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Lecture15 anti aliasing

Jan 13, 2015

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  • 1. CS 455 Computer Graphics Antialiasing

2. Aliasing

  • Aliasing:a high-frequency signal masquerading as a low frequency
    • Caused by insufficient sampling(sampling interval too large)

Sampling Interval Actual (high-frequency) signal Sampled (aliased) signal 3.

  • Strobe light on dripping water:Temporal aliasing
  • Spokes on a rotating wheel:Temporal aliasing
  • Moir patterns:Spatial aliasing

Examples of Aliasing 4. Aliasing and Line Drawing

  • We draw lines by sampling at intervals of one pixel and drawing the closest pixels

Sampling Interval Sampling Interval

  • Results in stair-stepping(i.e., the dreaded jaggies)

5. Antialiasing Lines

  • Idea:
    • Make line fatter
    • Fade line out (removes high frequencies)
    • Now sample the line

6. Antialiasing Lines

  • Solution 1 Unweighted Area Sampling:
    • Treat line as a single-pixel wide rectangle
    • Color pixels according to the percentage of each pixel that is covered by the rectangle

7. Solution 1: Unweighted Area Sampling

  • Pixel area is unit square
  • Constant weighting function
  • Pixel color is determined by computing the amount of the pixel covered by the line, then shading accordingly
  • Easy to compute, gives reasonable results

Line One Pixel 8. Solution 2: Weighted Area Sampling

  • Treat pixel area as a circle with a radius of one pixel
  • Use a radially symmetric weighting function(e.g., cone) :
    • Areas closer to the pixel center are weighted more heavily
  • Better results than unweighted, slightly higher cost

Line One Pixel 9. Solution 3:Gupta-Sproull algorithm

  • Calculate pixel intensity by computing distance from pixel center to line using the midpoint line algorithm

x p NE m Ex p+1 Line to draw v y p y p+1 D 10. Gupta-Sproull algorithm (cont)

  • D is the perpendicular distance from E to the line
  • How do we compute it?

a How does triangle abc compare to triangle ade? Dc = e, and a = a, so b must equal d b c d e dx dy v r r 11. Gupta-Sproull algorithm (cont)

  • D is the perpendicular distance from E to the line
  • How do we compute it?

a So: Db c d e dx dy v r r And: Then: 12. Gupta-Sproull algorithm(cont)

  • Recall from the midpoint algorithm:
  • So
  • For pixel E:
  • So:

x p NE m Ex p+1 Line to draw v y p y p +1 D 13. Gupta-Sproull algorithm (cont)

  • From previous slide:
  • So
  • From the midpoint computation,
  • So:

x p NE m Ex p+1 Line to draw v y p y p+1 D 14. Gupta-Sproull algorithm (cont)

  • From the midpoint algorithm, we had the decision variable (remember?)
  • Going back to our previous equation:

x p NE m Ex p+1 Line to draw v y p y p +1 D 15. Gupta-Sproull algorithm (cont)

  • So,
  • And the denominator is constant
  • Since we are blurring the line, we also need to compute the distances to points y p 1 and y p+ 1

16. Gupta-Sproull algorithm (cont)

  • If the NE pixel had been chosen:

17. Gupta-Sproull algorithm (cont)

  • Compute midpoint line algorithm, with the following alterations:
  • At each iteration of the algorithm:
    • If the E pixel is chosen, set numerator = d + dx
    • If the NE pixel is chosen, set numerator = d dx
    • Update d as in the regular algorithm
    • Compute D = numerator/denominator
    • Color the current pixel according to D
    • Compute D upper= (2dx-2vdx)/denominator
    • Compute D lower= (2dx+2vdx)/denominator
    • Color upper and lower accordingly

18. Solution 4: Super-sampling

  • Divide pixel up into sub-pixels:2 2, 3 3, 4 4, etc.
  • Sub-pixel is colored if inside line
  • Pixel color is the average of its sub-pixel colors
  • Easy to implement(in software and hardware)

No antialiasing Antialiasing(2 2 super-sampling) 19. Solution 5: Sum of Foreground and Background

  • Compute percent of pixel covered by line,p
  • Line color isc l
  • Background color isc b
  • Pixel color is the sum of this percent multiplied by the line color, plus the percent of the pixel not covered by the line multiplied by the background color, i.e.,
  • color = p * c l+ (1-p) * c b

20. Polygon Antialiasing

  • To antialias a line, we treat it as a polygon(a rectangle)
  • Antialiasing a polygon(or any shape primitive)is similar
  • Some concerns:
    • Corners:Complicate the coverage
    • computation
    • Micro-polygons:smaller than a pixel
    • Super-sampling:There may still be
    • polygons that slip between the cracks