View in EDS

Partition of unity parametrics: a framework for meta-modeling.

Saved in:
Bibliographic Details
Title: Partition of unity parametrics: a framework for meta-modeling.
Authors: Runions, Adam1 runionsa@cpsc.ucalgary.ca, Samavati, Faramarz1
Source: Visual Computer. Jun2011, Vol. 27 Issue 6-8, p495-505. 11p.
Subjects: Partition of unity method, Arbitrary constants, Geometry, Curves, Geometric surfaces
Abstract: We propose Partition of Unity Parametrics (PUPs), a natural extension of NURBS that maintains affine invariance. PUPs replace the weighted basis functions of NURBS with arbitrary weight-functions (WFs). By choosing appropriate WFs, PUPs yield a comprehensive geometric modeling framework, accounting for a variety of beneficial properties, such as local support, specified smoothness, arbitrary sharp features and approximating or interpolating curves. Additionally, we consider interactive specification of WFs to fine-tune the character of curves and generate non-trivial effects. This serves as a basis for a system where users model the tools used for modeling, here weight-functions, in tandem with the model itself, which we dub a meta-modeling system. PUP curves and surfaces are considered in detail. Curves illustrate basic concepts that apply directly to surfaces. For surfaces, the advantages of PUPs are more pronounced; permitting non-tensor WFs and direct parameter space manipulations. These features allow us to address two difficult geometric modeling problems (sketching features onto surfaces and converting planar meshes into parametric surfaces) in a conceptually and computationally simple way. [ABSTRACT FROM AUTHOR]
Copyright of Visual Computer is the property of Springer Nature 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
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 60672781
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Partition of unity parametrics: a framework for meta-modeling.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Runions%2C+Adam%22">Runions, Adam</searchLink><relatesTo>1</relatesTo><i> runionsa@cpsc.ucalgary.ca</i><br /><searchLink fieldCode="AR" term="%22Samavati%2C+Faramarz%22">Samavati, Faramarz</searchLink><relatesTo>1</relatesTo>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Visual+Computer%22">Visual Computer</searchLink>. Jun2011, Vol. 27 Issue 6-8, p495-505. 11p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Arbitrary+constants%22">Arbitrary constants</searchLink><br /><searchLink fieldCode="DE" term="%22Geometry%22">Geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Curves%22">Curves</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+surfaces%22">Geometric surfaces</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: We propose Partition of Unity Parametrics (PUPs), a natural extension of NURBS that maintains affine invariance. PUPs replace the weighted basis functions of NURBS with arbitrary weight-functions (WFs). By choosing appropriate WFs, PUPs yield a comprehensive geometric modeling framework, accounting for a variety of beneficial properties, such as local support, specified smoothness, arbitrary sharp features and approximating or interpolating curves. Additionally, we consider interactive specification of WFs to fine-tune the character of curves and generate non-trivial effects. This serves as a basis for a system where users model the tools used for modeling, here weight-functions, in tandem with the model itself, which we dub a meta-modeling system. PUP curves and surfaces are considered in detail. Curves illustrate basic concepts that apply directly to surfaces. For surfaces, the advantages of PUPs are more pronounced; permitting non-tensor WFs and direct parameter space manipulations. These features allow us to address two difficult geometric modeling problems (sketching features onto surfaces and converting planar meshes into parametric surfaces) in a conceptually and computationally simple way. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Visual Computer is the property of Springer Nature 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.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=60672781
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s00371-011-0567-x
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 11
        StartPage: 495
    Subjects:
      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Arbitrary constants
        Type: general
      – SubjectFull: Geometry
        Type: general
      – SubjectFull: Curves
        Type: general
      – SubjectFull: Geometric surfaces
        Type: general
    Titles:
      – TitleFull: Partition of unity parametrics: a framework for meta-modeling.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Runions, Adam
      – PersonEntity:
          Name:
            NameFull: Samavati, Faramarz
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 06
              Text: Jun2011
              Type: published
              Y: 2011
          Identifiers:
            – Type: issn-print
              Value: 01782789
          Numbering:
            – Type: volume
              Value: 27
            – Type: issue
              Value: 6-8
          Titles:
            – TitleFull: Visual Computer
              Type: main
ResultId 1