We consider the X-ray transform in a projective space over a finite field. It is well known (after E. Bolker) that this transform is injective. We formulate an analog of I.M. Gelfand’s admissibility problem for the Radon transform, which asks for a classification of all minimal sets of lines for which the restricted Radon transform is injective. The solution involves doubly ruled quadric surfaces.

This paper addresses the problem of interpolating three points with a surface whose normal and orientation is also defined at those points. Conditions are derived for the existence of a quadric surface interpolant and it is shown that a cubic interpolant always exists. Finally, the paper describes a new cubic construction that provides a family of suitable surfaces with four geometrically intui...

A new branching blend between two natural quadrics (circular cylinders/cones or spheres) in many positions is proposed. The blend is a ring shaped patch of a PN surface (surface with rational offset) parametrized by rational bivariant functions of degree (6, 3). General theory of PN surfaces is developed using Laguerre geometry and a universal rational parametrization of the Blaschke cylinder. ...

A modified quadric error metric (QEM) for simplification of Loop subdivision surfaces is presented. The suggested error metric not only measures the geometric difference but also controls the smoothness and well-shapedness of the triangles that result from the decimation process. Minimizing the error with respect to the original limit surface, our method allows for drastic simplification of Loo...

Estimation of local surface geometry (i.e. principle frame and principle quadric) is discussed. It is shown that surface tting methods are more robust that-nite diierence based approaches for a number of reasons. The local surface geometry is used to segment the surfaces into regions corresponding to smooth patches, separated by visibility boundaries, occluding contours, and ridges. Points with...

In this paper, we present a new key exchange protocol in which Alice and Bob have secret keys given by quadric surfaces embedded large ambient space means of the Veronese embedding public hyperplanes containing quadrics. Both them reconstruct isomorphism class intersection is curve genus 1, uniquely determined j-invariant. An eavesdropper, to find j-invariant, has solve problems are conjectural...

Levin’s method produces a parameterization of the intersection curve of two quadrics in the form p(u)= a(u)± d(u)√s(u), where a(u) and d(u) are vector valued polynomials, and s(u) is a quartic polynomial. This method, however, is incapable of classifying the morphology of the intersection curve, in terms of reducibility, singularity, and the number of connected components, which is critical str...

In two experiments, the active haptic identification of three-dimensional mathematically well-defined objects is investigated. The objects, quadric surfaces, are defined in terms of the shape index, a quantity describing the shape, and curvedness, a quantity describing overall curvature. Both shape index and curvedness are found to have a significant influence on haptic shape identification. Co...