Output Primitive

1
Output Primitive
????? ??? ???? ???
2
Contents

• Points
• Lines
• DDA Algorithm
• Bresenhams Algorithm
• Polygons
• Scan-Line Polygon Fill
• Inside-Outside Tests
• Boundary-Fill Algorithm
• Antialiasing

3
Points

• Single Coordinate Position
• Set the bit value(color code) corresponding to a
  specified screen position within the frame buffer

y
setPixel (x, y)
x
4
Lines

• Intermediate Positions between Two Endpoints
• DDA, Bresenhams line algorithms

Jaggies Aliasing
5
DDA Algorithm

• Digital Differential Analyzer
• 0 lt Slope lt 1
• Unit x interval 1

6
DDA Algorithm

• Digital Differential Analyzer
• 0 lt Slope lt 1
• Unit x interval 1
• Slope gt 1
• Unit y interval 1

7
DDA Algorithm

• Digital Differential Analyzer
• 0 lt Slope lt 1
• Unit x interval 1
• Slope gt 1
• Unit y interval 1
• -1 lt Slope lt 0
• Unit x interval -1

8
DDA Algorithm

• Digital Differential Analyzer
• Slope gt 1
• Unit x interval 1
• 0 lt Slope lt 1
• Unit y interval 1
• -1 lt Slope lt 0
• Unit x interval -1
• Slope lt -1
• Unit y interval -1

9
Bresenhams Line Algorithm

• Midpoint Line Algorithm
• Decision variable
• d gt 0 choose NE
• dnew
  doldab
• d lt 0 choose E
• dnew
  dolda

NE
Q
M
P(xp, yp)
E
10
Bresenhams Algorithm(cont.)

• Initial Value of d
• Update d

11
Polygons

• Filling Polygons
• Scan-line fill algorithm
• Inside-Outside tests

• Boundary fill algorithm

11
1
2
3
4
5
6
7
8
9
6
7
8
9
10
5
1
2
3
4
12
Scan-Line Polygon Fill

• Topological Difference between 2 Scan lines
• y intersection edges are opposite sides
• y intersection edges are same side

y
y
13
Scan-Line Polygon Fill (cont.)

• Edge Sorted Table

B
yC
yB
xC
1/mCB
C
C
E
yD
yC
xD
1/mDC
yE
xD
1/mDE
D
yA
yE
xA
1/mAE
yB
xA
1/mAB
A
1
0
Scan-Line Number
14
Inside-Outside Tests

• Self-Intersections
• Odd-Even rule

• Nonzero winding number rule

exterior
interior
15
Boundary-Fill Algorithm

• Proceed to Neighboring Pixels
• 4-Connected
• 8-Connected

16
Antialiasing

• Aliasing
• Undersampling Low-frequency sampling
• Nyquist sampling frequency
• Nyquist sampling interval

original
sample
reconstruct
17
Antialiasing (cont.)

• Supersampling (Postfiltering)
• Pixel-weighting masks
• Area Sampling (Prefiltering)
• Pixel Phasing
• Shift the display location of pixel areas
• Micropositioning the electron beam in relation to
  object geometry

18
Supersampling

• Subpixels
• Increase resolution

22
(10, 20) Maximum Intensity (11, 21) Next
Highest Intensity (11, 20) Lowest Intensity
21
20
10
11
12
19
Supersampling

• Subpixels
• Increase resolution

22
(10, 20) Maximum Intensity (11, 21) Next
Highest Intensity (11, 20) Lowest Intensity
21
20
10
11
12
20
Pixel-Weighting Masks

• Give More Weight to Subpixels Near the Center of
  a Pixel Area

21
Area Sampling

• Set Each Pixel Intensity Proportional to the Area
  of Overlap of Pixel
• 2 Adjacent vertical (or horizontal) screen grid
  lines ? trapezoid

22
(10, 20) 90 (10, 21) 15
21
20
10
11
12
22
Filtering Techniques

• Filter Functions (Weighting Surface)

Box Filter
Cone Filter
Gaussian Filter