We prove that, for q odd and n ≥ 3, the group G = On(q) · 2 is maximal in either the orthogonal group O2n(q) or the special orthogonal group SO2n(q). The group G corresponds to the stabilizer of a spread of lines of PG(2n − 1, q) in which some lines lie on a quadric, some are secant to the quadric and others are external to the quadric.

A principal quadric estimator is described which is based on independently fitting cubic facets to the 3 components of position in a small neighbourhood of each data point. From the parameters of the fitted facets, the first and second order differential properties of the surface at the data point, and hence the principal quadric parameters, can be estimated. This method is compared with severa...

Exponential polynomials are essential in subdivision for the reconstruction of specific families curves and surfaces, such as conic sections quadric surfaces. It is well known that if a linear scheme able to reproduce certain space exponential polynomials, then it must be level-dependent, with rules depending on frequencies (and eventual multiplicities) defining considered space. This work disc...

This paper is concerned with the robust identiication of patches from simple geometric surfaces such as planes, spheres, and cylinders. This is done from 3D data acquired using a range scanner, along with principal quadric estimates at each point. Properties of the Gaus-sian and mean curvature (e.g., their sign) at points on surfaces of the target class are used to reject all points that could ...

Automatic extraction of CAD descriptions which are ultimately intended for human manipulation requires the accurate inference of geometric and topological information. We present a system which applies segmentation techniques from computer vision to automatically extract CAD models from range images of parts with curved surfaces. The output of the system is a B-rep of the object which is suitab...

We deene Picard-Einstein metrics on complex algebraic surfaces as KK ahler-Einstein metrics with negative constant sectional curvature pushed down from the unit ball via Picard modular groups allowing degenerations along cycles. We demonstrate how the tool of orbital heights, especially the Proportionality Theorem presented in H98], works for detecting such orbital cycles on the projective plan...

We describe convex quadric hypersurfaces in Rn and characterize them as convex hypersurfaces with quadric sections by a continuous family of hyperplanes.

This paper is concerned with the robust identiication of patches from simple geometric surfaces such as planes, spheres, and cylinders. This is done from 3D data acquired using a range scanner, along with principal quadric estimates at each point. Properties of the Gaussian and mean curvature (e.g., their sign) at points on surfaces of the target class are used to reject all points that could n...

Various schemes have been proposed for creating rational surface patches with a variable number of sides. Although these schemes appear to be unrelated, they all produce surface parameterizations that have parameter values for which the numerator and denominator of the deening rational functions vanish simultaneously. These parameter values are base points of the rational parameterization. This...

All families of sextic surfaces with the maximal number of isolated triple points are found. Surfaces in P3(C) with isolated ordinary triple points have been studied in [EPS]. The results are most complete for degree six. A sextic surface can have at most ten triple points, and such surfaces exist. For up to nine triple points [EPS] contains a complete classification. In this note I achieve the...