Algorithms of Computer Graphics

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DDA Algorithm DDA algorithm is the most fundamental algorithm of Computer Graphics. DDA stands for “Digital Differential Analyzer”. It is both a hardware and software to interpolate variables across intervals between the starting and the ending point. One can realize shapes like Triangles, Polygons and lines with the help of DDA. DDA may be extrapolated to draw polynomial functions and quadratic curves. The simplest interpretation of the DDA algorithm is DDA lines.

Equation of the line can be given as Xq = Xq?1 + 1, Yi = Yi?1 + m. In these equations, m is the slope and can either be expressed as a DDA algorithm or any other algorithms like Rasterization.

Bresenham’s Line Generation It is a line drawing algorithm and helps determine the points on the screen to be used to plot lines by identifying n-dimensional rasters to be selected in an order that forms a close approximation of a straight line. It uses simpler arithmetic like integer calculations and avoids any floating-point divisions or multiplications, which saves time and space in terms of computer resources. It takes unit increments as it moves along the X-axis and decides to choose the value of the other axis, i.e., Y in this case at every increment.

Mid-Point Algorithm The Mid-Point algorithm arises from the concepts of the Bresenham algorithm. Academicians like Pitteway and Van Aken modified Brenham’s formula to invent the Mid-Point Algorithm.

Let us assume that we have a point P at coordinates x,y and slope of the line is 0 ? m ? 1.

The algorithm would now determine if the next point is placed at point E or at point N. This is decided by looking at the intersection Q which is closest to the point N or either E. The point that this intersection is closest to is considered as the point to be plotted next in the algorithm.

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