, A General Hybrid Optimisation Strategy for Curve Fitting in the NURBS Framework

, Mathematical Formulation of the Curve Fitting Problem, p.263

.. .. Numerical-strategy,

, Studied Cases and Results for curve fitting

. .. Nurbs-framework,

, Conclusions and Perspectives on Approximation Problems, p.285

, Introductionà la Reconstruction de Courbes et Surfaces, p.291

N. .. Le-cadre, 293 7.2.1 L'´ enoncé mathématique duprobì eme de Fitting de Courbes, Une stratégie d'Optimisation Hybride Générale pour le Fitting des Courbes dans, p.295

, Conclusions sur lesProbì emes d'Approximation

, le but du calcul génétique est de fournir un point potentiel sous-optimal dans l'espace de conception, qui constitue la premì ere estimation pour la phase suivante, c'est-` a-dire l'optimisation locale, En raison de la forte non-linéarité duprobì eme (7.19)

, En particulier, le nombre maximal de points de contrôle doitêtredoitêtre inférieur au nombre de points cibles, tandis que le minimum doit toujoursêtretoujoursêtre supérieur oú egaì

, Enfin, la gestion des points cible est une opération qui doitêtredoitêtre soigneusementévaluéesoigneusementévaluée

, 25), o` u le même formalisme de l'´ eq. (7.1) est utilisé. Dans le cas de l'´ eq. (7.25), le vecteur ? recueille toutes les variables d'optimisation, c'est-` a-dire tous ou partie des paramètres (de nature différente) définissant la forme de la surface NURBS, De même que pour leprobì eme d'approximation de courbes, leprobì eme de fitting de surfaces peutêtrepeutêtre exprimé comme indiqué dans l'´ eq

, Afin de mettre enévidenceenévidence les effets de la secondé etape dans l'algorithme d'optimisation, des résultats numériques ontétéontété collectés dans le Tableau 7.8 et la fonction objectifàobjectif`objectifà la fin de lapremì eré etape d'optimisation (f obj?A ) est comparécomparéà celui résultant du second

, Comme il peutêtrepeutêtre facilement remarqué par les résultats numériques, l'effet des poids sélection des exigences nécessitant une formulation de contraintes et celles pouvantêtre pouvantêtre traitées a priori, en définissant correctement certains paramètres d'optimisation ou en modifiant

, Comme cela a ´ eté fait pour l'´ epaisseur minimale dans le chapitre 5, les contraintes d'optimisation doiventêtredoiventêtre développées en considérant directement les paramètres NURBS : de cettemanì ere seulement, ces quantités peuvent avoir une signification physique et, D'après les considérations précédentes, il estévidentestévident que l'impact des paramètres intervenant dans l'OT doitêtredoitêtre clarifié

, De plus, l'efficacité de l'algorithme présenté doitêtredoitêtre améliorée enélargissantenélargissant la bibliothèque de grandeurs mécaniques. En particulier, dans ce manuscrit

, Une fois que les aspects susmentionnés seront traités et que l'efficacité de l'approche basée sur les NURBS sera définitivement prouvée, desprobì emes plus complexes pourrontêtre pourrontêtre résolus. Par exemple, lesprobì emes multi-physiques et multi-´ echelles peuventêtrepeuventêtre The optimised Knot Vector, 1904.

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