A new approach is introduced to 3-D parameterized object estimation and recognition. Though the theory is applicable for any parameterization, we use a model for which objects are approximated by patches of spheres, cylinders, and planes---primitive objects. These primitive surfaces are special cases of 3-D quadric surfaces. Primitive surface estimation is treated as parameter estimation using ...

We study the moduli space M(6; 3, 6, 4) of simple rank 6 vector bundles E on P with Chern polynomial 1 + 3t + 6t+4t and properties of these bundles, especially we prove some partial results concerning their stability. We first recall how these bundles are related to the construction of sextic nodal surfaces in P having an even set of 56 nodes (cf. [Ca-To]). We prove that there is an open set, c...

Comparisons of joint surface curvature at the base of the thumb have long been made to discern differences among living and fossil primates in functional capabilities of the hand. However, the complex shape of this joint makes it difficult to quantify differences among taxa. The purpose of this study is to determine whether significant differences in curvature exist among selected catarrhine ge...

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational Bézier patch using quartic Bézier patch. We show that our approximation method yields G (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fast and produces high quality approximations in practice. Here we provide some theory to explain w...

It is known that every ovoid of the parabolic quadric Q(4,q), q = ph, p prime, intersects every three-dimensional elliptic quadric in 1 mod p points. We present a new approach which gives us a second proof of this result and, in the case when p = 2, allows us to prove that every ovoid of Q(4,q) either intersects all the three-dimensional elliptic quadrics in 1 mod 4 points or intersects all the...

1. Given a 3-dimensional Pappian projective space, it is well known that the Grassmannian which is representing its set of lines is a quadric (called the Pltcker quadric) in a 5-dimensional projective space. The link between the set of lines and the Pltcker quadric is the bijective Klein map g. Under g pencils of lines become lines of the Pltcker quadric. Cf. e.g. [5,287], [15,28], [16,13], [20...

We introduce planar grouping, a technique where planar relationship information is gathered for a set of rigid points. This information is used to accelerate affine transformations and clipping. The planar grouping technique is an optimization problem, implemented in a best-first greedy search. We present two error metrics, one simple and fast, one based on the quadric error metric (QEM) to ach...

The set of points obtained by projecting a quadric from a point off the quadric on a hyperplane has many interesting properties. Hirschfeld and Thas [12, 13] provided a characterization of this set, only by means of its intersection pattern with lines. However, their result only holds when the finite field has even order. Here, we extend their result to finite fields of odd order.

We study multidimensional quadrilateral lattices satisfying simultaneously two inte-grable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Möbius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constrain...