article

Developable surface fitting to point clouds

Author:

Martin PeternellAuthors Info & Claims

Computer Aided Geometric Design, Volume 21, Issue 8

Pages 785 - 803

Published: 01 October 2004 Publication History

Abstract

Given a set of data points as measurements from a developable surface, the present paper investigates the recognition and reconstruction of these objects. We investigate the set of estimated tangent planes of the data points and show that classical Laguerre geometry is a useful tool for recognition, classification and reconstruction of developable surfaces. These surfaces can be generated as envelopes of a one-parameter family of tangent planes. Finally we give examples and discuss the problems especially arising from the interpretation of a surface as set of tangent planes.

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Cited By

Verhoeven FVaxman AHoffmann TSorkine-Hornung O(2022)Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable SurfacesACM Transactions on Graphics10.1145/351000241:3(1-18)Online publication date: 7-Mar-2022
https://dl.acm.org/doi/10.1145/3510002
Sellán SAigerman NJacobson A(2020)Developability of heightfields via rank minimizationACM Transactions on Graphics10.1145/3386569.339241939:4(109:1-109:15)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392419
Stein OGrinspun ECrane K(2018)Developability of triangle meshesACM Transactions on Graphics10.1145/3197517.320130337:4(1-14)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201303
Show More Cited By

Index Terms

Developable surface fitting to point clouds
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
  2. Machine learning
    1. Machine learning algorithms
      1. Feature selection
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image Computer Aided Geometric Design

Computer Aided Geometric Design Volume 21, Issue 8

October, 2004

105 pages

ISSN:0167-8396

Issue’s Table of Contents

Copyright © Elsevier B.V. © 2004.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 October 2004

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Cited By

Verhoeven FVaxman AHoffmann TSorkine-Hornung O(2022)Dev2PQ: Planar Quadrilateral Strip Remeshing of Developable SurfacesACM Transactions on Graphics10.1145/351000241:3(1-18)Online publication date: 7-Mar-2022
https://dl.acm.org/doi/10.1145/3510002
Sellán SAigerman NJacobson A(2020)Developability of heightfields via rank minimizationACM Transactions on Graphics10.1145/3386569.339241939:4(109:1-109:15)Online publication date: 12-Aug-2020
https://dl.acm.org/doi/10.1145/3386569.3392419
Stein OGrinspun ECrane K(2018)Developability of triangle meshesACM Transactions on Graphics10.1145/3197517.320130337:4(1-14)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3197517.3201303
Kilian MMonszpart AMitra N(2017)String Actuated Curved Folded SurfacesACM Transactions on Graphics10.1145/3072959.301546036:4(1)Online publication date: 16-Jul-2017
https://dl.acm.org/doi/10.1145/3072959.3015460
Kilian MMonszpart AMitra N(2017)String Actuated Curved Folded SurfacesACM Transactions on Graphics10.1145/301546036:3(1-13)Online publication date: 19-May-2017
https://dl.acm.org/doi/10.1145/3015460
Tang CBo PWallner JPottmann H(2016)Interactive Design of Developable SurfacesACM Transactions on Graphics10.1145/283290635:2(1-12)Online publication date: 15-Jan-2016
https://dl.acm.org/doi/10.1145/2832906
Dimitrov AGu RGolparvar-Fard M(2016)Non-Uniform B-Spline Surface Fitting from Unordered 3D Point Clouds for As-Built ModelingComputer-Aided Civil and Infrastructure Engineering10.1111/mice.1219231:7(483-498)Online publication date: 1-Jul-2016
https://dl.acm.org/doi/10.1111/mice.12192
Schreck CRohmer DHahmann SCani MJin SWang CBloch J(2015)Nonsmooth Developable Geometry for Interactively Animating Paper CrumplingACM Transactions on Graphics10.1145/282994835:1(1-18)Online publication date: 29-Dec-2015
https://dl.acm.org/doi/10.1145/2829948
Jung AHahmann SRohmer DBegault ABoissieux LCani M(2015)Sketching FoldsACM Transactions on Graphics10.1145/274945834:5(1-12)Online publication date: 3-Nov-2015
https://dl.acm.org/doi/10.1145/2749458
Ridel BGuennebaud GReuter PGranier X(2015)Parabolic-cylindrical moving least squares surfacesComputers and Graphics10.1016/j.cag.2015.05.00651:C(60-66)Online publication date: 1-Oct-2015
https://dl.acm.org/doi/10.1016/j.cag.2015.05.006
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