CS248 Final Review

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CS248 Final Review
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CS248 Final

• Monday, December 6, 330 to 630 pm, Gates B01
• Closed book, closed notes
• Mainly from material in the second half of the
  quarter
• will not include material from last part of last
  lecture (volume rendering, image-based rendering)
• Review session slides available from class
  website

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CS248 Final Review Contents

• Image warping, texture mapping
• Perspective
• Visibility
• Lighting / Shading

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Texture Mapping

• Coordinate systems
• u,v,q gt xo, yo zo, wo gt xw, yw zw, ww gt
  x, y, w
• Assuming all transforms are linear, then
• Au, v, q x, y, w

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Texture Warps

• Rotation, translation
• Perspective
• Minification (decimation)
• unweighted average average projected texel
  elements that fall within a pixels filter
  support
• area-weighted average average based on area of
  texel support

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Texture Warps

• Magnification
• Unweighted
• Area-weighted
• bilinear interpolation

texel
pixel
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Textures

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

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Questions

• 1. What are some of the problems associated with
  Mipmaps?
• 2. What are some of the problems associated with
  SAT?

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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

How many vanishing points are there in an image
produced by parallel projection?
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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 normalized device coordinates
• Window coordinates

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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
• What has to be done to render transparent
  polygons?

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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, add those
  events

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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
• Why is this so difficult?

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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

• 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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Sample question (2000)

• Q. As every scout knows, you can start a fire on
  a sunny day by holding a magnifying glass between
  the sun and a piece of paper placed on the
  ground.
• Is the radiance of the sun as seen from the focal
  point of the lens more, less, or the same as the
  radiance as seen from the same point in the
  absence of the magnifying glass?
• Is the irradiance due to the sun at the focal
  point more, less, or the same as the irradiance
  at the same point in the absence of the
  magnifying glass?

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Lighting

• Point to area transport
• Computing the irradiance to a surface
• Cos falloff N L
• E Fatt x I x (N L)

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Lighting

• Lambertian (diffuse) surfaces
• Radiant intensity has cosine fall off with
  respect to angle
• Radiance is constant with respect to angle
• Reason the projected unit area ALSO gets smaller
  as a cosine fall off!
• Fatt x I x Kd x (N L)

N
N
V
I ? length cos(t)
V
Radiance intensity intensity/solid angle
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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
• Dont forget the 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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Lighting

• N H model
• H is the halfway vector between the viewer and
  the light
• What is the difference in specular highlight?

N
H
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
• mach bands!

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Shading

• Angle interpolation
• interpolate normal angles according to the
  implicit surface
• compute shading at each point of the implicit
  surface
• CORRECT! But very expensive

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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)
• Problems? Difference with angle interpolation?

N2
N1
Implicit surface
Polygon approximation
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Lighting and Shading

• Know the OpenGL 1.1, 1.2 light equations (what
  terms mean what)

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Good Luck!
Good Luck on the Final! ?
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Ray Tracing

• Point in polygon tests
• Odd, even rule
• draw a line from point to infinity in one
  direction
• count intersections odd inside, even outside
• Non-zero winding rule
• counts number of times polygon edges wind around
  a point in the clockwise direction
• winding number non zero inside, else outside

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Exotic uses of textures

• Environment/reflection mapping
• Alphas for selecting between textures/shading
  parameters
• Bump mapping
• Displacement mapping
• Object placement
• 3d textures