Adapted Delaunay triangulation method for free-form surface generation from random point clouds for stochastic optimization applications

Suyesh Bhattarai*, Keshav Dahal, Parag Vichare, Wenbing Chen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Free-form surfaces are defined with NURBS (non-uniform rational basis spline) for most computer-aided engineering (CAE) applications. The NURBS method requires the definition of parameters such as weights, knot vectors and degree of the curves which make the configuration of the surface computationally expensive and complex. When the control points are randomly spaced in the point cloud and the topology of the desired surface is unknown, surface configuration with NURBS method becomes a challenging task. Optimization attempts for such surfaces create enormous amounts of computing data when coupled with physics solvers such as finite element analysis (FEA) tools and computational fluid dynamics (CFD) tools. In this paper, an adapted Delaunay triangulation (ADT) method for surface generation from the random points cloud is proposed and compared with widely used implicit functions based NURBS fitting method. The surface generated from ADT method can be simultaneously used with stochastic optimization algorithms (SOA) and CFD applications to search for the optimal results with minimum computational costs. It was observed while comparing ADT with NURBS-based geometry configuration that the computation time can be reduced by 3 folds. The corresponding deviation between both geometry configuration methods has been observed as low as 5% for all optimisation scenarios during the comparison. In addition, ADT method can provide light weight CFD approach as any instance of design iteration has at least half storage footprint as compared to corresponding NURBS surface. The proposed approach provides novel methodology towards establishing light weight CFD geometry, absence of which currently isolates methodologies for optimization and CFD analysis.

Original languageEnglish
Pages (from-to)649–660
Number of pages12
JournalStructural and Multidisciplinary Optimization
Early online date29 Aug 2019
Publication statusPublished - Feb 2020

Bibliographical note

© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.


  • Delaunay
  • Optimization
  • Surface generation
  • Three-dimensional surfaces


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