Freeform rational parametric curves and surfaces have been playing a major role in computer aided design for several decades. The ability to analyze local (differential) properties of parametric curves is well established and extensively exploited. In this work, we explore a different lifting approach to global analysis of freeform geometry, mostly curves, in IR and IR. In this lifting scheme, ...

the economic growth and development programs in iran call for particular attention for environmental quality control and protection through designing proper sewage treatment and disposal. to design such system, 'the frequency analysis of rainfall is required for the estimation of quantities of flows. there are few places in iran, with adequate rainfall data to permit frequency analysis, an...

The Pythagorean hodograph (PH) curves are polynomial parametric curves whose hodograph (derivative) components satisfy the Pythagorean condition. Lots of research works had been done with PH curves relevant topics due that PH curves own many remarkable properties, e.g., its offset curves have exact rational representations. In this paper, ball curves with rational polynomial offset are studied....

Recently, Wang et al. [1] proposed a new method for constructing pairingfriendly elliptic curves of embedding degree 1. Authors claim that this method significantly improves the efficiency of generating elliptic curves. In this paper, we give the arithmetic of pairing-friendly elliptic curves of embedding degree 1. We prove that conventional classification of pairings into Type 1, 2, 3 and 4 is...

This paper presents the design and develops of voltage acceptability curves for LED lamps. It is done with the mathematical representation of DC bus voltage of LED lamps internal ballast circuit during voltage sags. First, experimental analysis was done to determine the effect of voltage sag of LED lamp. From the findings on the variation of DC bus voltage during voltage sag, a mathematical equ...

Lastly, I wish to illustrate and to stress the necessity of assessing goodness of fit by making use of several tests and not relying on only one or two such tests. Referring to Table 1, the xz test and the Runs test indicate that model 3 is a good fit, whereas the curved Rankits plot, the slow convergence, the non-linearity at the minimum sum of squares and the wide range of the coefficients of...

Design by optimization of curves and surfaces is a powerful design technique. The mathematical modeling of the design problem often results in a multi-objective optimization (MOO) problem which cannot be handled as such by traditional single objective optimization algorithms. Hence an evolutionary MOO algorithm is used to handle this case. The use of MOO algorithm enhances the design process by...

Abstract The aim of this paper is to investigate curve or surface design and modeling with geometric constraint by subdivision scheme. To construct a curve with a given length, constraint is employed on the free parameter of a newly proposed 4-point approximating subdivision scheme. Feasibility to this problem is investigated, convergence and smoothness analysis are presented, and more properti...

This paper presents an interactive framework for the design of truss structures with incorporation of the subjective influence of user feedback in the design process. In the devised framework, the truss chords are described using Non-Uniform Rational Basis Splines (NURBS), a representation typically used in computer aided design (CAD) for describing free-form geometry. This allows for a conveni...

A knowledge of rainfall distribution over a finite area is needed for small bydraulic structures design. Hydrologists have always been concerned about Depth- Area- Duration (DAD) for a specific storm in a watershed. An intense storm occurred on June 6, 1992 which claimed some lives in parts of Mashhad, Khorasan Province, Iran. Data of rainfall depth at 29 raingauge stations around the city and ...