CS248 Final Review

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CS248 Final Review

• Derek Chan and Abe Davis

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CS248 Final

• Monday, December 8, 330 to 630 pm
• Closed book, closed notes
• Mainly from material in the second half of the
  quarter
• Project submission and writeups along with
  partner evaluations due today

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CS248 Final Review Contents

• Topics from second half of the course
• Image warping, texture mapping
• Perspective
• Visibility
• Lighting / Shading

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Textures

• Mipmapping
• multi-resolution texture
• bilinear interpolation at 2 closest resolutions
  to get 2 color values
• linear interpolate 2 color values based on actual
  resolution
• Summed area tables
• fast calculation of prefilter integral in texture
  space

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Viewing Planar Projections

• Perspective Projection
• rays pass through center of projection
• parallel lines intersect at vanishing points
• Parallel Projection
• center of projection is at infinity
• oblique
• orthographic

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Specifying Perspective Views

• Observer position (eye, center of projection)?
• Viewing direction (normal to picture plane)?
• Clipping planes (near, far, top, bottom, left,
  right)?

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Viewing OpenGL Pipeline

• Object Space
• Eye Coordinates
• Projection Matrix
• Clipped to Frustum
• Homogenize to device coordinates
• Window coordinates
• Why is clipping before homogenization?

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Visibility

1. 6 visible-surface determination algorithms
2. Z-buffer
3. Watkins
4. Warnock
5. Weiler-Atherton
6. BSP Tree
7. Ray Tracing

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Things to know

• how does it work
• what are the necessary preconditions?
• asymptotic time complexity
• well-suited for hardware?
• how can anti-aliasing be done?
• how can shading be incorporated?
• parallelizable?
• ease of implementation
• best-case/worst-case scenarios

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Z-buffer

• Project all polygons to the image plane, at each
  pixel, pick the color corresponding to closest
  polygon

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Watkins

• Scanline depth
• progressing across scanline, if pixel is inside
  two or more polygons, use depth to pick
• process interpenetrating polygons

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Warnock Subdivision

• Start with area as original image
• subdivide areas until either
• all surfaces are outside the area
• only one inside, overlapping or surrounding
• a surrounding surface obscures all other surfaces

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Weiler-Atherton Subdivision

• Cookie-cutter algorithm clips polygons against
  polygons
• front to back sort of list
• clip with front polygon

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BSP Trees/List Priority

• Provides a data structure for back-to-front or
  front-to-back traversal
• split polygons according to specified planes
• create a tree where edges are front/back, leaves
  are polygons

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Ray Tracing

• Ray Casting
• for each pixel, cast a ray into the scene, and
  use the color of the closest polygon
• Parametric form of a line u(t) a(b-a)t
• Implicit form of the object

a
t
y
b
(0,0)?
x
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Lighting

• Photometry vs Radiometry
• What's the difference?

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Lighting

• Terminology
• Radiant flux energy/time (joules/sec watts)?
• Irradiance amount of incident radiant flux /
  area (how much light energy hitting a unit area,
  per unit time)?
• Radiant intensity (of point source) radiant flux
  over solid angle
• Radiance radiant intensity over a unit area

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Lighting

• BRDF Bidirectional Reflectance Distribution
  Function
• Description of how the surface interacts with
  incident light and emits reflected light
• Isotropic
• Independent of absolute incident and reflected
  angles
• Anisotropic
• Absolute angles matter
• Generalizations to the BRDF!
• Spatially/spectrally varying, florescence,
  phosphorescence, etc.

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Lighting

• Phong specular model
• Isnt true to the physics, but works pretty well
• Reflected light is greatest near the reflection
  angle of the incident light, and falls off with a
  cosine power
• Lspec Ks x cosn(a), a angle between viewer
  and reflected ray

N
L
R
V
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Shading

• Gouraud shading
• Compute lighting information (ie colors) at
  polygon vertices, interpolate those colors
• Problems?
• Misses highlights
• need high resolution mesh to catch highlights

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Shading

• Phong shading
• Compute lighting normals at all points on the
  polygon via interpolation, and do the lighting
  computation on the interpolated normals (of the
  polygon)?

N2
N1
Implicit surface
Polygon approximation
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Good Luck!
Good Luck on the Final! ?