The Universe of Quadrics

Abstract

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Orthoptic Sets and Quadric Hypersurfaces

“…In Section 4 we consider ellipsoid and hyperboloid hypersurfaces. For ellipsoid, the technique in R 3 seems to be due to Monge, as reported in [5] where it is referred to [3]. We present here that it can be extended not only to ellipsoid in R n , but also to hyperboloid in R n .…”

“…The contribution of this paper is to present results for orthoptic sets, not only for conics in R 2 [4] and quadrics in R 3 [5], but also for quadric hypersurfaces in R n . Even thought it can be said that the technique for ellipsoid in R 3 can be extended to higher dimension [5], we present this extension not only for ellipsoids, but also for hyperboloids and paraboloids. We will see that it is a nice application of the trace operator of a matrix.…”

Polyhedrons the Faces of which are Special Quadric Patches

“…There can occur different cases of such a normal projection, see Figures 6 and 7. For example, for the case shown in Figure 6, left, by adding segment lengths we obtain (see also [4])…”

Interactive 4-D Visualization of Stereographic Images From the Double Orthogonal Projection

“…For a brief overview see [20], pp. 154-163, and for more general view with the construction of a spherical inversion used in Section 2.1 see [15], pp. 368-378.…”