Rounded square A shape similar to a squircle, called a '''', may be generated by separating four quarters of a circle and connecting their loose ends with straight
lines, or by separating the four sides of a square and connecting them with quarter-circles. Such a shape is very similar but not identical to the squircle. Although constructing a rounded square may be conceptually and physically simpler, the squircle has a simpler equation and can be generalised much more easily. One consequence of this is that the squircle and other superellipses can be scaled up or down quite easily. This is useful where, for example, one wishes to create nested squircles.
Truncated circle Another similar shape is a
truncated circle, the boundary of the
intersection of the regions enclosed by a square and by a concentric circle whose
diameter is both greater than the length of the side of the square and less than the length of the diagonal of the square (so that each figure has interior points that are not in the interior of the other). Such shapes lack the tangent continuity possessed by both superellipses and rounded squares.
Rounded cube A
rounded cube can be defined in terms of
superellipsoids.
Sphube Similar to the name
squircle, a
sphube is a portmanteau of 'sphere' and 'cube'. It is the three-dimensional counterpart to the squircle. The equation for the FG-squircle in three dimensions is: x^2 + y^2 + z^2 - \frac{s^2}{r^2}\left(x^2 y^2 + y^2 z^2 + x^2 z^2 - \frac{s^2}{r^2}x^2 y^2 z^2\right) = r^2 In polar coordinates, the sphube is expressed parametrically as \begin{align} x &= \frac{r \cos\theta\ \cos\phi}{\sqrt{1-s\cos^2\theta\sin^2\phi - s\sin^2\theta}}\\ y &= \frac{r \cos\theta\ \sin\phi}{\sqrt{1-s\cos^2\theta\cos^2\phi - s\sin^2\theta}}\\ z &= \frac{r \sin\theta}{\sqrt{1 - s\cos^2\theta}} \end{align} While the squareness parameter in this case does not behave identically to its squircle counterpart, nevertheless the surface is a sphere when equals 0, and approaches a cube with sharp corners as approaches 1. ==Uses==