The problem of rendering large trimmed NURBS models at interactive frame rates is of great interest for industry, since nearly all their models are designed on the basis of this surface type. Most existing approaches first transform the NURBS surfaces into polygonal representation and subsequently build static levels of detail upon them, as current graphics hardware is optimized for rendering t...

This paper is concerned with approximating noisy samples by NURBS curves with special emphasis on free knots. We consider the knots as unknown parameters so as to find their optimal positions. The original problem which is linear with respect to the weights and the control points but is nonlinear with respect to the knots is reformulated such that the knots are the only variable set. We show ho...

We consider curves defined over small finite fields with points of large prime order over an extension field. Such curves are often referred to as Koblitz curves and are of considerable cryptographic interest. An interesting question is whether such curves are easy to construct as the target point order grows asymptotically. We show that under certain number theoretic conjecture, if q is a prim...

A Q-curve is an elliptic curve defined over Q that is isogenous to all its Galois conjugates. The term Q-curve was first used by Gross to denote a special class of elliptic curves with complex multiplication having that property, and later generalized by Ribet to denote any elliptic curve isogenous to its conjugates. In this paper we deal only with Q-curves with no complex multiplication, the c...

Threads and wires are deformable 3-dimensional (3D) and curvilinear objects which are commonly manipulated by humans in various medical and manufacturing tasks. Several applications, including computerassisted evaluation, augmented reality guidance, and autonomous robotic manipulation [2, 3] would benefit from the real-time estimation of the 3D shapes of these deformable objects from images. Th...

A technique for modeling fur, but not long human hair, quickly using the facilities of common graphics workstations is described. The user selects a variety of parameters to achieve the desired appearance for a particular animal, such as hair density, length, stiffness, and color properties. Undercoat and overcoat may have separate specifications, and degrees of randomness may be specified, for...

Parametric surface [Fari02] is a surface defined by a tensor-product of parametric curves, which are represented by parametric equations. As such surface comes with a well defined mathematical definition, it becomes one of the most common geometric tools for computer-aided geometric design and object modeling aids for many computer graphics applications. Typical examples of such surface include...

Elliptic curve point multiplication kP on an elliptic curve is required in every elliptic curve cryptosystem. The operation can be significantly accelerated by using a special type of elliptic curves called the Koblitz curves and by representing the integer k in τ -adic nonadjacent form (τNAF). Hardware-friendly modifications of existing τNAF conversion algorithms are presented and an efficient...

Rating curves are the means by which readings of surface elevation at gauging stations on rivers are converted to discharges. Their implicit assumption of a unique relationship between stage and discharge overlooks some of the hydraulics of the problem by ignoring the effects of surface slope. This paper describes a method for allowing for possible variable slope by incorporating time derivativ...

A potential-based model of three-dimensional (3D) workspace is proposed in this paper for ensuring obstacle avoidance in path planning. It is assumed that the workspace boundary is uniformly distributed with generalized charges. The potential due to a point charge is inversely proportional to the distance to the power of an integer, the order of the potential function. It is shown that such pot...