Effective Circle Generation by Generating Series obtained from the Equation of Circle

In 1960, 'we' at Boeing coined the term Computer Graphics", written by William Allen Fetter in Print magazine's issue of 1966. Computer Graphics is an immense field of computer science and engineering which has been recently become highly developed in terms of research as well as applications. The core objective of this field of computer science is to display visual images and designs efficaciously and in actuality which generates meaningful visual conclusions to the user. And then the challenge arises that how to represent a real world scene over a computer screen in real time? A picture is divided into large number of pixels with varying intensities of Hue, Saturation and Brightness, whereas scene objects are created by geometrical structures referred to as Output Primitives. This paper focuses on an output primitive: Circle. In generation of circle over computer screen two things are considered the most important ones i.e. First is, keeping the calculation in integer only. Second is, lessening the time complexity, which is an important factor in real time displays of visual content. The paper explores the equation of the circle (x – a) ^ 2 + (y – b) ^ 2 = r ^ 2 for two dimensional Cartesian coordinate system which follows from the Pythagorean theorem applied to any point on the circle. In displaying a circle over computer screen this equation can be used to formulate a series and then that series can be used to generate the circle eliminating the direct use of the equation, which results in achieving the two major objectives i.e. Obviating the use of floating point calculations and diminution in the execution time of the procedure that generates the circle.