This document discusses various topics related to computer graphics including anti-aliasing, area sampling, the Koch curve, and the C curve. Anti-aliasing is a technique used to reduce jagged edges by blending pixels. Area sampling is an anti-aliasing method that treats pixels as areas and calculates color based on object overlap. The Koch curve is a fractal curve generated by recursively altering line segments. The C curve replaces lines with two shorter lines at 90 degrees to form triangles at each iteration.

1. Anti Aliasing
Area Sampling
Koch Curve
C Curve
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Prepared and presented by:
Pallab Kumar Nandi
ID: 20151046010

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Topics:
Anti Aliasing
Area Sampling
Koch Curve
C Curve

4. Anti Aliasing
Anti aliasing is a technique used in digital imaging to reduce the
visual defects that occur when high-resolution images are
presented in a lower resolution.
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5. Anti Aliasing (Cont..)
Pixel
 A pixel is the smallest unit of a digital image or graphic
that can be displayed and represented on a digital display
device.
 A pixel is represented by a dot or square on a computer
monitor display screen.
 Example:
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6. Aliased & Anti-aliased
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 It exhibits jagged or stair stepped lines.
 Antialiasing is a technique for diminishing jaggies -
stairstep-line
 lines that should be smooth.

7. Anti Aliasing Techniques
 Supersampling or Post filtering
 Areasampling or Pre filtering
1. Unweighted
2. Weighted
 Filtering Techniques
 Pixel Phasing
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8. Area Sampling(Cont..)
 Prefiltering methods treat a pixel as an area, and compute pixel
color based on the overlap of the scene's objects with a pixel's area.
 These techniques compute the shades of gray based on how much
of a pixel's area is covered by a object.
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9. Area Sampling(Cont..)
 Shade pixels according to the area covered by thickened line
 This is unweighted area sampling
 A rough approximation formulated by dividing each pixel into a finer grid
of pixels
 Primitive cannot affect intensity of pixel if it does not intersect the pixel
 Equal areas cause equal intensity, regardless of distance from pixel center
to area.
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Fig: Area Sampling
Area Sampling(Cont..)

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Koch Curve
The Koch curve is to divide a line into three equal segments and replace the
middle segment with two lines of the same length.

12. The Koch snowflake can be constructed by starting with an equilateral
triangle, then recursively altering each line segment as follows:
 divide the line segment into fore segments of equal length.
 draw an equilateral triangle that has the middle segment from step 1 as
its base and points outward.
 remove the line segment that is the base of the triangle from step 2.
 After one iteration of this process, the resulting shape is the outline of a
hexagram.
Koch Curve(Construction)
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13. Depth 1
1 line segment
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Depth 2
Contains 4 depth-1 curves
(4 line segments)

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Depth 3
Contains 4 depth-2 curves
(16 line segments)

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Depth 4
Contains 4 depth-3 curves
(64 line segments)

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Depth 5
Contains 4 depth-4 curves
(256 line segments)

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Koch Curve(Example)

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C Curve

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The C curve is to replace a line by two shorter, equal-length
lines joining each other at 90 degree angle, with the original
line and two new lines forming a right angle triangle.
What is C curve?

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Depth 1
1 line segment
C Curve(Construction)

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Depth 2
Contains 1 depth-1 curves
(2 line segments)
C Curve(Construction)

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Depth 3
Contains 2 depth
(4 line segments)
C Curve(Construction)

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Depth 4
Contains 4 depth
(8 line segments)
C Curve(Construction)

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Depth 5
Contains 8 depth
(16 line segments)
C Curve(Construction)

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Depth 5
Contains 16 depth
(32 line segments)
C Curve(Construction)

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Depth 5
C Curve(Construction)

28. “
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All problems in computer
graphics c a n be solved
with matrix inversion.
-Jim Blinn
Conclusion

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Credits
Special Thanks to all this awesome resource for free:
 Computer Graphics (Schum’s outlines)
 Wikipedia
 Youtube

30. Thanks!
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