Precise Construction of Micro-structures and Porous Geometry via Functional Composition

  • Gershon ElberEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10521)


We introduce a modeling constructor for micro-structures and porous geometry via curve-trivariate, surface-trivariate and trivariate-trivariate function (symbolic) compositions. By using 1-, 2- and 3-manifold based tiles and paving them multiple times inside the domain of a 3-manifold deforming trivariate function, smooth, precise and watertight, yet general, porous/micro-structure geometry might be constructed, via composition. The tiles are demonstrated to be either polygonal meshes, (a set of) Bézier or B-spline curves, (a set of) Bézier or B-spline (trimmed) surfaces, (a set of) Bézier or B-spline (trimmed) trivariates or any combination thereof, whereas the 3-manifold deforming function is either a Bézier or a B-spline trivariate.

We briefly lay down the theoretical foundations, only to demonstrate the power of this modeling constructor in practice, and also present a few 3D printed tangible examples. We then discuss these results and conclude with some future directions and limitations.


Freeform deformation Trivariate splines Symbolic computation Freeform tiling 



This research was supported in part by the ISRAEL SCIENCE FOUNDATION (grant No. 278/13). I also like to thank Boris van Sosin for his help in implementing the trivariate-trivariate composition operator.

The IGA of the model in Fig. 12 has been performed with the help of Pablo Antolin (EPFL Lausanne), Annalisa Buffa (EPFL Lausanne and IMATI-CNR Pavia), Massimiliano Martinelli (IMATI-CNR Pavia); Giancarlo Sangalli (University of Pavia and IMATI-CNR Pavia)


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnion – IITHaifaIsrael

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