CS 445: Introduction to Computer Graphics

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Review

• CS 445 Introduction to Computer Graphics
• David Luebke
• University of Virginia

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Admin

• Course evaluations please do during class today
  (available on Toolkit)

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Math

• Mathematical foundations
• Vector arithmetic
• Affine spaces points, vectors, scalars
• Parametric representation of a line/ray/segment
• Dot product, cross product
• Matrix-matrix and matrix-vector arithmetic

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Display technologies

• CRTs
• Underlying technology
• Vector vs. raster
• Framebuffer, pixel, scanline, rasterize
• LCDs
• Underlying technology
• Pros cons
• Other dont need to know details
• Plasma display
• OLED

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Rendering pipeline

• Know the various stages
• Transforms
• Modeling
• Camera
• Projection
• Illuminate
• Clip
• Homogeneous divide
• Rasterize
• Be able to reason about which stages go where

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Transformations

• Modeling transforms
• Object?world coords
• Common xforms
• Translate
• Rotate
• Scale (uniform vs. nonuniform)
• Composing xforms
• Multiplying matrices know the correct order!
• Be able to compose a rotation matrix about an
  arbitrary axis
• Be able to compose rotation translation
  matrices

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Transformations

• Homogeneous coordinates
• Homogeneous coordinate akin to a scale factor
• Homogeneous points vs. vectors
• Enables translation, projection
• Projection transforms
• Uses the homogeneous coordinate
• Be ready to reason about simple projection xforms

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OpenGL

• Specifying transforms
• Understand how to use the matrix stacks
• GL_MODELVIEW
• GL_PROJECTION
• Understand the principles of hierarchical
  transforms
• Nest xforms
• Functions shouldnt have side effects
• Understand the concept of a scene graph

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Clipping

• 2D Cohen-Sutherland
• Outcodes how to use them
• Clipping a line segment to an edge
• 3D Sutherland-Hodgeman
• Clipping in the graphics pipeline

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Rasterization

• Line rasterization
• DDA
• Optimization strategies
• Triangle rasterization
• Edge walking
• Edge equations
• Polygon rasterization
• Parity test
• Active edge table

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Color

• Physiology of the eye
• Cornea, lens, retina
• Photoreceptors
• Rods (low light, luminance) vs. cones (high light
  levels, color)
• Color-sensitivity of cones S, M, L (B, G, R)
• Density fovea (high spatial resolution, all
  cones) vs. periphery (low spatial resolution,
  largely rods)
• Metamers different spectra with the same
  perceptual response
• E.g., a monochromatic orange light (spectral
  spike) vs. combinations of red, green, tiny bit
  of blue same perceived color!
• Color gamuts and CIE chromaticity diagram

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The Human Visual System

• The human visual system has four types of
  sensors rods and S, M, and L cones

sensitivity
rods
100
10
cones
L
1
M
Courtesy Nathaniel Hoffman
0.1
?
0.01
S
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The Human Visual System

• Rods are the most sensitive
• Used in weak illumination (scotopic) conditions
• Sensitivity peaks at cyan (blue-green)
• Only one kind monochromatic vision
• Cones enable color vision
• Used in strong illumination (photopic) conditions
• Total sensitivity peaks at yellow-green
• Three kinds trichromatic vision

Courtesy Nathaniel Hoffman
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The Human Visual System

• Trichromatic vision enables us to somewhat sense
  the spectral distribution

sensitivity
1
L
M
0.5
?
0.25
S
0.1
Courtesy Nathaniel Hoffman
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Metamers

• A spectral power distribution is an
  infinite-dimensional signal.
• Since we perceive color only as a
  three-dimensional signal, there is an infinite
  number of different spectral power distributions
  which map onto the same perceived color.
• These are known as metamers.

Courtesy Nathaniel Hoffman
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Metamers
spectral locus
600nm
700nm
500nm
white
more yellow
480nm
470nm
more blue
more red
more green
400nm
Courtesy Nathaniel Hoffman
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Metamers
spectral locus
600nm
700nm
500nm
white
more yellow
480nm
470nm
more blue
more red
more green
400nm
Courtesy Nathaniel Hoffman
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Metamers
spectral locus
600nm
700nm
500nm
white
more yellow
480nm
470nm
more blue
more red
more green
400nm
Courtesy Nathaniel Hoffman
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Metamers
spectral locus
600nm
700nm
500nm
white
more yellow
480nm
470nm
more blue
more red
more green
400nm
Courtesy Nathaniel Hoffman
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Lighting

• Illumination models
• Global vs. local illumination models
• Empirical vs. physically based
• Know and understand the Phong model
• Local, empirical, implemented in OpenGL
• Ambient, diffuse, and specular terms
• Shading flat vs. smooth (Gouraud) vs. Phong

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Phong LightingOpenGL Implementation

• The final Phong model as we studied it
• OpenGL variations
• Every light has an ambient component
• Surfaces can have emissive component to
  simulate glow
• Added directly to the visible reflected intensity
• Not actually a light source (does not illuminate
  other surfaces)

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Visibility in the small

• Painters algorithm
• Z-buffer
• BSP trees organize all of space (hence
  partition) into a binary tree
• Preprocess overlay a binary tree on objects in
  the scene
• Runtime correctly traversing this tree
  enumerates objects from back to front
• Idea divide space recursively into half-spaces
  by choosing splitting planes
• Splitting planes can be arbitrarily oriented
• Notice nodes are always convex

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Visibility in the large

• View-frustum culling
• Cells portals (architectural/urban models)
• Cells form the basic unit of PVS
• Create an adjacency graph of cells
• Starting with cell containing eyepoint, traverse
  graph, rendering visible cells
• A cell is only visible if it can be seen through
  a sequence of portals
• So cell visibility reduces to testing portal
  sequences for a line of sight
• Occlusion query (modern hardware)

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Texture mapping

• Establishing correspondences (parameterization)
  texture coordinates
• Interpolating texture coordinates in screen space
  during rasterization
• Texture map antialiasing
• know MIP-mapping, be aware of others
• Related to antialiasing subject prefiltering
• Applications of texture mapping
• Bump mapping, gloss mapping, displacement
  mapping, light mapping

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Modern GPUs

• Programmable GPUs
• Programmable vertex fragment engines
• Render to texture
• Floating point precision
• Programming model stream computing
• Registers zeroed out, no accumulators across
  vertices/fragments
• Lends itself to efficient parallel implementation
• Cg language

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GPGPU

• Trends GPUs fast, getting faster faster
• Approach data as textures, computational kernels
  as fragment programs
• Advance simulation step-by-step using
  render-to-texture

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Ray tracing

• Basic algorithm recursive ray tracing
• Reflection
• Refraction
• Shadows
• Ray-primitive intersection
• Be able to reason about common primitives, or
  figure out a new intersection test
• Acceleration structures

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Antialiasing

• Reason at a high level about what aliasing is and
  how we can prevent/mitigate it
• Basic signal theory behind Nyquist limit
• Supersampling pros and cons
• Prefiltering pros and cons
• Stochastic supersampling high freqs ? noise, not
  aliases

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LOD

• Basic concept (easy)
• Discrete vs. continuous vs. view-dependent pros
  and cons

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Shadows

• Basic concept of shadow volumes
• Stencil buffer
• Problem case clipping