Lines

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Lines

• DDA Line Drawing, Antialiasing

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Line Drawing

• How does a machine go about drawing a line
  defined by a mathematical representation (e.g.
  vector, endpoints, parametric, etc.)?
• How does the continuous line description get
  converted to the discrete pixel representation.
• Important part of Rasterization process
• Some common algorithms
• DDA
• Bresenhams

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DDA Algorithm

• Digital Differential Analyser a scan conversion
  line algorithm
• Based on calculating the rate of change of x or y
  coordinates (Dx or Dy respectively)
• Given two endpoints
• Step for the larger of length(x) or length(y)
• Starting at first endpoint increment by Dx or Dy
  rounding off to the nearest pixel coordinate.

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void lineDDA (int xa, int ya, int xa, int xb)
int dx xb - xa, dy yb - ya, steps, k float
xIncr, yIncr, x xa, y ya if (
abs(dx)gtabs(dy) ) steps abs(dx) else steps
abs(dy) xIncr dx / (float) steps yIncr
dy / (float) steps drawPixel ( ROUND(x),
ROUND(y) ) for (k0 kltsteps k) x
xIncr y yIncr drawPixel(
ROUND(x), ROUND(y) )
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Antialiasing

• Distortion of information due to low-frequency
  sampling
• In raster images leads to jagged edges with
  staircase effect
• We can reduce effects by antialiasing methods to
  compensate for undersampling

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Antialiasing by supersampling
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