Combining distance-based formation shape control with formation translation

2012 ◽  
pp. 121-130 ◽  
Author(s):  
Brian Anderson ◽  
Zhiyun Lin ◽  
Mohammad Deghat
Keyword(s):  
Shape Control

Constrained plasma shape control in ITER

2009 ◽  
Author(s):  
Massimiliano Mattei ◽  
Domenico Famularo ◽  
Carmelo Vincenzo Labate
Keyword(s):  
Shape Control

scholarly journals Seeded Growth of HgTe Nanocrystals for Shape Control and Their Use in Narrow Infrared Electroluminescence

2021 ◽  
Vol 33 (6) ◽  
pp. 2054-2061
Author(s):  
Yoann Prado ◽  
Junling Qu ◽  
Charlie Gréboval ◽  
Corentin Dabard ◽  
Prachi Rastogi ◽  
...  
Keyword(s):  
Shape Control ◽  
Seeded Growth

scholarly journals On the BIC for determining the number of control points in B-spline surface approximation in case of correlated observations

2020 ◽  
Vol 10 (1) ◽  
pp. 110-123
Author(s):  
Gaël Kermarrec ◽  
Hamza Alkhatib
Keyword(s):  
Shape Control ◽  
Simple Procedure ◽  
Spline Approximation ◽  
Autoregressive Process ◽  
Optimal Number ◽  
Information Criteria ◽  
General Effect ◽  
Control Points ◽  
B Spline ◽  
Correlated Observations

Abstract B-spline curves are a linear combination of control points (CP) and B-spline basis functions. They satisfy the strong convex hull property and have a fine and local shape control as changing one CP affects the curve locally, whereas the total number of CP has a more general effect on the control polygon of the spline. Information criteria (IC), such as Akaike IC (AIC) and Bayesian IC (BIC), provide a way to determine an optimal number of CP so that the B-spline approximation fits optimally in a least-squares (LS) sense with scattered and noisy observations. These criteria are based on the log-likelihood of the models and assume often that the error term is independent and identically distributed. This assumption is strong and accounts neither for heteroscedasticity nor for correlations. Thus, such effects have to be considered to avoid under-or overfitting of the observations in the LS adjustment, i.e. bad approximation or noise approximation, respectively. In this contribution, we introduce generalized versions of the BIC derived using the concept of quasi- likelihood estimator (QLE). Our own extensions of the generalized BIC criteria account (i) explicitly for model misspecifications and complexity (ii) and additionally for the correlations of the residuals. To that aim, the correlation model of the residuals is assumed to correspond to a first order autoregressive process AR(1). We apply our general derivations to the specific case of B-spline approximations of curves and surfaces, and couple the information given by the different IC together. Consecutively, a didactical yet simple procedure to interpret the results given by the IC is provided in order to identify an optimal number of parameters to estimate in case of correlated observations. A concrete case study using observations from a bridge scanned with a Terrestrial Laser Scanner (TLS) highlights the proposed procedure.

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