Dda algorithm

Dda algorithm

• 1.
  SUBJECT : COMPUTERGRAPHICS
• 2.
   In ComputerGraphics the first basic line drawing algorithm is Digital Differential Analyzer (DDA) Algorithm.  A line connects two points. It is a basic element in graphics. To draw a line, you need two points between which you can draw a line.  In computer graphics, a digital differential analyzer (DDA) is hardware or software used for interpolation of variables over an interval between start and end point. DDAs are used for rasterization of lines, triangles and polygons. They can be extended to non linear functions, such as perspective correct texture mapping, quadratic curves, and traversing voxels. DIGITAL DIFFERENTIAL ANALYZER (DDA) ALGORITHM.
• 3.
  COMPUTER HAS TOTAKE CARE OF 2 THINGS:  Pixels - Which pixels to plot.  Computations - Computations required to calculate pixel positions
• 4.
  SLOPE INTERCEPT LINEEQ:  y = mx + b  m = slope  b = is the y intercept, is called as “slope intercept line equation.”  Therefore  Slope(m) = dy/dx  Slope(m) = y2 - y1 / x2 - x1  b= y1 – m.x1 (y intercept)
• 5.
  (DDA) ALGORITHM  Walkthrough the line, starting at (x0,y0)  Constrain x, y increments to values in [0,1] range  Case a: x is incrementing faster (m < 1)  Step in x=1 increments, compute and round y  Case b: y is incrementing faster (m > 1)  Step in y=1 increments, compute and round x
• 6.
  DDA LINE DRAWINGALGORITHM (CASE A: M < 1)  x = x0 y = y0  (x, round(y)  Here y = y0+m.x  x=1  Similarly  x=x0+1 y=y0+m  m<1 = x↑↑ more than y or dy/dx<1  Until x == x1
• 7.
  DDA LINE DRAWINGALGORITHM (CASE B: M > 1)  m>1 = this implies y↑↑ more than x or dy/dx >1  x k+1=x k+1/m y k+1= y k+1  x = x0 y = y0  Plot (round(x), y) x = x+1/m y= y+ 1  … Until y == y1
• 8.
  ADVANTAGES  1. Itis the simplest algorithm and it does not require special skills for implementation.  2. It is a faster method for calculating pixel positions than the direct use of equation y=mx + b. It eliminates the multiplication in the equation by making use of raster characteristics, so that appropriate increments are applied in the x or y direction to find the pixel positions along the line path.
• 9.
  DISVANTANGES  1. Floatingpoint arithmetic in DDA algorithm is still time-consuming.  2. The algorithm is orientation dependent. Hence end point accuracy is poor.