CS248 Final Review

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CS248 Final Review
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CS248 Final

• Thurs, December 12, 7-10 pm, Gates B01, B03
• 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
• Office hours as regularly scheduled

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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
• Common mappings
• forward mapping (scatter), texture-gtscreen
• backward mapping (gather)

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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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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
• how can anti-aliasing be done?
• how can shading be incorporated?
• well-suited for hardware?
• 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 closet
  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, add those
  events

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Warnock Subdivision

• Start with area as original image
• subdivide areas until either
• all surfaces are our 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 algorithmclips polygons against
  polygons
• front to back sort of list
• clip with front polygon

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BSP Trees

• 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 point on the closest polygon
  
• Parametric form of a line u(t) a(b-a)t

a
t
y
b
(0,0)
x
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Ray Tracing

• Sphere P-Pc2 r2 0
• Plane N P -D
• Can you compute the intersection of a ray and a
  plane? A ray and a sphere?

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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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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

• 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 toangle
• 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
• how do you compute the reflected ray vector?

N
L
R
V
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Lighting

• Local vs. infinite lights
• Understand them! Know how to draw the goniometric
  diagrams for various light/viewer combinations
• 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

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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

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Good Luck!
Good Luck on the Final! ?
More review questions at http//graphics.stanford
.edu/courses/cs248-99/final_review