This paper describes a novel idea of path planning for multiple UAVs (Unmanned Aerial Vehicles). The path planning ensures safe and simultaneous arrival of the UAVs to the target while meeting curvature and safety constraints. Pythagorean Hodograph (PH) curve is used for path planning. The PH curve provides continuous curvature of the paths. The offset curves of the PH paths define safety margi...

Abstract—Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being...

The present study aimed to characterize the effect of a nearby distractor on vertical, horizontal, and oblique saccade curvature under normal saccade preparation times. Consistent with previous findings, longer-latency vertical saccades showed greater curvature away from a distractor than did oblique or horizontal saccades. At short latencies, vertical saccades also showed greater curvature tow...

This paper explores the possibilities of very simple analysis on derivation of spiral regions for a single segment of cubic function matching positional, tangential, and curvature end conditions. Spirals are curves of monotone curvature with constant sign and have the potential advantage that the minimum and maximum curvature exists at their end points. Therefore, spirals are free from singular...

In this paper, we study the Ricci flow on higher dimensional compact manifolds. We prove that nonnegative isotropic curvature is preserved by the Ricci flow in dimensions greater than or equal to four. In order to do so, we introduce a new technique to prove that curvature functions defined on the orthonormal frame bundle are preserved by the Ricci flow. At a minimum of such a function, we comp...

Wetting, meniscus structure, and capillary interactions for polystyrene microspheres deposited on constant curvature cylindrical liquid interfaces, constructed from nonvolatile ionic or oligomeric liquids, were studied by optical interferometry and optical microscopy. The liquid interface curvature resulted from the preferential wetting of finite width lines patterned onto planar silicon substr...

We aimed to establish standards for tobacco Valor de Cultivo e Uso (VCU) in Brazil. We obtained information regarding the size and design of plots of two varietal groups of tobacco (Virginia and Burley). Ten inbred lines of each varietal group were evaluated in a randomized complete block design with four replications. The plot contained 42 plants with six rows of seven columns each. For each e...

Cyclic fatigue of nickel-titanium, engine-driven instruments was studied by determining the effect of canal curvature and operating speed on the breakage of Lightspeed instruments. A new method of canal curvature evaluation that addressed both angle and abruptness of curvature was introduced. Canal curvature was simulated by constructing six curved stainless-steel guide tubes with angles of cur...

Li and Zaidi (Li, A., and Zaidi, Q. (2000) Vision Research, 40, 217-242) showed that the veridical perception of the 3-dimensional (3D) shape of a corrugated surface from texture cues is entirely dependent on the visibility of critical patterns of oriented energy. These patterns are created by perspective projection of surface markings oriented along lines of maximum 3D curvature. In images mis...

Given the diversity of vertebral morphologies among fishes, it is tempting to propose causal links between axial morphology and body curvature. We propose that shape and size of the vertebrae, intervertebral joints, and the body will more accurately predict differences in body curvature during swimming rather than a single meristic such as total vertebral number alone. We examined the correlati...