A circle in a three dimensional space is a simple figure that is useful for illustrating HiSee's projection methods.
Under coordinate projection a circle either remains circular, becomes an ellipse, or becomes a line segment. The elliptical case is shown above on the left. The edge-on case is shown above on the right. The points on the circle are equally spaced along the circle and colored sequentially. In the edge on case we can see how the points appear compressed along the top and bottom of the circle due to the fact that these parts of the circle point away from the viewer.
Since a circle is a planar figure, PCA and the Sammon map isometrically embed the circle in the plane regardless of how it is situated in 3-space. This is shown to the left.