Lecture15 anti aliasing

• 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