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2D Scan-line Conversion

This article explores the efficiency of DDA and Bresenham's algorithms for 2D scan-line conversion in computer graphics. DDA is simple but requires floating points, while Bresenham's uses only integer addition, making it more efficient. The Bresenham's Midpoint Algorithm selects between NE and E pixels based on the relative position of the midpoint and the line. By choosing between E and NE based on the sign of the decision variable, these algorithms offer incremental calculation for smoother line rendering.

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2D Scan-line Conversion

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  1. 2D Scan-line Conversion University of Missouri at Columbia

  2. 2D Scan-line Conversion • DDA algorithm • Bresenham’s algorithm

  3. DDA algorithm • The simplest algorithm. • Named after Digital Differential Analyzer. (x1, y1) dy (x0, y0) dx

  4. DDA Algorithm

  5. DDA Algorithm

  6. DDA Algorithm

  7. DDA Algorithm

  8. DDA Algorithm

  9. DDA Algorithm

  10. 2D Scan-line Conversion • DDA algorithm • Bresenham’s algorithm

  11. Bresenham’s Midpoint Algorithm • DDA is simple, efficient, but needs floating points. • Bresenham’s use integer addition only. (x1, y1) dy (x0, y0) dx

  12. Bresenham’s Midpoint Algorithm • To choose from the two pixels NE or E depending on the relative position of the midpoint Mand the line. • Choose E if M is above the line, • Choose NE if M is below the line. NE M E (x0, y0)

  13. Bresenham’s Midpoint Algorithm • Choose E if d is positive, • Choose NE if d is negative. NE M E (x0, y0)

  14. Bresenham’s Midpoint Algorithm • Choose E if d is positive, • Choose NE if d is negative. NE M E (x0, y0)

  15. Incremental Calculation of the decision variable dnew NE M E (x0, y0)

  16. Bresenham’s Midpoint Algorithm NE M E (x0, y0)

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