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Dda algorithm

This document discusses the Digital Differential Analyzer (DDA) algorithm, which is a basic line drawing algorithm used in computer graphics. The DDA algorithm uses slope-intercept form (y=mx+b) to incrementally calculate pixel positions along the line between two points. It handles cases where the slope is less than or greater than 1 by incrementing either the x or y coordinate by 1 at each step. The DDA algorithm is simple to implement but requires floating point calculations and has orientation dependency issues.

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SUBJECT : COMPUTER GRAPHICS
 In Computer Graphics 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.
COMPUTER HAS TO TAKE CARE OF 2 THINGS:  Pixels - Which pixels to plot.  Computations - Computations required to calculate pixel positions
SLOPE INTERCEPT LINE EQ:  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)
(DDA) ALGORITHM  Walk through 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
DDA LINE DRAWING ALGORITHM (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
DDA LINE DRAWING ALGORITHM (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
ADVANTAGES  1. It is 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.
DISVANTANGES  1. Floating point arithmetic in DDA algorithm is still time-consuming.  2. The algorithm is orientation dependent. Hence end point accuracy is poor.
Dda algorithm