## Eight-way Symmetry

A circle is a symmetrical figure. It possesses eight-way symmetry. It means when a circle is divided into eight part at 45° angle all eight parts have same shape. The circle generating algorithm takes advantage of the circle symmetry to plot eight points by calculating the coordinates of any one point.

Thus, for a circle centered at the origin, any point (x, y) on the circle gives rise to seven other points by this symmetry. In this way, we need to calculate only one 45° segment i.e. one octant to generate the complete circle. All eight octants are similar except for their placement in the circle. If point 1 calculated using a circle algorithm then seven more points could found by reflection.

This reflection is accomplished by reversing the x, y coordinates as in point 2, reversing the x, y coordinates and reflecting about the y-axis as in point 3, reflecting about the y-axis as in point 4, switching the signs of x and y as in point 5, reversing the x, y coordinates, reflecting about the y-axis and reflecting about the x-axis as in point 6, reversing the x, y coordinates and reflecting about the y-axis as in point 7 and reflecting about the x-axis as in point 8.

**Thus, various points generated are:**

- (x, y)
- (y, x)
- (-y, x)
- (-x, y)
- (-x, -y)
- (-y,- x)
- (y,- x)
- (x, -y)

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