Given a set of data points as measurements from a developable surface, the present paper investigates the recognition and reconstruction of these objects. We investigate the set of estimated tangent planes of the data points and show that classical Laguerre geometry is a useful tool for recognition, classification and reconstruction of developable surfaces. These surfaces can be generated as en...

Reconstruction of surface discontinuities from unorganized 3D points is a difficult problem. Both the polygonization and surface fitting approaches to surface reconstruction face the same chicken-and-egg problem: to correctly reconstruct surface discontinuities, the points that lie on the same side of the discontinuities should be used to reconstruct the surfaces to form the discontinuities. Ho...

We show that any set of n pairwise disjoint ovals in a finite projective plane of even order has a unique common tangent. As a consequence, any set of q+1 pairwise disjoint ovoids in PG(3, q), q even, has exactly q2+1 common tangent lines, constituting a regular spread. Also, if q−1 ovoids in PG(3, q) intersect pairwise exactly in two given points x ̸= y and share two tangent planes πx, πy at th...

In PG(2, q3), let π be a subplane of order q that is tangent to `∞. The tangent splash of π is defined to be the set of q2 + 1 points on `∞ that lie on a line of π. This article investigates properties of the tangent splash. We show that all tangent splashes are projectively equivalent, investigate sublines contained in a tangent splash, and consider the structure of a tangent splash in the Bru...

With the deenition of discrete line introduced by Reveilles REV91], there have been a wide range of research in discrete geometry and more precisely on the study of discrete line. By the use of the linear time line recognition algorithm of Debled and Reveilles DR94], A Vialard has proposed a O(n:l) algorithm for computing the tangent at all the points of a discrete curve. The complexity of her ...

With the abundance of video data, the interest in more effective methods for recognizing faces from unconstrained videos has grown. State-of-the-art algorithms for describing an image set use descriptors that are either very high-dimensional and/or sensitive to outliers and image misalignment. In this paper, we represent image sets as dictionaries of Symmetric Positive Definite (SPD) matrices t...

in this paper, we discuss the geometric properties of solution and lower bound estimate of ∆um−1 of the cauchy problem for a degenerate parabolic equation with periodic source term ut =∆um+ upsint. our objective is to show that: (1)with continuous variation of time t, the surface ϕ = [u(x,t)]mδq is a complete riemannian manifold floating in space rn+1and is tangent to the space rn at ∂h0(t); (2...

If we consider the quotient space of each tangent plane with respect to this equivalence relation, and the related quotient tangent bundle TS/∼1, a field FD : S −→ TS/∼1 maps each point on the surface to a direction. It is customary to take unit-length vectors as representatives of their equivalence classes, so that a direction field can be regarded as a vector field where the length of all vec...