DDA Line Drawing Algorithm

DDA (Digital Differential Analyzer) algorithm is a computer graphics algorithm used for drawing lines on a raster display. The algorithm is based on the mathematical concept of the slope of a line and uses a step-by-step approach to calculate the pixels needed to draw the line.

The basic steps of the DDA line drawing algorithm are as follows:

1. Determine the endpoints of the line drawn, and calculate the difference in x and y coordinates between the endpoints.
2. Determine the number of steps needed to draw the line by taking the maximum difference (either in x or y coordinates) and dividing it by the length of the line.
3. Calculate the incremental values of x and y for each step by dividing the differences in x and y coordinates by the number of steps.
4. Starting at the first endpoint, use the incremental values of x and y to calculate the coordinates of each pixel along the line, and plot these pixels on the screen.
5. Continue this process until the last endpoint of the line is reached.

The DDA algorithm is simple and easy to implement, and it works well for lines that are not too steep or too shallow. However, it can produce inaccurate results for lines that are very steep or very shallow, as the algorithm relies on floating-point arithmetic, which can introduce rounding errors.

To improve the accuracy of the DDA algorithm for steep or shallow lines, other algorithms such as Bresenham’s line drawing algorithm can be used.

Rules of DDA

Case 1:
if m<1 then xn = x1+1 and yn = y1+m
Case 2:
if m>1 then xn = x1+1/m and yn = y1+1
Case 3:
if m=1 then xn = x1+1 and yn = y1+1

Example

A (5, 6) and B (8, 12)

Δx = x2 - x1 = 8-5 = 3
Δy = y2 - y1 = 12-6 = 6
m = Δy/Δx = 6/3 = 2

K = abs(Δx)>abs(Δy)
K = Δy = 6 (Steps)

So, m>1 then
xn = x1+1/m and yn = y1+1

x0	y0	xp+1	yp+1	Round off (xp+1, yp+1)
5	6	0.5+5=5.5	6+1=7	6,7
		5.5+0.5=6	7+1=8	6,8
		6+0.5=6.5	8+1=9	7,9
		6.5+0.5=7	9+1=10	7,10
		7+0.5=7.5	10+1=11	8,11
		7.5+0.5=8	11+1=12	8,12

Advantages of the DDA Line Drawing Algorithm:

• The DDA algorithm is simple and easy to understand and implement.
• The algorithm uses only basic arithmetic operations, which makes it fast and efficient.
• The DDA algorithm can be used to draw lines of any slope, including vertical and horizontal lines.
• The algorithm is suitable for implementation on both software and hardware platforms.

Disadvantages of the DDA Line Drawing Algorithm:

• The DDA algorithm can produce inaccurate results for lines that are very steep or very shallow, as the algorithm relies on floating-point arithmetic, which can introduce rounding errors.
• The algorithm can be slow and inefficient for lines that are very long, as it requires a large number of calculations to plot each pixel along the line.
• The algorithm may not produce satisfactory results for lines with jagged or uneven edges, as the pixels are plotted at regular intervals along the line, rather than following the actual shape of the line.
• The algorithm does not take into account the thickness of the line being drawn, which can lead to gaps or overlaps between adjacent lines.