Discussion
Given \(r_{x} = r_{y}\), the following super ellipse has the parameter value ρ = .......... .
Answer: D
The parameter is 2.
A superellipse is given by
\[ \begin{aligned} &\left(\frac{x}{r_x}\right)^{2/\rho} \\ &\quad + \left(\frac{y}{r_y}\right)^{2/\rho} = 1 \end{aligned} \]
With \(r_x = r_y = r\) and \(\rho = 2\) the exponents become 1, so \(|x| + |y| = r\): four straight edges meeting at the axes, which is exactly the diamond shown.
\(\rho = 1\) gives the ordinary ellipse, here a circle. Values below 1, such as 0.5, bulge outwards towards a square with rounded corners, and values between 1 and 2, such as 1.5, give a shape between the circle and the diamond, with curved sides.
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