Barendrecht, Pieter

Splines are piecewise polynomial, rational or trigonometric functions that are ubiquitous in a wide variety of areas. Popular applications include function approximation as well as parametric curves and surfaces. In this dissertation, we study them from the perspective of both numerical methods and computer graphics. A pragmatic and richly illustrated approach is used to explain the different subject matters.Following a refresher on spline basics, we consider a spline-based subdivision scheme for three-valent meshes (that is, meshes composed of mostly hexagons). This provides us with a good understanding of subdivision surfaces in general, a modelling technique used in animated movies, VFX and computer games. We then move on to study improved quadrature (that is, numerical integration) for the widely used Catmull-Clark subdivision scheme for quad-dominant meshes, something keenly awaited by spline-based numerical methods such as isogeometric analysis (IgA). These methods deal with the numerical simulation of all sorts of physical phenomena, including heat conduction and (elastic) deformation. Finally, we shift our focus to a more artistic use of splines in the context of vector graphics. Here, we propose user-friendly additions such as local refinement for the gradient mesh primitive, facilitating the creation of resolution-independent (almost) photo-realistic illustrations

Proceedings - University of Groningen

   University of GroningenSplines for engineersBarendrecht, PieterDOI:10.33612/diss.102688532IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2019Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Barendrecht, P. (2019). Splines for engineers: with selected applications in numerical methods andcomputer graphics. Rijksuniversiteit Groningen. https://doi.org/10.33612/diss.102688532CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 12-10-2022Propositions accompanying the PhD dissertationSplines for engineersby Pieter Barendrecht1. Although Bézier curves and surfaces form the foundation for manytypes of splines, they are often too elementary to be used directly.— Chapter 22. Watertight surfaces of arbitrary manifold topology are indispens-able for modelling as well as spline-based numerical methods.— Chapters 3 and 43. The patch test for an element should not be considered failed solelybecause of an inefficient quadrature rule.— Chapter 44. Modern OpenGL will, for the foreseeable future, continue to be thegraphics API of choice for a wide range of applications.— Chapter 55. Support fromweb browsers is crucial for both gradient meshes anddiffusion curves to become commonplace.— Chapter 66. Local refinement is an essential feature for both modelling andspline-based numerical methods, not merely an optional one.— Chapters 2, 4 and 67. More interaction and collaboration among academics, program-mers and artists would greatly benefit the field of computer graph-ics.8. Any programme in computer science should include a mandatorycourse on the use, development and licensing of open source soft-ware.

English

Splines for engineers:with selected applications in numerical methods and computer graphics

University of Groningen

Dissertations of the University of Groningen

   University of GroningenSplines for engineersBarendrecht, PieterDOI:10.33612/diss.102688532IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2019Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Barendrecht, P. (2019). Splines for engineers: with selected applications in numerical methods andcomputer graphics. [Thesis fully internal (DIV), University of Groningen]. Rijksuniversiteit Groningen.https://doi.org/10.33612/diss.102688532CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 11-09-2023Propositions accompanying the PhD dissertationSplines for engineersby Pieter Barendrecht1. Although Bézier curves and surfaces form the foundation for manytypes of splines, they are often too elementary to be used directly.— Chapter 22. Watertight surfaces of arbitrary manifold topology are indispens-able for modelling as well as spline-based numerical methods.— Chapters 3 and 43. The patch test for an element should not be considered failed solelybecause of an inefficient quadrature rule.— Chapter 44. Modern OpenGL will, for the foreseeable future, continue to be thegraphics API of choice for a wide range of applications.— Chapter 55. Support fromweb browsers is crucial for both gradient meshes anddiffusion curves to become commonplace.— Chapter 66. Local refinement is an essential feature for both modelling andspline-based numerical methods, not merely an optional one.— Chapters 2, 4 and 67. More interaction and collaboration among academics, program-mers and artists would greatly benefit the field of computer graph-ics.8. Any programme in computer science should include a mandatorycourse on the use, development and licensing of open source soft-ware.

   University of GroningenSplines for engineersBarendrecht, PieterDOI:10.33612/diss.102688532IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2019Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Barendrecht, P. (2019). Splines for engineers: with selected applications in numerical methods andcomputer graphics. [Thesis fully internal (DIV), University of Groningen]. Rijksuniversiteit Groningen.https://doi.org/10.33612/diss.102688532CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 21-01-2023Propositions accompanying the PhD dissertationSplines for engineersby Pieter Barendrecht1. Although Bézier curves and surfaces form the foundation for manytypes of splines, they are often too elementary to be used directly.— Chapter 22. Watertight surfaces of arbitrary manifold topology are indispens-able for modelling as well as spline-based numerical methods.— Chapters 3 and 43. The patch test for an element should not be considered failed solelybecause of an inefficient quadrature rule.— Chapter 44. Modern OpenGL will, for the foreseeable future, continue to be thegraphics API of choice for a wide range of applications.— Chapter 55. Support fromweb browsers is crucial for both gradient meshes anddiffusion curves to become commonplace.— Chapter 66. Local refinement is an essential feature for both modelling andspline-based numerical methods, not merely an optional one.— Chapters 2, 4 and 67. More interaction and collaboration among academics, program-mers and artists would greatly benefit the field of computer graph-ics.8. Any programme in computer science should include a mandatorycourse on the use, development and licensing of open source soft-ware.

   University of GroningenSplines for engineersBarendrecht, PieterDOI:10.33612/diss.102688532IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2019Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Barendrecht, P. (2019). Splines for engineers: with selected applications in numerical methods andcomputer graphics. [Thesis fully internal (DIV), University of Groningen]. Rijksuniversiteit Groningen.https://doi.org/10.33612/diss.102688532CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 29-04-2023Propositions accompanying the PhD dissertationSplines for engineersby Pieter Barendrecht1. Although Bézier curves and surfaces form the foundation for manytypes of splines, they are often too elementary to be used directly.— Chapter 22. Watertight surfaces of arbitrary manifold topology are indispens-able for modelling as well as spline-based numerical methods.— Chapters 3 and 43. The patch test for an element should not be considered failed solelybecause of an inefficient quadrature rule.— Chapter 44. Modern OpenGL will, for the foreseeable future, continue to be thegraphics API of choice for a wide range of applications.— Chapter 55. Support fromweb browsers is crucial for both gradient meshes anddiffusion curves to become commonplace.— Chapter 66. Local refinement is an essential feature for both modelling andspline-based numerical methods, not merely an optional one.— Chapters 2, 4 and 67. More interaction and collaboration among academics, program-mers and artists would greatly benefit the field of computer graph-ics.8. Any programme in computer science should include a mandatorycourse on the use, development and licensing of open source soft-ware.

ARTS repository - University of Groningen

   University of GroningenSplines for engineersBarendrecht, PieterDOI:10.33612/diss.102688532IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2019Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Barendrecht, P. (2019). Splines for engineers: with selected applications in numerical methods andcomputer graphics. [Thesis fully internal (DIV), University of Groningen]. Rijksuniversiteit Groningen.https://doi.org/10.33612/diss.102688532CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 13-02-2023Propositions accompanying the PhD dissertationSplines for engineersby Pieter Barendrecht1. Although Bézier curves and surfaces form the foundation for manytypes of splines, they are often too elementary to be used directly.— Chapter 22. Watertight surfaces of arbitrary manifold topology are indispens-able for modelling as well as spline-based numerical methods.— Chapters 3 and 43. The patch test for an element should not be considered failed solelybecause of an inefficient quadrature rule.— Chapter 44. Modern OpenGL will, for the foreseeable future, continue to be thegraphics API of choice for a wide range of applications.— Chapter 55. Support fromweb browsers is crucial for both gradient meshes anddiffusion curves to become commonplace.— Chapter 66. Local refinement is an essential feature for both modelling andspline-based numerical methods, not merely an optional one.— Chapters 2, 4 and 67. More interaction and collaboration among academics, program-mers and artists would greatly benefit the field of computer graph-ics.8. Any programme in computer science should include a mandatorycourse on the use, development and licensing of open source soft-ware.

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Splines for engineers:with selected applications in numerical methods and computer graphics

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University of Groningen

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Dissertations of the University of Groningen

University of Groningen

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Proceedings - University of Groningen