Rectifying control polygon for planar Pythagorean hodograph curves

2017 ◽  
Vol 54 ◽  
pp. 1-14 ◽  
Author(s):  
Soo Hyun Kim ◽  
Hwan Pyo Moon
Keyword(s):  
Control Polygon ◽  
Pythagorean Hodograph

A New Method to Design Cubic Pythagorean-Hodograph Spline Curves with Control Polygon

2018 ◽  
Vol 7 (3) ◽  
pp. 363-381
Author(s):  
Hongmei Kang ◽  
Xin Li
Keyword(s):  
New Method ◽  
Control Polygon ◽  
Spline Curves ◽  
Pythagorean Hodograph

Interpolation of Hermite data by clamped Minkowski Pythagorean hodograph B-spline curves

2021 ◽  
pp. 113469
Author(s):  
Michal Bizzarri ◽  
Miroslav Lávička
Keyword(s):  
B Spline ◽  
Spline Curves ◽  
Pythagorean Hodograph

Geometric Hermite interpolation by spatial Pythagorean-hodograph cubics

2005 ◽  
Vol 22 (4) ◽  
pp. 325-352 ◽  
Author(s):  
Francesca Pelosi ◽  
Rida T. Farouki ◽  
Carla Manni ◽  
Alessandra Sestini
Keyword(s):  
Hermite Interpolation ◽  
Pythagorean Hodograph ◽  
Geometric Hermite Interpolation

Path Planning of Multiple UAV’s in an Environment of Restricted Regions

2005 ◽  
Author(s):  
Madhavan Shanmugavel ◽  
Antonios Tsourdos ◽  
Rafal Zbikowski ◽  
Brian White
Keyword(s):  
Path Planning ◽  
Path Length ◽  
Mathematical Property ◽  
Multiple Uavs ◽  
Safety Margins ◽  
Pythagorean Hodograph ◽  
Offset Curves ◽  
Safety Constraints ◽  
Continuous Curvature ◽  
Ph Curve

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 margins around and along each flight path. The simultaneous arrival is satisfied by generation of paths of equal lengths. This paper highlights the mathematical property — changing path-shape and path-length by manipulating the curvature and utilises this to achieve the following constraints: (i) Generation of paths of equal length, (ii) Achieving maximum bound on curvature, and, (iii) Meeting the safety constraints by offset paths.

scholarly journals Tensor-product surface patches with Pythagorean-hodograph isoparametric curves

2015 ◽  
Vol 36 (3) ◽  
pp. 1389-1409 ◽  
Author(s):  
Rida T. Farouki ◽  
Francesca Pelosi ◽  
Maria Lucia Sampoli ◽  
Alessandra Sestini
Keyword(s):  
Tensor Product ◽  
Surface Patches ◽  
Pythagorean Hodograph ◽  
Product Surface ◽  
Tensor Product Surface

scholarly journals Arc lengths of rational Pythagorean–hodograph curves

2015 ◽  
Vol 34 ◽  
pp. 1-4 ◽  
Author(s):  
Rida T. Farouki
Keyword(s):  
Pythagorean Hodograph ◽  
Arc Lengths

Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable

2008 ◽  
Author(s):  
Rida T. Farouki
Keyword(s):  
Pythagorean Hodograph

Design of C 2 Spatial Pythagorean-Hodograph Quintic Spline Curves by Control Polygons

2012 ◽  
pp. 253-269 ◽  
Author(s):  
Rida T. Farouki ◽  
Carla Manni ◽  
Francesca Pelosi ◽  
Maria Lucia Sampoli
Keyword(s):  
Quintic Spline ◽  
Spline Curves ◽  
Pythagorean Hodograph

A solution to simultaneous arrival of multiple UAVs using Pythagorean hodograph curves

2006 ◽  
Author(s):  
M. Shanmugavel ◽  
A. Tsourdos ◽  
R. Zbikowski ◽  
B.A. White ◽  
C.A. Rabbath ◽  
...  
Keyword(s):  
Multiple Uavs ◽  
Pythagorean Hodograph
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