A k-ellipse is a plane curve consisting of all points whose distances from k fixed foci sum to constant. We determine the singularities and genus its Zariski closure in complex projective plane. The paper resolves an open problem stated by Nie, Parrilo Sturmfels 2008.

We propose a new algorithm for real-time detection and tracking of elliptic patterns suitable real-world robotics applications. The method fits ellipses to each contour in the image frame rejects that do not yield good fit. resulting is lightweight enough be used on robots' resource-limited onboard computers, can deal with lighting variations detect pattern even when view partial. tested an exa...

Topology is the mathematical study of properties of objects which are preserved through deformations, twisting, and stretching. Tearing, however, is not allowed. A square is topologically equivalent to a circle and a circle is topologically equivalent to an ellipse, into which it can be deformed by stretching. In this work, we discuss the properties of ellipses when an ellipse is continuously s...

A complete calibration method to characterize a static planar two-dimensional detector for use in X-ray diffraction at an arbitrary wavelength is described. This method is based upon geometry describing the point of intersection between a cone's axis and its elliptical conic section. This point of intersection is neither the ellipse centre nor one of the ellipse focal points, but some other poi...