We introduce order-k α-hulls and αshapes — generalizations of α-hulls and α-shapes. Being also a generalization of k-hull (known in statistics as “k-depth contour”), order-k α-hull provides a link between shape reconstruction and statistical depth. As a generalization of α-hull, order-k α-hull gives a robust shape estimation by ignoring locally up to k outliers in a point set. Order-k α-shape p...

We investigate interlacing properties of zeros Laguerre polynomials Ln(α)(x) and Ln+1(α+k)(x), α>−1, where n∈N k∈{1,2}. prove that, in general, the these interlace partially not fully. The sharp t-interval within which two equal degree Ln(α+t)(x) are for every each α>−1 is 0<t≤ 2, [Driver K, Muldoon ME. Sharp interval polynomials. J Approx Theory, to appear.], consecutive Ln−1(α+t)(x) 0≤t≤ Comm...