On curves defined by generalised cubic blending functions |
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| Affiliation: | 1. Centre de Recherche des Cordeliers, Equipe labellisée par la Ligue Contre le Cancer, Université de Paris, Sorbonne Université, INSERM U1138, Institut Universitaire de France, Paris, France;2. Metabolomics and Cell Biology Platforms, Institut Gustave Roussy, Villejuif, France;3. Departamento de Bioquímica y Biología Molecular, Facultad de Medicina, Instituto Universitario de Oncología del Principado de Asturias (IUOPA), Universidad de Oviedo, 33006, Oviedo, Spain;4. Université de Paris, BFA, UMR 8251, CNRS, F-75013 Paris, France;5. Unité de Biologie Fonctionnelle et Adaptative, Sorbonne Paris Cité, CNRS UMR8251, Université Paris Diderot, Paris, France;6. Pôle de Biologie, Hôpital Européen Georges Pompidou, AP-, HP, Paris, France;7. Suzhou Institute for Systems Medicine, Chinese Academy of Medical Sciences, Suzhou, China;8. Karolinska Institute, Department of Women''s and Children''s Health, Karolinska University Hospital, Stockholm, Sweden |
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| Abstract: | As the relationship between the control polygon and the curve specified by generalised cubic blending functions has been defined rather vaguely previously, the present paper proves that the curve is tangent to the middle side of its control polygon only when the blending functions reduce to those of Timmer which are a special case of the former. Otherwise, the curve looses the convex hull property of the Bézier curve formulation and may be discontinuous. |
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