Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. Cubic Bézier curves are commonly used in curve and surface design because they are of low degree, are easily evaluated, and allow inflection points. This paper generalises earlier results on p...

We describe an elastic matching procedure between plane curves based on computing a minimal deformation cost between the curves. The design of the deformation cost is based on a geodesic distance defined on an infinite dimensional group acting on the curves. The geodesic paths also provide an optimal deformation process, which allows interpolation between any plane curves. q 1999 Elsevier Scien...

We present an extension to Sierpinski’s curve that is useful for generating a large variety of highly symmetric curves. We propose a scheme for automated construction of these curves, capable of producing millions of curves. Because of their high-degree of symmetry, these curves can be utilized in various graphics design applications. In particular, we briefly describe a web-based system for au...

The design of curves and surfaces in C.A.D. systems has many applications in car, plane or ship industry. Because they offer more flexibility, rational functions are often prefered to polynomial functions to modelize curves and surfaces. In this work, several methods to generate rational Bezier curves and surfaces which minimize some functionals are proposed. The functionals measure a technical...

‎in this work‎, ‎first the differential equation characterizing position vector‎ ‎of spacelike curve is obtained in lorentzian plane $mathbb{l}^{2}.$ then the‎ ‎special curves mentioned above are studied in lorentzian plane $mathbb{l}%‎‎^{2}.$ finally some characterizations of these special curves are given in‎ ‎$mathbb{l}^{2}.$‎

From the Departments of Neurology and Pathology, Cornell University Medical College, New York, N. 1. Supported in part by Research Grants HE-04872 and NB-03346, NB-04161 from USPHS and from the Winthrop Laboratories. Dr. Kutt is a recipient of a Research Career Development Award JKO 3 NB 35003, NINDB, USPH. First submitted October 2, 1968; accepted for publication December 13, 1968. KARL VEREBE...

From the Departments of Neurology and Pathology, Cornell University Medical College, New York, N. 1. Supported in part by Research Grants HE-04872 and NB-03346, NB-04161 from USPHS and from the Winthrop Laboratories. Dr. Kutt is a recipient of a Research Career Development Award JKO 3 NB 35003, NINDB, USPH. First submitted October 2, 1968; accepted for publication December 13, 1968. KARL VEREBE...

Throughout this work we deal with a natural number g ≥ 2 and with an algebraically closed field k whose characteristic differs from 2. A hyperelliptic curve of genus g over k is a smooth curve of genus g, that is a double cover of the projective line P. The Riemann-Hurwitz formula implies that this covering should be ramified at 2g + 2 points. Because of this explicit description, hyperelliptic...

In this article we apply signal detection theory to qualitatively unify the intensity justnoticable difference (JND) and masking data of Wegel and Lane (1924), Fletcher and Munson (1933 – 1938), Miller (1947), and Egan and Hake (1950). We do this by treating the loudness as the first moment, and the intensity JND as the second moment, of the random variable we call the single-trial loudness. Fr...

This paper aims to figure out difference of our impressions on curves that are used in shape designs, and also contribute industrial designers by implementing a smart computer aided design (CAD) systems which have as same feelings on curves as human designer’s. The proposed K-Vector is a mathematical form of classifying such curves by designer’s impressions.