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Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature

We propose a method for the construction of a planar curve based on piecewise clothoids and straight lines that intuitively interpolates a given sequence of control points. Our method has several desirable properties that are not simultaneously fulfilled by previous approaches: Our interpolating cur...

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Detalles Bibliográficos
Autores principales: Binninger, Alexandre, Sorkine‐Hornung, Olga
Formato: Online Artículo Texto
Lenguaje:English
Publicado: John Wiley and Sons Inc. 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9827861/
https://www.ncbi.nlm.nih.gov/pubmed/36636107
http://dx.doi.org/10.1111/cgf.14600
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author Binninger, Alexandre
Sorkine‐Hornung, Olga
author_facet Binninger, Alexandre
Sorkine‐Hornung, Olga
author_sort Binninger, Alexandre
collection PubMed
description We propose a method for the construction of a planar curve based on piecewise clothoids and straight lines that intuitively interpolates a given sequence of control points. Our method has several desirable properties that are not simultaneously fulfilled by previous approaches: Our interpolating curves are C(2) continuous, their computation does not rely on global optimization and has local support, enabling fast evaluation for interactive modeling. Further, the sign of the curvature at control points is consistent with the control polygon; the curvature attains its extrema at control points and is monotone between consecutive control points of opposite curvature signs. In addition, we can ensure that the curve has self‐intersections only when the control polygon also self‐intersects between the same control points. For more fine‐grained control, the user can specify the desired curvature and tangent values at certain control points, though it is not required by our method. Our local optimization can lead to discontinuity w.r.t. the locations of control points, although the problem is limited by its locality. We demonstrate the utility of our approach in generating various curves and provide a comparison with the state of the art.
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spelling pubmed-98278612023-01-10 Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature Binninger, Alexandre Sorkine‐Hornung, Olga Comput Graph Forum Curves and Features We propose a method for the construction of a planar curve based on piecewise clothoids and straight lines that intuitively interpolates a given sequence of control points. Our method has several desirable properties that are not simultaneously fulfilled by previous approaches: Our interpolating curves are C(2) continuous, their computation does not rely on global optimization and has local support, enabling fast evaluation for interactive modeling. Further, the sign of the curvature at control points is consistent with the control polygon; the curvature attains its extrema at control points and is monotone between consecutive control points of opposite curvature signs. In addition, we can ensure that the curve has self‐intersections only when the control polygon also self‐intersects between the same control points. For more fine‐grained control, the user can specify the desired curvature and tangent values at certain control points, though it is not required by our method. Our local optimization can lead to discontinuity w.r.t. the locations of control points, although the problem is limited by its locality. We demonstrate the utility of our approach in generating various curves and provide a comparison with the state of the art. John Wiley and Sons Inc. 2022-10-06 2022-08 /pmc/articles/PMC9827861/ /pubmed/36636107 http://dx.doi.org/10.1111/cgf.14600 Text en © 2022 The Author(s) Computer Graphics Forum © 2022 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd. https://creativecommons.org/licenses/by/4.0/This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
spellingShingle Curves and Features
Binninger, Alexandre
Sorkine‐Hornung, Olga
Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title_full Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title_fullStr Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title_full_unstemmed Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title_short Smooth Interpolating Curves with Local Control and Monotone Alternating Curvature
title_sort smooth interpolating curves with local control and monotone alternating curvature
topic Curves and Features
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9827861/
https://www.ncbi.nlm.nih.gov/pubmed/36636107
http://dx.doi.org/10.1111/cgf.14600
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