When designers begin a product design, they create their ideas and expand them. This process is performed on paper, and designers’ hand-drawn lines are called sketches. If the designers’ hand-drawn sketches can be realized as real curves, it would be effective in shortening the design period. We have developed a method to extract five degree Bézier curves based on a hand-drawn sketch. The basic...

various scaling methods such as relative viscosity, peclet and reynolds scaling were used to find the best scaling law. scaling and modeling of the flow curves of various model emulsions consist of tragacanth gum (tg) (0.5, 1 % wt), oleic acid (5, 10% v/v) and wpi (2, 4 % wt) were investigated and the best models were selected. as these emulsions are non-newtonian, they do not obey the usual, si...

The vibration criterion (VC) curves, commonly used in the design of facilities which house vibration-sensitive instruments and tools, were developed by the author and his colleagues, in the early 80’s, published by SPIE in 1991 and by IEST in 1993. Each of the criterion curves A through E is associated with a “line width” or “detail size” which was an attempt by the authors to describe the capa...

The efficient support of cryptographic protocols based on elliptic curves is crucial when embedded processors are adopted as the target hardware platforms. The implementation of Elliptic Curve Cryptography (ECC) offers a variety of design options, mostly covering the specific family of curves and the related coordinate system. At the same time, theory shows that a limited set of solutions can a...

We discuss the following problem which arises in robot motion planning, NC machining and computer animation: Given are a fixed surface Ψ and N positions Φi of a moving surface Φ such that the Φi are in point contact with Ψ. Compute a smooth and fair Euclidean gliding motion Φ(t) of the surface Φ on the surface Ψ which interpolates (or approximates) the given positions Φi at time instances ti. F...

‎In the present study‎, ‎we consider a regular curve in Galilean‎ ‎$4$-space $mathbb{G}_{4}$ whose position vector is written as a‎ ‎linear combination of its Frenet vectors‎. ‎We characterize such‎ ‎curves in terms of their curvature functions‎. ‎Further‎, ‎we obtain‎ ‎some results of rectifying‎, ‎constant ratio‎, ‎$T$-constant and‎ ‎$N$-constant curves in $mathbb{G}_{4}$‎.

Extreme climatic events are growing more severe and frequent, calling into question how prepared our infrastructure is to deal with these changes. Current infrastructure design is primarily based on precipitation Intensity-Duration-Frequency (IDF) curves with the so-called stationary assumption, meaning extremes will not vary significantly over time. However, climate change is expected to alter...

Hydrologic Engineering, April __________________________________________________________________________________ DESIGN RAINFALL CURVE James C.Y. Guo, Professor, Civil Engineering, U. of Colorado at Denver. __________________________________________________________________________ Abstract To design urban storm water infrastructures, hydrologists apply the SCS Type I and II 24-hr rainfall distr...