hyperellipses

Noun

hyperellipse (plural hyperellipses)

1. A superellipse: a curve in two dimensions of a certain type, a generalization of the ellipse.
   • The hyperellipse is defined by (x/a)ⁿ + (y/b)ⁿ = 1 with b ≤ a, where n is the shape parameter and a and b are the axes along the x and y axes, respectively.2003, M. M. Yovanovich and E. E. Marotta, "Thermal Spreading and Contact Resistances", chapter 4 of Adrian Bejan and Allan D. Kraus (editors), Heat Transfer Handbook, Wiley-IEEE, page 286
2. Specifically, a superellipse with an exponent (shape parameter) greater than that of the ellipse (two).
3. A multi-dimensional manifold of a certain type, a generalization of the ellipse and ellipsoid.
   • This algorithm extends the model of RNS by incorporating multiple hypershape (hypersphere, hyperrectangle, or hyperellipse) detector representation in the unit hypercube [0, 1]ⁿ (Balachandran et al., 2007).2008, Dipankar Dasgupta, Luis Fernando Niño, Immunological Computation: Theory and Applications, CRC Press, →ISBN, page 97