A B-spline based framework for volumetric object modeling

Fady Massarwi, Gershon Elber

Research output: Contribution to journalArticlepeer-review


With the recent development of Iso-geometric Analysis (IGA) (Cottrell et al., 2009) and advanced manufacturing technologies employing heterogeneous materials, such as additive manufacturing (AM) of functionally graded material, there is a growing emerging need for a full volumetric representation of 3D objects, that prescribes the interior of the object in addition to its boundaries. In this paper, we propose a volumetric representation (V-rep) for geometric modeling that is based on trimmed B-spline trivariates and introduce its supporting volumetric modeling framework. The framework includes various volumetric model (V-model) construction methods from basic non-singular volumetric primitives to high level constructors, as well as Boolean operations’ support for V-models. A V-model is decomposed into and defined by a complex of volumetric cells (V-cells), each of which can also represent a variety of additional varying fields over it, and hence over the entire V-model. With these capabilities, the proposed framework is able of supporting volumetric IGA needs as well as represent and manage heterogeneous materials for AM. Further, this framework is also a seamless extension to existing boundary representations (B-reps) common in all contemporary geometric modeling systems, and allows a simple migration of existing B-rep data, tools and algorithms. Examples of volumetric models constructed using the proposed framework are presented.

Original languageEnglish
Pages (from-to)36-47
Number of pages12
JournalComputer-Aided Design
StatePublished - 1 Sep 2016


  • Additive manufacturing
  • Domain decomposition
  • Iso-Geometric analysis
  • Trimmed volumes
  • Trivariate functions
  • Volumetric Boolean operations

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering


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