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Subdivision and multiresolution for PUPs.

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Title: Subdivision and multiresolution for PUPs.
Authors: Moltaji, Amirhessam1, Runions, Adam2, Samavati, Faramarz F.1
Source: Computers & Graphics. Feb2017, Vol. 62, p53-66. 14p.
Subjects: Subdivision surfaces (Geometry), Partition of unity method, Radial basis functions, Parametric equations, Tensor products
Abstract: Partition of Unity Parametrics (PUPs) is a generalization of NURBS that permits the use of arbitrary basis functions to model parametric curves and surfaces. An interesting problem for PUPs is the identification of subdivision, reverse subdivision, and multiresolution schemes for this recently developed and flexible class of parametric curves and surfaces. In this paper, we introduce a systematic approach to derive uniform subdivision schemes for PUPs curves and tensor-product surfaces. Our approach formulates PUPs subdivision as a least squares problem. This allows us to find exact subdivision filters for refinable basis functions and optimal approximate schemes for irrefinable ones. Additionally, we derive PUPs multiresolution masks based on their subdivision filters. We formulate the problem as a constrained least squares optimization, such that the resulting multiresolution schemes are banded and optimal in terms of minimizing multiresolution reconstruction error. Finally, to illustrate our methods, we provide sample subdivision and multiresolution schemes with different properties. These include specific examples targeted towards applications of PUPs multiresolution schemes for compression, feature transfer, and macroscopic editing. [ABSTRACT FROM AUTHOR]
Copyright of Computers & Graphics is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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PubType: Academic Journal
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  Data: <searchLink fieldCode="DE" term="%22Subdivision+surfaces+%28Geometry%29%22">Subdivision surfaces (Geometry)</searchLink><br /><searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Radial+basis+functions%22">Radial basis functions</searchLink><br /><searchLink fieldCode="DE" term="%22Parametric+equations%22">Parametric equations</searchLink><br /><searchLink fieldCode="DE" term="%22Tensor+products%22">Tensor products</searchLink>
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  Data: Partition of Unity Parametrics (PUPs) is a generalization of NURBS that permits the use of arbitrary basis functions to model parametric curves and surfaces. An interesting problem for PUPs is the identification of subdivision, reverse subdivision, and multiresolution schemes for this recently developed and flexible class of parametric curves and surfaces. In this paper, we introduce a systematic approach to derive uniform subdivision schemes for PUPs curves and tensor-product surfaces. Our approach formulates PUPs subdivision as a least squares problem. This allows us to find exact subdivision filters for refinable basis functions and optimal approximate schemes for irrefinable ones. Additionally, we derive PUPs multiresolution masks based on their subdivision filters. We formulate the problem as a constrained least squares optimization, such that the resulting multiresolution schemes are banded and optimal in terms of minimizing multiresolution reconstruction error. Finally, to illustrate our methods, we provide sample subdivision and multiresolution schemes with different properties. These include specific examples targeted towards applications of PUPs multiresolution schemes for compression, feature transfer, and macroscopic editing. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computers & Graphics is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.cag.2016.12.001
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 53
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      – SubjectFull: Subdivision surfaces (Geometry)
        Type: general
      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Radial basis functions
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      – SubjectFull: Parametric equations
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      – SubjectFull: Tensor products
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      – TitleFull: Subdivision and multiresolution for PUPs.
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              Text: Feb2017
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              Y: 2017
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