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DDA Algorithm (Digital Differential Analyzer)

The Digital Differential Analyzer (DDA) algorithm is one of the simplest line-drawing algorithms. Given the starting and ending coordinates of a line, DDA can efficiently compute the intermediate points to draw the line.

Algorithm Overview

Given:

  • Starting coordinates: (X0, Y0)
  • Ending coordinates: (Xn, Yn)
  • Initial values: Xp = X0, Yp = Y0

Step 1: Calculate ΔX, ΔY, and M

These parameters are calculated based on the starting and ending coordinates:

  • ΔX = Xn - X0
  • ΔY = Yn - Y0
  • M = ΔY / ΔX (slope of the line)

Step 2: Determine the Number of Steps

The number of steps or points to be calculated is determined by the following condition:

  • If |ΔX| > |ΔY|:
    • Steps = |ΔX|
  • Else:
    • Steps = |ΔY|

Step 3: Calculate Next Points

Suppose the current point is (Xp, Yp), and the next point is (Xp+1, Yp+1). The following cases apply:

Case 1: If M < 1

  • Xp+1 = round(Xp + 1)
  • Yp+1 = round(M + Yp)

Case 2: If M = 1

  • Xp+1 = round(Xp + 1)
  • Yp+1 = round(Yp + 1)

Case 3: If M > 1

  • Xp+1 = round(Xp + 1/M)
  • Yp+1 = round(Yp + 1)

Step 4: Repeat Until the End Point is Reached

Keep calculating the next point (Xp+1, Yp+1) until:

  • The end point (Xn, Yn) is reached, or
  • The number of generated points (including the start and end points) equals the calculated Steps.

DDA Visualization:

Here is a visual representation of how the DDA algorithm works:

DDA

Documentation:

For a more detailed explanation of the DDA algorithm, check out the full documentation:

Click here for Documentation