The Curvature of Digital Illustration: Spline Curves

2015 ◽  
pp. 11-24
Author(s):  
Wallace Jackson
Keyword(s):  
Spline Curves

scholarly journals Chaotic Path Planning for 3D Area Coverage Using a Pseudo-Random Bit Generator from a 1D Chaotic Map

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1821
Author(s):  
Lazaros Moysis ◽  
Karthikeyan Rajagopal ◽  
Aleksandra V. Tutueva ◽  
Christos Volos ◽  
Beteley Teka ◽  
...  
Keyword(s):  
Path Planning ◽  
Chaotic Map ◽  
Dynamical Behavior ◽  
Area Coverage ◽  
Phase Portraits ◽  
Planning Strategy ◽  
Spline Curves ◽  
Key Space ◽  
Aerial Vehicle ◽  
Discrete Motion

This work proposes a one-dimensional chaotic map with a simple structure and three parameters. The phase portraits, bifurcation diagrams, and Lyapunov exponent diagrams are first plotted to study the dynamical behavior of the map. It is seen that the map exhibits areas of constant chaos with respect to all parameters. This map is then applied to the problem of pseudo-random bit generation using a simple technique to generate four bits per iteration. It is shown that the algorithm passes all statistical NIST and ENT tests, as well as shows low correlation and an acceptable key space. The generated bitstream is applied to the problem of chaotic path planning, for an autonomous robot or generally an unmanned aerial vehicle (UAV) exploring a given 3D area. The aim is to ensure efficient area coverage, while also maintaining an unpredictable motion. Numerical simulations were performed to evaluate the performance of the path planning strategy, and it is shown that the coverage percentage converges exponentially to 100% as the number of iterations increases. The discrete motion is also adapted to a smooth one through the use of B-Spline curves.

On parametric smoothness of generalised B-spline curves

2006 ◽  
Vol 23 (8) ◽  
pp. 655-668 ◽  
Author(s):  
Tomasz Popiel
Keyword(s):  
B Spline ◽  
Spline Curves

scholarly journals Conditions for regular $B$-spline curves and surfaces

1992 ◽  
Vol 26 (1) ◽  
pp. 177-190 ◽  
Author(s):  
N. Dyn ◽  
D. Levin ◽  
I. Yad-Shalom
Keyword(s):  
B Spline ◽  
Curves And Surfaces ◽  
Spline Curves
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