scholarly journals C2 interpolation of spatial data subject to arc-length constraints using Pythagorean–hodograph quintic splines

2014 ◽  
Vol 76 (1) ◽  
pp. 30-42 ◽  
Author(s):  
Mathieu Huard ◽  
Rida T. Farouki ◽  
Nathalie Sprynski ◽  
Luc Biard
2021 ◽  
Vol 391 ◽  
pp. 125653
Author(s):  
Rida T. Farouki ◽  
Marjeta Knez ◽  
Vito Vitrih ◽  
Emil Žagar

Author(s):  
Rida T Farouki ◽  
Carlotta Giannelli ◽  
Duccio Mugnaini ◽  
Alessandra Sestini

Pythagorean-hodograph (PH) curves offer distinct advantages in planning curvilinear paths for unmanned or autonomous air, ground, or underwater vehicles. Although several authors have discussed their use in these contexts, prior studies contain misconceptions about the properties of PH curves or invoke heuristic approximate constructions when exact methods are available. To address these issues, the present study provides a basic introduction to the key properties of PH curves, and describes some exact constructions of particular interest in path planning. These include (a) maintenance of minimum safe separations within vehicle swarms; (b) construction of paths of different shape but identical arc length, ensuring simultaneous arrival of vehicles travelling at a constant speed; (c) determination of the curvature extrema of PH paths, and their modification to satisfy a given curvature bound; and (d) construction of curvature-continuous paths of bounded curvature through fields of polygonal obstacles.


1997 ◽  
Author(s):  
J. Farley Norman ◽  
Joseph S. Lappin ◽  
Hideko F. Norman

2020 ◽  
pp. 26-32
Author(s):  
M. I. Kalinin ◽  
L. K. Isaev ◽  
F. V. Bulygin

The situation that has developed in the International System of Units (SI) as a result of adopting the recommendation of the International Committee of Weights and Measures (CIPM) in 1980, which proposed to consider plane and solid angles as dimensionless derived quantities, is analyzed. It is shown that the basis for such a solution was a misunderstanding of the mathematical formula relating the arc length of a circle with its radius and corresponding central angle, as well as of the expansions of trigonometric functions in series. From the analysis presented in the article, it follows that a plane angle does not depend on any of the SI quantities and should be assigned to the base quantities, and its unit, the radian, should be added to the base SI units. A solid angle, in this case, turns out to be a derived quantity of a plane angle. Its unit, the steradian, is a coherent derived unit equal to the square radian.


2020 ◽  
Vol 5 (1) ◽  
pp. 414
Author(s):  
Amsar Yunan

Maps or remote sensing can be interpreted as the process of reading using various sensors where data collected remotely can be analyzed to obtain information about the object, area or phenomenon. In this study, the author develops a flood disaster mapping information system applying overlays with scoring between the parameters. The determinant factors to provide flood hazard levels includes rainfall factors in the dasarian unit, land-use factors and land-use arbitrary factors. Of all these parameters, a scoring process will be carried out by assigning weights and values according to their respective classifications, then an overlay process will be performed using ArcGIS software. The author conducted this study in Nagan Raya Regency since this area experiences flooding annually.  Framing a thematic map of flood-prone areas in Nagan Raya Regency was designed using the flood hazard method. Spatial data that has been presented in the form of thematic maps as parameters are land use maps, landform maps, and dasarian rainfall maps (per 10 daily). The design of thematic maps that are prone to flooding is done by overlapping (overlay process). In contrast, the determination of the classification is done by adding scores to each parameter, with low, medium and high hazard levels. Parameter analysis shows the level of flood vulnerability in Nagan Raya Regency of each district, namely Beutong: high 0.21%, medium 13.68%, low 86.12%. Seunagan District: high 51.17%, medium 48.83%, low 0%. Seunagan Timur District: high 10.07%, medium 46.18%, low 43.75%. Kuala Subdistrict: high 29.66%, medium 68.99%, low 1.35%. Darul Makmur District: high 8.57%, medium 63.37%, low 28.06%. From the overall results of the study, it can be concluded that the danger of flooding in Nagan Raya Regency with a level of vulnerability: high 9.92%, moderate 42.65% and low 47.43%.


Sign in / Sign up

Export Citation Format

Share Document