In this paper, we derive an explicit formula for the bivariate Lagrange basis polynomials of a general set checkerboard nodes. This generalizes existing results at Padua nodes, Chebyshev Morrow-Patterson and Geronimus We also construct subspace spanned by linearly independent vanishing that vanish nodes prove uniqueness in quotient space defined as with certain degree over polynomials.

We prove that alternating links with two totally geodesic checkerboard surfaces are three projection the 1-skeleton of octahedron, cuboctahedron and icosidodecahedron. also characterize these as right-angled completely realisable show all hyperbolic weaving knots exceptions have both not geodesic.

We describe a technique to detect and localize features on checkerboard calibration charts with high accuracy. Our approach is based on a model representing the sought features by a multiplicative combination of two edge functions, which, to allow for perspective distortions, can be arbitrarily oriented. First, candidate regions are identified by an eigenvalue analysis of the structure tensor. ...

The ecological environment offered by virtual reality is primarily supported by visual information. The different image contents and their rhythmic presentation imply specific bottom-up and top-down processing. Because these processes already occur during passive observation we studied the brain responses evoked by the presentation of specific 3D virtual tunnels with respect to 2D checkerboard....

We consider the subgroup of the abelian sandpile group of the grid graph consisting of configurations of sand that are symmetric with respect to central vertical and horizontal axes. We show that the size of this group is (i) the number of domino tilings of a corresponding weighted rectangular checkerboard; (ii) a product of special values of Chebyshev polynomials; and (iii) a double-product wh...

Multi-cameras system is widely applied in 3D computer vision especially when multiple 11 cameras are distributed on both sides of the measured object. The calibration methods of multi12 cameras system are critical to the accuracy of vision measurement and the key is to find an 13 appropriate calibration target. In this paper, a high-precision camera calibration method for multi14 cameras system...