Ellipsis & Superellipsis

Ellipsis

Equation:

[; \left( \frac{x-x_c}{a} \right)^2 \left( \frac{y-y_c}{a} \right)^2 =1 ;]

Parametrization:

[; \underline{r}(t) = \left(\begin{array}{c} a \cos{t}\\ b\sin{t} \end{array}\right), \quad 0 \leq t < 2 \pi ;]

Evolute: Asteroid

[; \underline{c}(t) = (a^2-b^2) \left(\begin{array}{c} a \cos^3{t}\\ -b\sin^3{t} \end{array}\right), \quad 0 \leq t < 2 \pi ;]

Super Ellipsis

Equation:

[; \left( \frac{x-x_c}{a} \right)^\rho \left( \frac{y-y_c}{a} \right)^\rho =1 ;]

Parametrization:

[; \underline{r}(t) = \left(\begin{array}{c} a \cos^{2/\rho}{t}\\ b\sin^{2/\rho}{t} \end{array}\right), \quad 0 \leq t < \pi/2 ;]

Generated: 31 Dec 1969, 21:00:00

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