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View all- Várady TSalvi PVaitkus M(2024)Genuine multi-sided parametric surface patches – A surveyComputer Aided Geometric Design10.1016/j.cagd.2024.102286110:COnline publication date: 1-May-2024
A Review of a B-spline based Volumetric Representation: : Design, Analysis and Fabrication of Porous and/or Heterogeneous Geometries
References
[1]
Cottrell J.A., Hughes T.J., Bazilevs Y., Isogeometric analysis: Toward integration of CAD and FEA, John Wiley & Sons, 2009.
[2]
Kagan P., Fischer A., Bar-Yoseph P., Mechanically based design: adaptive refinement for B-spline finite element, in: Proceedings international conference on shape modeling and applications, IEEE, 2001, pp. 345–366.
[3]
Irit P., The irit geometric modeling environment, version 12, 2023, https://csaws.cs.technion.ac.il/~gershon/irit.
[4]
Peltier S., Morin G., Aholou D., Tubular parametric volume objects: Thickening a piecewise smooth 3D stick figure, Comput Aided Geom Design 85 (2021).
[5]
Sederberg T.W., Parry S.R., Free-form deformation of solid geometric models, SIGGRAPH Comput Graph 20 (4) (1986) 151–160.
[6]
Feng J., Nishita T., Jin X., Peng Q., B-spline free-form deformation of polygonal object as trimmed Bezier surfaces, Vis Comput 18 (2002) 493–510.
[7]
Hu S.-M., Zhang H., Tai C.-L., Sun J.-G., Direct manipulation of FFD: efficient explicit solutions and decomposible multiple point constraints, Vis Comput 18 (2001) 370–379.
[8]
Bezier P., General distortion of an ensemble of biparametric patches, Comput Aided Des 10 (1978) 116–120.
[9]
Ferguson J., Multivariable curve interpolation, J ACM 11 (1964) 221–228.
[10]
Elber G., Free form surface analysis using a hybrid of symbolic and numerical computation, (Ph.D. thesis) University of Utah, 1992.
[11]
DeRose T.D., Goldman R.N., Hagen H., Mann S., Functional composition algorithms via blossoming, ACM Trans Graph 12 (2) (1993) 113–135.
[12]
Martin T., Cohen E., Kirby R., Volumetric parameterization and trivariate B-spline fitting using harmonic functions, Comput Aided Geom Design 26 (6) (2009) 648–664. Solid and Physical Modeling 2008.
[13]
Song Y., Cohen E., Making trimmed B-spline B-reps watertight with a hybrid representation, in: International design engineering technical conferences and computers and information in engineering conference, Vol. Volume 2B: 45th design automation conference, 2019.
[14]
Dokken T., Skytt V., Barrowclough O., Trivariate spline representations for computer aided design and additive manufacturing, Comput Math Appl 78 (7) (2019) 2168–2182. Simulation for Additive Manufacturing.
[15]
Raviv A., Elber G., Interactive direct rendering of trivariate B-spline scalar functions, IEEE Trans Vis Comput Graphics 7 (2001) 109–119.
[16]
Conkey J., Joy K., Using isosurface methods for visualizing the envelope of a swept trivariate solid, UC Davis: Institute for Data Analysis and Visualization, 2000.
[17]
Joy K., Duchaineau M.A., Boundry determination for trivariate solids, in: Proceedings of the 1999 Pacific graphics conference, 1999, pp. 82–91.
[18]
Hanniel I., Elber G., Subdivision termination criteria in subdivision multivariate solvers using dual hyperplanes representations, Comput Aided Des 39 (5) (2007) 369–378.
[19]
Bartoň M., Elber G., Hanniel I., Topologically guaranteed univariate solutions of underconstrained polynomial systems via no-loop and single-component tests, Comput Aided Des 43 (8) (2011) 1035–1044.
[20]
van Sosin B., Elber G., Solving piecewise polynomial constraint systems with decomposition and a subdivision-based solver, Comput Aided Des 90 (2017) 37–47.
[21]
Ezair B., Dikovsky D., Elber G., Fabricating functionally graded material objects using trimmed trivariate volumetric representations, in: Proceedings of SMI’2017 fabrication and sculpting event, FASE, 2017.
[22]
Antolin P., Buffa A., Martinelli M., Isogeometric analysis on V-reps: First results, Comput Methods Appl Mech Engrg 355 (2019) 976–1002.
[23]
Pimpalkar A., Agrawal V., Gautam S., Trivariate model construction from B-rep NURBS geometries for isogeometric analysis, in: Recent advances in computational and experimental mechanics, in: Lecture notes in mechanical engineering, vol. I, Springer, Singapore, 2022, pp. 459–471.
[24]
Borden M., Scott M., Evans J., Hughes T., Isogeometric finite element data structures based on Bezier extraction of NURBS, Internat J Numer Methods Engrg 87 (2011) 15–47.
[25]
Cobb J.E., Tiling the sphere with rational Bézier patches, University of Utah, USA, 1988.
[26]
Elber G., Kim Y.-J., Kim M.-S., Volumetric Boolean sum, Comput Aided Geom Design 29 (7) (2012) 532–540. Geometric Modeling and Processing 2012.
[27]
Massarwi F., Elber G., A B-spline based framework for volumetric object modeling, Comput Aided Des 78 (2016) 36–47. SPM 2016.
[28]
Mantyla M., An introduction to solid modeling, Computer Science Press, 1988.
[29]
Cirillo E., Elber G., Handling heterogeneous structures and materials using blending schemes in V-reps, Comput Aided Geom Design 83 (2020).
[30]
Masalha R., Cirillo E., Elber G., Heterogeneous parametric trivariate fillets, Comput Aided Geom Design 86 (2021).
[31]
Dahiya S., Shein A., Elber G., Shell-lattice construction based on regular and semi-regular tiling via functional composition, in: The hyperseeing magazine, Vol. Fall 2021, 2021, pp. 12–23.
[32]
Elber G., Precise construction of micro-structures and porous geometry via functional composition, in: International conference on mathematical methods for curves and surfaces, Springer, 2016, pp. 108–125.
[33]
Massarwi F., Machchhar J., Antolin P., Elber G., Hierarchical, random and bifurcation tiling with heterogeneity in micro-structures construction via functional composition, Comput Aided Des 102 (2018) 148–159.
[34]
Hong Q.Y., Elber G., Conformal microstructure synthesis in trimmed trivariate based V-reps, Comput Aided Des 140 (2021).
[35]
Hong Q.Y., Park Y., Elber G., Conformal parametric microstructure synthesis for boundary representations, in: The hyperseeing magazine, 2022.
[36]
Elber G., Kim M.-S., Synthesis of 3D jigsaw puzzles over freeform 2-manifolds, Comput Graph 102 (2022) 339–348.
[37]
Chen L., Huang J., Sun H., Bao H., Technical section: Cage-based deformation transfer, Comput Graph 34 (2) (2010) 107–118.
[38]
van Sosin B., Elber G., Crossing knot lines in composition of freeform B-spline geometry, Comput Aided Geom Design 62 (2018) 217–227.
[39]
Hu C., Lin H., Heterogeneous porous scaffold generation using trivariate B-spline solids and triply periodic minimal surfaces, Graph Models 115 (2021).
[40]
Hong Q.Y., Elber G., Kim M.S., Implicit functionally graded conforming microstructures, Comput-Aided Des (2023) to pear.
[41]
Michielsen K., Stavenga D.G., Gyroid cuticular structures in butterfly wing scales: biological photonic crystals, J R Soc Interface 5 (2008) 85–94.
[42]
Bendsoe M.P., Sigmund O., Topology optimization, Springer, 2002.
[43]
Saye R.I., High-order quadrature methods for implicitly defined surfaces and volumes in hyperrectangles, SIAM J Sci Comput 37 (2) (2015) A993–A1019.
[44]
Zwar J., Elber G., Elgeti S., Shape optimization for temperature regulation in extrusion dies, J Mech Des 145 (1) (2023).
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Published: 01 October 2023
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View all- Várady TSalvi PVaitkus M(2024)Genuine multi-sided parametric surface patches – A surveyComputer Aided Geometric Design10.1016/j.cagd.2024.102286110:COnline publication date: 1-May-2024
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