2.3 Scan Converting Circles

Cf. [FvDFH90, 3.3] and [PK87, 3.4]

A circle (through 0) with radius $R$ is given by the explicit equation $y=\pm\sqrt{R^2-x^2}$ or implicitly by $0=F(x,y):=x^2+y^2-R^2$. The straight forward method of drawing a circle by approximating the values $\pm\sqrt{R^2-i^2}$ is ineffective (since it involves: squaring, taking roots and $\operatorname{ROUND}$) and it gives an asymmetric distribution.

Figure: Straight forward scan converting a circle

We can make use of the 8-fold symmetry, so we only have to draw 1/8 of the circle say from $S$ to $SE$.

Figure: 8-fold symmetry of the circle