The quadrics are all surfaces that can be expressed as a second degree polynomialin x, y and z. We study the Gauss map G of quadric surfaces in the 3-dimensional Euclidean space R^3 with respect to the so called L_1 operator ( Cheng-Yau operator □) acting on the smooth functions defined on the surfaces. For any smooth functions f defined on the surfaces, L_f=tr(P_1o hessf), where P_1 is t...

This paper explores some of the basic and most interesting facts about quadric surfaces. It describes the canonical coordinate transformations required to eliminate cross terms from the equation of a general quadric equation. It explains how to use these coordinates to obtain each of the seventeen canonical quadrics. It further describes the determination of the physical axis and angle of rotat...

Surfaces subdivision is an important means for geometric computing of surfaces in CAD. This paper proposes a new quadric subdivision for canal surfaces in this paper, RQ-sphere decomposition, that subdivides canal surfaces as a set of truncated revolute quadric with joint spheres. Experimental results show that the RQ-sphere decomposition is better than existing methods.

We construct smooth irreducible curves of the lowest possible degrees in quadric and cubic surfaces whose complements are Kobayashi hyperbolically imbedded into those surfaces. Moreover we characterize line bundles on quadric and cubic surfaces such that the complete linear systems of the line bundles have a smooth irreducible curve whose complement is Kobayashi hyperbolically imbedded.

Locating and classifying quadric surfaces is a significant step in the recognition of 3D manufactured objects because quadric surfaces are commonly occuring shapes in man-made products. Surface fitting based on the input sample data point set is an effective strategy for quadric surface recognition. Two algorithms of quadric surface fitting that are especially useful for hyperboloid and parabol...

The reconstruction of 3D objects from 2D orthographic views is crucial for maintaining and further developing existing product designs. A B-rep oriented method for reconstructing curved objects from three orthographic views is presented by employing a hybrid wire-frame in place of an intermediate wire-frame. The Link-Relation Graph (LRG) is introduced as a multi-graph representation of orthogra...

In the present paper, we provide general bounds for the torsion in the codimension 2 Chow groups of the products of projective homogeneous surfaces. In particular, we determine the torsion for the product of four Pfister quadric surfaces and the maximal torsion for the product of three Severi-Brauer surfaces. We also find an upper bound for the torsion of the product of three quadric surfaces w...

We study the functional codes C2(X) defined on projective varieties X , in the case where X ⊂ P is a 1-degenerate quadric or a non-degenerate quadric (hyperbolic or elliptic). We find the minimum distance of these codes, the second weight, and the third weight. We also show the geometrical structure of the first weight and second weight codewords. One result states that the codes C2(X) defined ...