
  projection plane
• rays which reach COP after passing through
  viewing plane are actually seen
• colour of pixels is determined by our interaction
  model

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Interaction Between Light and Materials

• The nature of interaction is determined by the
  material property
• colour, smoothness and brightness of an object is
  determined by these interactions
• Light hitting a surface is either absorbed,
  reflected or transmitted through material to
  interact with other objects
• Shading also depends on the orientation of the
  surface

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Specular Surfaces

• Three general groups of interactions

• Specular Surfaces
• appear shiny
• reflected light is scattered in a narrow range of
  angles close to angle of reflection
• Mirrors are perfectly specular surface all
  reflected light is at single angle (angle of
  reflection)

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Diffuse Surfaces

• Characterized by
• light scattered in all directions
• rough surfaces
• end up appearing to have consistent chalky
  texture
• perfectly diffuse surfaces scatter light equally
  in all directions

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Translucent Surfaces

• Properties
• allow some light to penetrate and emerge from
  another location
• an accurate model possibly involves refraction
• some incident light may also be reflected at the
  surface

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BRDF

• Bi-directional reflectance distribution function
  describes reflected radiance given incident
  radiance. i.e. proportion of incoming light that
  is reflected

Ideal specular
Ideal diffuse
Rough specular
Directional diffuse