We complete the topological classification of real algebraic non-singular curves bidegree $(5, 5)$ on quadric ellipsoid. show in particular that previously known restrictions form a system for this bidegree. Therefore, main part paper concerns construction curves. Our strategy is first to reduce second Hirzebruch surface by degenerating ellipsoid quadratic cone. Next, we combine different class...

ÐThis paper addresses the problem of invariant-based recognition of quadric configurations from a single image. These configurations consist of a pair of rigidly connected translationally repeated quadric surfaces. This problem is approached via a reconstruction framework. A new mathematical framework, using relative affine structure, on the lines of Luong and Vieville [12], has been proposed. ...

Conic sections embedded in a torus must be circles of special types: (i) proole circles, (ii) cross-sectional circles , and (iii) Yvone-Villarceau circles. Based on this classiication, we present eecient and robust geometric algorithms that detect and compute all degenerate conic sections (circles) in torus/plane and torus/natural-quadric intersections. 2 Introduction Simple surfaces (such as p...

This thesis is focused on the developement of an algorithm for the computation of all edge cycles bounding the faces of a three-dimensional arrangement of algebraic surfaces of degree two (quadrics). We develop the concepts of required data structures and a concrete implementation of the algorithm. The algorithm is based on the approach and the implementation by Hemmer et.al. [31] for computing...

CONTENTS Introduction. 79 1. Fundamental equations for a surface referred to its asymptotic curves. 85 2. Reciprocal congruences and the relation R. 86 3. The developables of the congruences T and r". 88 4. The focal points of the lines I and I'. 90 5. The directrix congruences. 91 6. Some general properties of reciprocal congruences. 93 7. The osculating quadric, and its connection-with recipr...

In the present article, we consider Algebraic Geometry codes on some rational surfaces. The estimate of the minimum distance is translated into a point counting problem on plane curves. This problem is solved by applying the upper bound à la Weil of Aubry and Perret together with the bound of Homma and Kim for plane curves. The parameters of several codes from rational surfaces are computed. Am...

This paper describes a model based robot vision system for bin-picking of curved object utilizing range images. Surface properties and 3-D shape of the object are derived from the range image. This system extracts an object and detects its location and orientation based on models. The object is to be represented by a set of quadric curved surfaces. The Gaussian and the mean curvature are used a...

In this paper we classify and derive closed formulas for geometric elements of quadrics in rational Bézier triangular form (such as the center, the conic at infinity, the vertex and the axis of paraboloids and the principal planes), using just the control vertices and the weights for the quadric patch. The results are extended also to quadric tensor product patches. Our results rely on using te...