1. Scan converting a circle
Circle is one of the most widely used shape in drawing pictures and graphs and in computer graphics, various procedures are developed to draw complete circles or any portion of it such as arcs and sectors.
A circle is such a geometric shape that is defined by a center position and a fixed distance from the center which is called radius. It is drawn by combining all the points that are at a fixed distance from the center. Scan converting a circle requires each point on the circumference of the circle to be illuminated. Various algorithms and techniques are employed in computer graphics to scan convert a circle that uses equation of circle. The Polynomial equation of the circle in Cartesian coordinates whose center …show more content…
Suppose at ith position, plotted pixel is (xi , yi ). At position (i + 1)th , we have two candidate y-coordinates for xi+1 = xi + 1 as shown in figure 4.11. These candidate locations are marked as S(xi + 1 , yi -1) and T(xi + 1 , yi ). From the above figure, it can be seen that if we generating points from 90° to 45°(i.e. from x= 0 to x= y), each new pixel position closest to the actual circumference of the circle can be found by taking either of the two actions: moving in the x-direction by unit interval and not changing the y-coordinate. moving in the x-direction by unit interval and moving in the negative y-direction by unit interval (i.e. decrementing y-coordinate by unit interval).
Distance of the pixel T from the origin is calculated by using distance formula i.e. CT = √(〖(x_i + 1)〗^2+〖y_i〗^2 )
Similarly Distance of the pixel S from the origin is given as CS = √(〖(x_i + 1)〗^2+〖(y_i -1)〗^2 )
Here we are using a function D( ) that provides a relative measurement of the distance from the center of the pixel from the actual circle. Let D(T) be the square of the distance from the origin to the pixel T minus square of the distance to the actual circle ( i.e. r