Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
research-article

Tubular parametric volume objects: : Thickening a piecewise smooth 3D stick figure

Published: 01 February 2021 Publication History

Abstract

In this paper, a volume parametric model is computed from a piecewise smooth skeleton. Generating a volume model from a stick figure S defined in 3D is an intuitive process: given S whose topology is a pseudo-graph and whose edges are embedded as Bézier curves in R 3, we propose a method for creating a thick volume parametric model “around” S. The volume model we generate is based on semi-simploidal sets, which guarantees a proper topology and provides a 3D parametric domain for Bézier spaces. This volume is a continuous piecewise Bézier representation which boundary corresponds to a B-Rep made of tensor product Bézier patches.

References

[1]
J. Bærentzen, M. Misztal, K. Wełnicka, Converting skeletal structures to quad dominant meshes, Shape Modeling International (SMI) Conference 2012, Comput. Graph. 36 (2012) 555–561,.
[2]
V. Batagelj, An inductive definition of the class of 3-connected quadrangulations of the plane, Special Double Issue in Memory of Tory Parsons, Discrete Math. 78 (1989) 45–53.
[3]
G. Brinkmann, S. Greenberg, C. Greenhill, B.D. McKay, R. Thomas, P. Wollan, Generation of simple quadrangulations of the sphere, Discrete Math. 305 (2005) 33–54,.
[4]
R. Brown, P.J. Higgins, On the algebra of cubes, J. Pure Appl. Algebra 21 (1981) 233–260.
[5]
J.A. Cottrell, T.J. Hughes, Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, John Wiley & Sons, 2009.
[6]
W. Dahmen, C.A. Micchelli, On the linear independence of multivariate b-splines I. Triangulation of simploids, SIAM J. Numer. Anal. 19 (1982).
[7]
G. Damiand, P. Lienhardt, Combinatorial Maps: Efficient Data Structures for Computer Graphics and Image Processing, A K Peters/CRC Press, 2014.
[8]
T. DeRose, R.N. Goldman, H. Hagen, S. Mann, Functional composition algorithms via blossoming, Trans. Graph. 12 (1993) 113–135.
[9]
D. Dobkin, M. Laszlo, Primitives for the manipulation of three-dimensional subdivisions, in: 3rd Symposium on Computational Geometry, Waterloo, Canada, 1987, pp. 86–99.
[10]
J. Edmonds, A combinatorial representation for polyhedral surfaces, Not. Am. Math. Soc. 7 (1960) 646.
[11]
S. Eilenberg, J. Zilber, Semi-simplicial complexes and singular homology, Ann. Math. 51 (1950) 499–513.
[12]
G. Farin, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide, Elsevier, 2014.
[13]
A. Fuentes Suárez, E. Hubert, Scaffolding skeletons using spherical Voronoi diagrams: feasibility, regularity and symmetry, Proceeding of SPM 2018 Symposium, Comput. Aided Des. 102 (2018) 83–93,.
[14]
L. Guibas, G. Stolfi, Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams, Trans. Graph. 4 (1985) 74–123.
[15]
A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.
[16]
T. Hughes, J. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Eng. 194 (2005) 4135–4195,.
[17]
V. Lang, P. Lienhardt, Simplicial sets and triangular patches, in: Computer Graphics International Conference, CGI 1996, Pohang, Korea, June 24-28, 1996, 1996, pp. 154–163.
[18]
P. Lienhardt, Subdivisions of n-dimensional spaces and n-dimensional generalized maps, in: ACM Symposium on Computational Geometry, 1989, pp. 228–236.
[19]
P. Lienhardt, Topological models for boundary representation: a comparison with n-dimensional generalized maps, Comput. Aided Des. 23 (1991) 59–82,.
[20]
M. Livesu, A. Muntoni, E. Puppo, R. Scateni, Skeleton-driven adaptive hexahedral meshing of tubular shapes, Comput. Graph. Forum 35 (2016) 237–246,.
[21]
M. Livesu, S. Ellero, J. Martínez, S. Lefebvre, M. Attene, From 3d models to 3d prints: an overview of the processing pipeline, in: Computer Graphics Forum, Wiley Online Library, 2017, pp. 537–564.
[22]
M. Lyon, D. Bommes, L. Kobbelt, Hexex: robust hexahedral mesh extraction, ACM Trans. Graph. (TOG) 35 (2016) 1–11.
[23]
M. Mäntylä, An Introduction to Solid Modeling, Computer Science Press, 1988.
[24]
F. Massarwi, G. Elber, A b-spline based framework for volumetric object modeling, Comput. Aided Des. 78 (2016) 36–47.
[25]
F. Massarwi, P. Antolin, G. Elber, Volumetric untrimming: precise decomposition of trimmed trivariates into tensor products, Comput. Aided Geom. Des. 71 (2019) 1–15.
[26]
G. Morin, R. Goldman, On the smooth convergence of subdivision and degree elevation for Bézier curves, Comput. Aided Geom. Des. 18 (2001) 657–666.
[27]
J.R. Munkres, Elements of Algebraic Topology, Perseus Books, 1984.
[28]
A. Nakamoto, Diagonal transformations in quadrangulations of surfaces, J. Graph Theory 21 (1996) 289–299,.
[29]
A. Panotopoulou, E. Ross, K. Welker, E. Hubert, G. Morin, Scaffolding a skeleton, in: Research in Shape Analysis, Springer, 2018, pp. 17–35.
[30]
S. Peltier, P. Lienhardt, Simploidal sets: a data structure for handling simploidal Bezier spaces, Comput. Aided Geom. Des. 62 (2018) 44–62,.
[31]
S. Peltier, L. Fuchs, P. Lienhardt, Simploidals sets: definitions, operations and comparison with simplicial sets, Discrete Appl. Math. 157 (2009) 542–557. (extended version of “Homology of Simploidal Sets”, DGCI 2006, Szeged, Hungary, 235–246).
[32]
M. Raptis, D. Kirovski, H. Hoppe, Real-time classification of dance gestures from skeleton animation, in: Proceedings of the 2011 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, 2011, pp. 147–156.
[33]
C. Sanderson, R. Curtin, Armadillo: a template-based C++ library for linear algebra, J. Open Sour. Softw. 1 (2016) 26.
[34]
H. Sundar, D. Silver, N. Gagvani, S. Dickinson, Skeleton based shape matching and retrieval, in: 2003 Shape Modeling International, IEEE, 2003, pp. 130–139.
[35]
F. Usai, M. Livesu, E. Puppo, M. Tarini, R. Scateni, Extraction of the quad layout of a triangle mesh guided by its curve skeleton, ACM Trans. Graph. 35 (2016),.
[36]
A. Vince, Combinatorial maps, J. Comb. Theory 34 (1983) 1–21.
[37]
W. Wang, B. Jüttler, D. Zheng, Y. Liu, Computation of rotation minimizing frames, ACM Trans. Graph. (TOG) 27 (2008) 1–18.
[38]
K. Weiler, Edge-based data structures for solid modelling in curved-surface environments, Comput. Graph. Appl. 5 (1985) 21–40.

Index Terms

  1. Tubular parametric volume objects: Thickening a piecewise smooth 3D stick figure
    Index terms have been assigned to the content through auto-classification.

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image Computer Aided Geometric Design
    Computer Aided Geometric Design  Volume 85, Issue C
    Feb 2021
    127 pages

    Publisher

    Elsevier Science Publishers B. V.

    Netherlands

    Publication History

    Published: 01 February 2021

    Author Tags

    1. Tubular objects
    2. Topological based geometric modeling
    3. Bézier volumes
    4. Semi-simploidal sets

    Qualifiers

    • Research-article

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • 0
      Total Citations
    • 0
      Total Downloads
    • Downloads (Last 12 months)0
    • Downloads (Last 6 weeks)0
    Reflects downloads up to 10 Nov 2024

    Other Metrics

    Citations

    View Options

    View options

    Get Access

    Login options

    Media

    Figures

    Other

    Tables

    Share

    Share

    Share this Publication link

    Share on social media